Daily Papers

We introduce the novel task of interactive scene exploration, wherein robots autonomously explore environments and produce an action-conditioned scene graph (ACSG) that captures the structure of the underlying environment. The ACSG accounts for both low-level information (geometry and semantics) and high-level information (action-conditioned relationships between different entities) in the scene. To this end, we present the Robotic Exploration (RoboEXP) system, which incorporates the Large Multimodal Model (LMM) and an explicit memory design to enhance our system's capabilities. The robot reasons about what and how to explore an object, accumulating new information through the interaction process and incrementally constructing the ACSG. Leveraging the constructed ACSG, we illustrate the effectiveness and efficiency of our RoboEXP system in facilitating a wide range of real-world manipulation tasks involving rigid, articulated objects, nested objects, and deformable objects.

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

We introduce Object Graph Programming (OGO), which enables reading and modifying an object graph (i.e., the entire state of the object heap) via declarative queries. OGO models the objects and their relations in the heap as an object graph thereby treating the heap as a graph database: each node in the graph is an object (e.g., an instance of a class or an instance of a metadata class) and each edge is a relation between objects (e.g., a field of one object references another object). We leverage Cypher, the most popular query language for graph databases, as OGO's query language. Unlike LINQ, which uses collections (e.g., List) as a source of data, OGO views the entire object graph as a single "collection". OGO is ideal for querying collections (just like LINQ), introspecting the runtime system state (e.g., finding all instances of a given class or accessing fields via reflection), and writing assertions that have access to the entire program state. We prototyped OGO for Java in two ways: (a) by translating an object graph into a Neo4j database on which we run Cypher queries, and (b) by implementing our own in-memory graph query engine that directly queries the object heap. We used OGO to rewrite hundreds of statements in large open-source projects into OGO queries. We report our experience and performance of our prototypes.

Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset O in terms of datasets I) is a logical specification involving the source data I and the interface data O. It is a valid definition of O in terms of I, if any two models of the specification agreeing on I agree on O. In contrast, an explicit definition is a query that produces O from I. Variants of Beth's theorem state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous effective implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be effectively converted to explicit definitions in the nested relational calculus NRC. As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category. More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category. In this paper, we show that the two concepts are tightly linked. We show both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functor embedding the category of learners into a category of symmetric lenses.

We present EMMa, an Extensible, Multimodal dataset of Amazon product listings that contains rich Material annotations. It contains more than 2.8 million objects, each with image(s), listing text, mass, price, product ratings, and position in Amazon's product-category taxonomy. We also design a comprehensive taxonomy of 182 physical materials (e.g., Plastic rightarrow Thermoplastic rightarrow Acrylic). Objects are annotated with one or more materials from this taxonomy. With the numerous attributes available for each object, we develop a Smart Labeling framework to quickly add new binary labels to all objects with very little manual labeling effort, making the dataset extensible. Each object attribute in our dataset can be included in either the model inputs or outputs, leading to combinatorial possibilities in task configurations. For example, we can train a model to predict the object category from the listing text, or the mass and price from the product listing image. EMMa offers a new benchmark for multi-task learning in computer vision and NLP, and allows practitioners to efficiently add new tasks and object attributes at scale.

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a recursively defined function: one is for its recursive calls and the other is for its calls outside its definition. Bimorphic recursion in this paper can be nested. This paper shows bimorphic recursion has principal types and decidable type inference. Hence bimorphic recursion gives us flexible typing for recursion with decidable type inference. This paper also shows that its typability becomes undecidable because of nesting of recursions when one removes the instantiation property from the bimorphic recursion.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

Object categories are typically organized into a multi-granularity taxonomic hierarchy. When classifying categories at different hierarchy levels, traditional uni-modal approaches focus primarily on image features, revealing limitations in complex scenarios. Recent studies integrating Vision-Language Models (VLMs) with class hierarchies have shown promise, yet they fall short of fully exploiting the hierarchical relationships. These efforts are constrained by their inability to perform effectively across varied granularity of categories. To tackle this issue, we propose a novel framework (HGCLIP) that effectively combines CLIP with a deeper exploitation of the Hierarchical class structure via Graph representation learning. We explore constructing the class hierarchy into a graph, with its nodes representing the textual or image features of each category. After passing through a graph encoder, the textual features incorporate hierarchical structure information, while the image features emphasize class-aware features derived from prototypes through the attention mechanism. Our approach demonstrates significant improvements on 11 diverse visual recognition benchmarks. Our codes are fully available at https://github.com/richard-peng-xia/HGCLIP.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

For many segmentation tasks, especially for the biomedical image, the topological prior is vital information which is useful to exploit. The containment/nesting is a typical inter-class geometric relationship. In the MICCAI Brain tumor segmentation challenge, with its three hierarchically nested classes 'whole tumor', 'tumor core', 'active tumor', the nested classes relationship is introduced into the 3D-residual-Unet architecture. The network comprises a context aggregation pathway and a localization pathway, which encodes increasingly abstract representation of the input as going deeper into the network, and then recombines these representations with shallower features to precisely localize the interest domain via a localization path. The nested-class-prior is combined by proposing the multi-class activation function and its corresponding loss function. The model is trained on the training dataset of Brats2018, and 20% of the dataset is regarded as the validation dataset to determine parameters. When the parameters are fixed, we retrain the model on the whole training dataset. The performance achieved on the validation leaderboard is 86%, 77% and 72% Dice scores for the whole tumor, enhancing tumor and tumor core classes without relying on ensembles or complicated post-processing steps. Based on the same start-of-the-art network architecture, the accuracy of nested-class (enhancing tumor) is reasonably improved from 69% to 72% compared with the traditional Softmax-based method which blind to topological prior.

Incorporating domain-specific priors in search and navigation tasks has shown promising results in improving generalization and sample complexity over end-to-end trained policies. In this work, we study how object embeddings that capture spatial semantic priors can guide search and navigation tasks in a structured environment. We know that humans can search for an object like a book, or a plate in an unseen house, based on the spatial semantics of bigger objects detected. For example, a book is likely to be on a bookshelf or a table, whereas a plate is likely to be in a cupboard or dishwasher. We propose a method to incorporate such spatial semantic awareness in robots by leveraging pre-trained language models and multi-relational knowledge bases as object embeddings. We demonstrate using these object embeddings to search a query object in an unseen indoor environment. We measure the performance of these embeddings in an indoor simulator (AI2Thor). We further evaluate different pre-trained embedding onSuccess Rate(SR) and success weighted by Path Length(SPL).

While learning models are typically studied for inputs in the form of a fixed dimensional feature vector, real world data is rarely found in this form. In order to meet the basic requirement of traditional learning models, structural data generally have to be converted into fix-length vectors in a handcrafted manner, which is tedious and may even incur information loss. A common form of structured data is what we term "semantic tree-structures", corresponding to data where rich semantic information is encoded in a compositional manner, such as those expressed in JavaScript Object Notation (JSON) and eXtensible Markup Language (XML). For tree-structured data, several learning models have been studied to allow for working directly on raw tree-structure data, However such learning models are limited to either a specific tree-topology or a specific tree-structured data format, e.g., synthetic parse trees. In this paper, we propose a novel framework for end-to-end learning on generic semantic tree-structured data of arbitrary topology and heterogeneous data types, such as data expressed in JSON, XML and so on. Motivated by the works in recursive and recurrent neural networks, we develop exemplar neural implementations of our framework for the JSON format. We evaluate our approach on several UCI benchmark datasets, including ablation and data-efficiency studies, and on a toy reinforcement learning task. Experimental results suggest that our framework yields comparable performance to use of standard models with dedicated feature-vectors in general, and even exceeds baseline performance in cases where compositional nature of the data is particularly important. The source code for a JSON-based implementation of our framework along with experiments can be downloaded at https://github.com/EndingCredits/json2vec.

Scientific knowledge is growing rapidly, making it challenging to track progress and high-level conceptual links across broad disciplines. While existing tools like citation networks and search engines make it easy to access a few related papers, they fundamentally lack the flexible abstraction needed to represent the density of activity in various scientific subfields. We motivate SCIENCE HIERARCHOGRAPHY, the goal of organizing scientific literature into a high-quality hierarchical structure that allows for the categorization of scientific work across varying levels of abstraction, from very broad fields to very specific studies. Such a representation can provide insights into which fields are well-explored and which are under-explored. To achieve the goals of SCIENCE HIERARCHOGRAPHY, we develop a range of algorithms. Our primary approach combines fast embedding-based clustering with LLM-based prompting to balance the computational efficiency of embedding methods with the semantic precision offered by LLM prompting. We demonstrate that this approach offers the best trade-off between quality and speed compared to methods that heavily rely on LLM prompting, such as iterative tree construction with LLMs. To better reflect the interdisciplinary and multifaceted nature of research papers, our hierarchy captures multiple dimensions of categorization beyond simple topic labels. We evaluate the utility of our framework by assessing how effectively an LLM-based agent can locate target papers using the hierarchy. Results show that this structured approach enhances interpretability, supports trend discovery, and offers an alternative pathway for exploring scientific literature beyond traditional search methods. Code, data and demo: https://github.com/JHU-CLSP/science-hierarchography{https://github.com/JHU-CLSP/science-hierarchography}

In this paper, we propose a multi-modal search engine for interior design that combines visual and textual queries. The goal of our engine is to retrieve interior objects, e.g. furniture or wall clocks, that share visual and aesthetic similarities with the query. Our search engine allows the user to take a photo of a room and retrieve with a high recall a list of items identical or visually similar to those present in the photo. Additionally, it allows to return other items that aesthetically and stylistically fit well together. To achieve this goal, our system blends the results obtained using textual and visual modalities. Thanks to this blending strategy, we increase the average style similarity score of the retrieved items by 11%. Our work is implemented as a Web-based application and it is planned to be opened to the public.

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

We introduce the ObjectFolder Benchmark, a benchmark suite of 10 tasks for multisensory object-centric learning, centered around object recognition, reconstruction, and manipulation with sight, sound, and touch. We also introduce the ObjectFolder Real dataset, including the multisensory measurements for 100 real-world household objects, building upon a newly designed pipeline for collecting the 3D meshes, videos, impact sounds, and tactile readings of real-world objects. We conduct systematic benchmarking on both the 1,000 multisensory neural objects from ObjectFolder, and the real multisensory data from ObjectFolder Real. Our results demonstrate the importance of multisensory perception and reveal the respective roles of vision, audio, and touch for different object-centric learning tasks. By publicly releasing our dataset and benchmark suite, we hope to catalyze and enable new research in multisensory object-centric learning in computer vision, robotics, and beyond. Project page: https://objectfolder.stanford.edu

Understanding complex scenes at multiple levels of abstraction remains a formidable challenge in computer vision. To address this, we introduce Nested Neural Feature Fields (N2F2), a novel approach that employs hierarchical supervision to learn a single feature field, wherein different dimensions within the same high-dimensional feature encode scene properties at varying granularities. Our method allows for a flexible definition of hierarchies, tailored to either the physical dimensions or semantics or both, thereby enabling a comprehensive and nuanced understanding of scenes. We leverage a 2D class-agnostic segmentation model to provide semantically meaningful pixel groupings at arbitrary scales in the image space, and query the CLIP vision-encoder to obtain language-aligned embeddings for each of these segments. Our proposed hierarchical supervision method then assigns different nested dimensions of the feature field to distill the CLIP embeddings using deferred volumetric rendering at varying physical scales, creating a coarse-to-fine representation. Extensive experiments show that our approach outperforms the state-of-the-art feature field distillation methods on tasks such as open-vocabulary 3D segmentation and localization, demonstrating the effectiveness of the learned nested feature field.

This paper discusses about a sorting algorithm which uses the concept of buckets where each bucket represents a certain number of digits. A two dimensional data structure is used where one dimension represents buckets i. e; number of digits and each bucket's corresponding dimensions represents the input numbers that belong to that bucket. Each bucket is then individually sorted. Since every preceding bucket elements will always be smaller than the succeeding buckets no comparison between them is required. By doing this we can significantly reduced the time complexity of any sorting algorithm used to sort the given set of inputs.

Referring expressions usually describe an object using properties of the object and relationships of the object with other objects. We propose a technique that integrates context between objects to understand referring expressions. Our approach uses an LSTM to learn the probability of a referring expression, with input features from a region and a context region. The context regions are discovered using multiple-instance learning (MIL) since annotations for context objects are generally not available for training. We utilize max-margin based MIL objective functions for training the LSTM. Experiments on the Google RefExp and UNC RefExp datasets show that modeling context between objects provides better performance than modeling only object properties. We also qualitatively show that our technique can ground a referring expression to its referred region along with the supporting context region.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

We have created a dataset of more than ten thousand 3D scans of real objects. To create the dataset, we recruited 70 operators, equipped them with consumer-grade mobile 3D scanning setups, and paid them to scan objects in their environments. The operators scanned objects of their choosing, outside the laboratory and without direct supervision by computer vision professionals. The result is a large and diverse collection of object scans: from shoes, mugs, and toys to grand pianos, construction vehicles, and large outdoor sculptures. We worked with an attorney to ensure that data acquisition did not violate privacy constraints. The acquired data was irrevocably placed in the public domain and is available freely at http://redwood-data.org/3dscan .

Learning the hierarchical structure of data in vision-language models is a significant challenge. Previous works have attempted to address this challenge by employing entailment learning. However, these approaches fail to model the transitive nature of entailment explicitly, which establishes the relationship between order and semantics within a representation space. In this work, we introduce Radial Cross-Modal Embeddings (RCME), a framework that enables the explicit modeling of transitivity-enforced entailment. Our proposed framework optimizes for the partial order of concepts within vision-language models. By leveraging our framework, we develop a hierarchical vision-language foundation model capable of representing the hierarchy in the Tree of Life. Our experiments on hierarchical species classification and hierarchical retrieval tasks demonstrate the enhanced performance of our models compared to the existing state-of-the-art models. Our code and models are open-sourced at https://vishu26.github.io/RCME/index.html.

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an EL-labeling. By use of this EL-labeling, we show the lattice is supersolvable and compute the M\"obius function of an interval of the poset.

Semantic text classification has undergone significant advances in recent years due to the rise of large language models (LLMs) and their high dimensional embeddings. While LLM-embeddings are frequently used to store and retrieve text by semantic similarity in vector databases, the global structure semantic relationships in text corpora often remains opaque. Herein we propose a nested density clustering approach, to infer hierarchical trees of semantically related texts. The method starts by identifying texts of strong semantic similarity as it searches for dense clusters in LLM embedding space. As the density criterion is gradually relaxed, these dense clusters merge into more diffuse clusters, until the whole dataset is represented by a single cluster -- the root of the tree. By embedding dense clusters into increasingly diffuse ones, we construct a tree structure that captures hierarchical semantic relationships among texts. We outline how this approach can be used to classify textual data for abstracts of scientific abstracts as a case study. This enables the data-driven discovery research areas and their subfields without predefined categories. To evaluate the general applicability of the method, we further apply it to established benchmark datasets such as the 20 Newsgroups and IMDB 50k Movie Reviews, demonstrating its robustness across domains. Finally we discuss possible applications on scientometrics, topic evolution, highlighting how nested density trees can reveal semantic structure and evolution in textual datasets.

Given appropriate representations of the semantic relations between carpenter and wood and between mason and stone (for example, vectors in a vector space model), a suitable algorithm should be able to recognize that these relations are highly similar (carpenter is to wood as mason is to stone; the relations are analogous). Likewise, with representations of dog, house, and kennel, an algorithm should be able to recognize that the semantic composition of dog and house, dog house, is highly similar to kennel (dog house and kennel are synonymous). It seems that these two tasks, recognizing relations and compositions, are closely connected. However, up to now, the best models for relations are significantly different from the best models for compositions. In this paper, we introduce a dual-space model that unifies these two tasks. This model matches the performance of the best previous models for relations and compositions. The dual-space model consists of a space for measuring domain similarity and a space for measuring function similarity. Carpenter and wood share the same domain, the domain of carpentry. Mason and stone share the same domain, the domain of masonry. Carpenter and mason share the same function, the function of artisans. Wood and stone share the same function, the function of materials. In the composition dog house, kennel has some domain overlap with both dog and house (the domains of pets and buildings). The function of kennel is similar to the function of house (the function of shelters). By combining domain and function similarities in various ways, we can model relations, compositions, and other aspects of semantics.

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.

We consider the problem of building an assistive robotic system that can help humans in daily household cleanup tasks. Creating such an autonomous system in real-world environments is inherently quite challenging, as a general solution may not suit the preferences of a particular customer. Moreover, such a system consists of multi-objective tasks comprising -- (i) Detection of misplaced objects and prediction of their potentially correct placements, (ii) Fine-grained manipulation for stable object grasping, and (iii) Room-to-room navigation for transferring objects in unseen environments. This work systematically tackles each component and integrates them into a complete object rearrangement pipeline. To validate our proposed system, we conduct multiple experiments on a real robotic platform involving multi-room object transfer, user preference-based placement, and complex pick-and-place tasks. Project page: https://sites.google.com/eng.ucsd.edu/home-robot

Interactive 3D simulations have enabled breakthroughs in robotics and computer vision, but simulating the broad diversity of environments needed for deep learning requires large corpora of photo-realistic 3D object models. To address this need, we present Google Scanned Objects, an open-source collection of over one thousand 3D-scanned household items released under a Creative Commons license; these models are preprocessed for use in Ignition Gazebo and the Bullet simulation platforms, but are easily adaptable to other simulators. We describe our object scanning and curation pipeline, then provide statistics about the contents of the dataset and its usage. We hope that the diversity, quality, and flexibility of Google Scanned Objects will lead to advances in interactive simulation, synthetic perception, and robotic learning.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.

This research proposes a new recommender system algorithm for online grocery shopping. The algorithm is based on the perspective that, since the grocery items are usually bought in bulk, a grocery recommender system should be capable of recommending the items in bulk. The algorithm figures out the possible dishes a user may cook based on the items added to the basket and recommends the ingredients accordingly. Our algorithm does not depend on the user ratings. Customers usually do not have the patience to rate the groceries they purchase. Therefore, algorithms that are not dependent on user ratings need to be designed. Instead of using a brute force search, this algorithm limits the search space to a set of only a few probably food categories. Each food category consists of several food subcategories. For example, "fried rice" and "biryani" are food subcategories that belong to the food category "rice". For each food category, items are ranked according to how well they can differentiate a food subcategory. To each food subcategory in the activated search space, this algorithm attaches a score. The score is calculated based on the rank of the items added to the basket. Once the score exceeds a threshold value, its corresponding subcategory gets activated. The algorithm then uses a basket-to-recipe similarity measure to identify the best recipe matches within the activated subcategories only. This reduces the search space to a great extent. We may argue that this algorithm is similar to the content-based recommender system in some sense, but it does not suffer from the limitations like limited content, over-specialization, or the new user problem.

We introduce Uncommon Objects in 3D (uCO3D), a new object-centric dataset for 3D deep learning and 3D generative AI. uCO3D is the largest publicly-available collection of high-resolution videos of objects with 3D annotations that ensures full-360^{circ} coverage. uCO3D is significantly more diverse than MVImgNet and CO3Dv2, covering more than 1,000 object categories. It is also of higher quality, due to extensive quality checks of both the collected videos and the 3D annotations. Similar to analogous datasets, uCO3D contains annotations for 3D camera poses, depth maps and sparse point clouds. In addition, each object is equipped with a caption and a 3D Gaussian Splat reconstruction. We train several large 3D models on MVImgNet, CO3Dv2, and uCO3D and obtain superior results using the latter, showing that uCO3D is better for learning applications.

State-of-the-art visual grounding models can achieve high detection accuracy, but they are not designed to distinguish between all objects versus only certain objects of interest. In natural language, in order to specify a particular object or set of objects of interest, humans use determiners such as "my", "either" and "those". Determiners, as an important word class, are a type of schema in natural language about the reference or quantity of the noun. Existing grounded referencing datasets place much less emphasis on determiners, compared to other word classes such as nouns, verbs and adjectives. This makes it difficult to develop models that understand the full variety and complexity of object referencing. Thus, we have developed and released the DetermiNet dataset , which comprises 250,000 synthetically generated images and captions based on 25 determiners. The task is to predict bounding boxes to identify objects of interest, constrained by the semantics of the given determiner. We find that current state-of-the-art visual grounding models do not perform well on the dataset, highlighting the limitations of existing models on reference and quantification tasks.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

In this work we explore how fine-grained differences between the shapes of common objects are expressed in language, grounded on images and 3D models of the objects. We first build a large scale, carefully controlled dataset of human utterances that each refers to a 2D rendering of a 3D CAD model so as to distinguish it from a set of shape-wise similar alternatives. Using this dataset, we develop neural language understanding (listening) and production (speaking) models that vary in their grounding (pure 3D forms via point-clouds vs. rendered 2D images), the degree of pragmatic reasoning captured (e.g. speakers that reason about a listener or not), and the neural architecture (e.g. with or without attention). We find models that perform well with both synthetic and human partners, and with held out utterances and objects. We also find that these models are amenable to zero-shot transfer learning to novel object classes (e.g. transfer from training on chairs to testing on lamps), as well as to real-world images drawn from furniture catalogs. Lesion studies indicate that the neural listeners depend heavily on part-related words and associate these words correctly with visual parts of objects (without any explicit network training on object parts), and that transfer to novel classes is most successful when known part-words are available. This work illustrates a practical approach to language grounding, and provides a case study in the relationship between object shape and linguistic structure when it comes to object differentiation.

Does structure in representations imply structure in computation? We study how Llama-3.1-8B reasons over cyclic concepts (e.g., "what month is six months after August?"). Even though Llama-3.1-8B's representations for these concepts are circularly structured, we find that instead of directly computing modular addition in the period of the cyclic concept (e.g., 12 for months), the model re-uses a generic addition mechanism across tasks that operates independently of concept-specific geometry. First, it computes the sum of its two inputs using base-10 addition (six + August=14). Then, it maps this sum back to cyclic concept space (14->February). We show that Llama-3.1-8B uses task-agnostic Fourier features to compute these sums--in fact, these features have periods that respect standard base-10 addition, e.g., 2, 5, and 10, rather than the cyclic concept period (e.g., 12 for months). Furthermore, we identify a sparse set of 28 MLP neurons re-used across all tasks (approximately 0.2% of the MLP at layer 18) that can be partitioned into disjoint clusters, each computing the sum for a Fourier feature with a different period. Our work highlights how an interplay between causal abstraction and feature geometry can deepen our mechanistic understanding of LMs.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

Representing and navigating hierarchy is a fundamental primitive of reasoning. Large language models have demonstrated proficiency in a wide variety of tasks requiring hierarchical reasoning, but there exists limited analysis on how the models geometrically represent the necessary latent constructions for such thinking. To this end, we develop H-probes, a collection of linear probes that extract hierarchical structure, specifically depth and pairwise distance, from latent representations. In synthetic tree traversal tasks, the H-probes robustly find the subspaces containing hierarchical structure necessary to complete the tasks; furthermore, in comprehensive ablation experiments, we show that these hierarchy-containing subspaces are low-dimensional, causally important for high task performance, and generalize within- and out-of-domain. Furthermore, we find analogous, though weaker, hierarchical structure in real-world hierarchical contexts such as mathematical reasoning traces. These results demonstrate that models represent hierarchy not only at the level of syntax and concepts, but at deeper levels of abstraction -- including the reasoning process itself.

Hierarchical structures are popular in recent vision transformers, however, they require sophisticated designs and massive datasets to work well. In this paper, we explore the idea of nesting basic local transformers on non-overlapping image blocks and aggregating them in a hierarchical way. We find that the block aggregation function plays a critical role in enabling cross-block non-local information communication. This observation leads us to design a simplified architecture that requires minor code changes upon the original vision transformer. The benefits of the proposed judiciously-selected design are threefold: (1) NesT converges faster and requires much less training data to achieve good generalization on both ImageNet and small datasets like CIFAR; (2) when extending our key ideas to image generation, NesT leads to a strong decoder that is 8times faster than previous transformer-based generators; and (3) we show that decoupling the feature learning and abstraction processes via this nested hierarchy in our design enables constructing a novel method (named GradCAT) for visually interpreting the learned model. Source code is available https://github.com/google-research/nested-transformer.

Object appearances change dramatically with pose variations. This creates a challenge for embedding schemes that seek to map instances with the same object ID to locations that are as close as possible. This issue becomes significantly heightened in complex computer vision tasks such as re-identification(reID). In this paper, we suggest that these dramatic appearance changes are indications that an object ID is composed of multiple natural groups, and it is counterproductive to forcefully map instances from different groups to a common location. This leads us to introduce Relation Preserving Triplet Mining (RPTM), a feature-matching guided triplet mining scheme, that ensures that triplets will respect the natural subgroupings within an object ID. We use this triplet mining mechanism to establish a pose-aware, well-conditioned triplet loss by implicitly enforcing view consistency. This allows a single network to be trained with fixed parameters across datasets while providing state-of-the-art results. Code is available at https://github.com/adhirajghosh/RPTM_reid.

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

Recent research has evidenced the significant potentials of Large Language Models (LLMs) in handling challenging tasks within 3D scenes. However, current models are constrained to addressing object-centric tasks, where each question-answer pair focuses solely on an individual object. In real-world applications, users may pose queries involving multiple objects or expect for answers that precisely reference various objects. We introduce the use of object identifiers to freely reference objects during a conversation. While this solution appears straightforward, it presents two main challenges: 1) How to establish a reliable one-to-one correspondence between each object and its identifier? 2) How to incorporate complex spatial relationships among dozens of objects into the embedding space of the LLM? To address these challenges, we propose a two-stage alignment method, which involves learning an attribute-aware token and a relation-aware token for each object. These tokens capture the object's attributes and spatial relationships with surrounding objects in the 3D scene. Once the alignment is established, we can fine-tune our model on various downstream tasks using instruction tuning. Experiments conducted on traditional datasets like ScanQA, ScanRefer, and Nr3D/Sr3D showcase the effectiveness of our proposed method. Additionally, we create a 3D scene captioning dataset annotated with rich object identifiers, with the assistant of GPT-4. This dataset aims to further explore the capability of object identifiers in effective object referencing and precise scene understanding.

We present a new dataset, Functional Map of the World (fMoW), which aims to inspire the development of machine learning models capable of predicting the functional purpose of buildings and land use from temporal sequences of satellite images and a rich set of metadata features. The metadata provided with each image enables reasoning about location, time, sun angles, physical sizes, and other features when making predictions about objects in the image. Our dataset consists of over 1 million images from over 200 countries. For each image, we provide at least one bounding box annotation containing one of 63 categories, including a "false detection" category. We present an analysis of the dataset along with baseline approaches that reason about metadata and temporal views. Our data, code, and pretrained models have been made publicly available.

JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON Schema documents comprises practically relevant problems, including schema satisfiability, inclusion, and equivalence. These three problems can be reduced to witness generation: given a schema, generate an element of the schema, if it exists, and report failure otherwise. Schema satisfiability, inclusion, and equivalence have been shown to be decidable, by reduction to reachability in alternating tree automata. However, no witness generation algorithm has yet been formally described. We contribute a first, direct algorithm for JSON Schema witness generation. We study its effectiveness and efficiency, in experiments over several schema collections, including thousands of real-world schemas. Our focus is on the completeness of the language, where we only exclude the uniqueItems operator, and on the ability of the algorithm to run in a reasonable time on a large set of real-world examples, despite the exponential complexity of the underlying problem.

The Airbnb search system grapples with many unique challenges as it continues to evolve. We oversee a marketplace that is nuanced by geography, diversity of homes, and guests with a variety of preferences. Crafting an efficient search system that can accommodate diverse guest needs, while showcasing relevant homes lies at the heart of Airbnb's success. Airbnb search has many challenges that parallel other recommendation and search systems but it has a unique information retrieval problem, upstream of ranking, called location retrieval. It requires defining a topological map area that is relevant to the searched query for homes listing retrieval. The purpose of this paper is to demonstrate the methodology, challenges, and impact of building a machine learning based location retrieval product from the ground up. Despite the lack of suitable, prevalent machine learning based approaches, we tackle cold start, generalization, differentiation and algorithmic bias. We detail the efficacy of heuristics, statistics, machine learning, and reinforcement learning approaches to solve these challenges, particularly for systems that are often unexplored by current literature.

Developing deep learning models that effectively learn object-centric representations, akin to human cognition, remains a challenging task. Existing approaches facilitate object discovery by representing objects as fixed-size vectors, called ``slots'' or ``object files''. While these approaches have shown promise in certain scenarios, they still exhibit certain limitations. First, they rely on architectural priors which can be unreliable and usually require meticulous engineering to identify the correct objects. Second, there has been a notable gap in investigating the practical utility of these representations in downstream tasks. To address the first limitation, we introduce a method that explicitly optimizes the constraint that each object in a scene should be associated with a distinct slot. We formalize this constraint by introducing consistency objectives which are cyclic in nature. By integrating these consistency objectives into various existing slot-based object-centric methods, we showcase substantial improvements in object-discovery performance. These enhancements consistently hold true across both synthetic and real-world scenes, underscoring the effectiveness and adaptability of the proposed approach. To tackle the second limitation, we apply the learned object-centric representations from the proposed method to two downstream reinforcement learning tasks, demonstrating considerable performance enhancements compared to conventional slot-based and monolithic representation learning methods. Our results suggest that the proposed approach not only improves object discovery, but also provides richer features for downstream tasks.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

Most object-level mapping systems in use today make use of an upstream learned object instance segmentation model. If we want to teach them about a new object or segmentation class, we need to build a large dataset and retrain the system. To build spatial AI systems that can quickly be taught about new objects, we need to effectively solve the problem of single-shot object detection, instance segmentation and re-identification. So far there is neither a method fulfilling all of these requirements in unison nor a benchmark that could be used to test such a method. Addressing this, we propose ISAR, a benchmark and baseline method for single- and few-shot object Instance Segmentation And Re-identification, in an effort to accelerate the development of algorithms that can robustly detect, segment, and re-identify objects from a single or a few sparse training examples. We provide a semi-synthetic dataset of video sequences with ground-truth semantic annotations, a standardized evaluation pipeline, and a baseline method. Our benchmark aligns with the emerging research trend of unifying Multi-Object Tracking, Video Object Segmentation, and Re-identification.

This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities between data points, but extensions to vector data are also discussed (2) the output is a "stepwise dendrogram", a data structure which is shared by all implementations in current standard software. We present algorithms (old and new) which perform clustering in this setting efficiently, both in an asymptotic worst-case analysis and from a practical point of view. The main contributions of this paper are: (1) We present a new algorithm which is suitable for any distance update scheme and performs significantly better than the existing algorithms. (2) We prove the correctness of two algorithms by Rohlf and Murtagh, which is necessary in each case for different reasons. (3) We give well-founded recommendations for the best current algorithms for the various agglomerative clustering schemes.

This paper introduces FGVC-Aircraft, a new dataset containing 10,000 images of aircraft spanning 100 aircraft models, organised in a three-level hierarchy. At the finer level, differences between models are often subtle but always visually measurable, making visual recognition challenging but possible. A benchmark is obtained by defining corresponding classification tasks and evaluation protocols, and baseline results are presented. The construction of this dataset was made possible by the work of aircraft enthusiasts, a strategy that can extend to the study of number of other object classes. Compared to the domains usually considered in fine-grained visual classification (FGVC), for example animals, aircraft are rigid and hence less deformable. They, however, present other interesting modes of variation, including purpose, size, designation, structure, historical style, and branding.

The goal of this paper is to detect objects by exploiting their interrelationships. Contrary to existing methods, which learn objects and relations separately, our key idea is to learn the object-relation distribution jointly. We first propose a novel way of creating a graphical representation of an image from inter-object relation priors and initial class predictions, we call a context-likelihood graph. We then learn the joint distribution with an energy-based modeling technique which allows to sample and refine the context-likelihood graph iteratively for a given image. Our formulation of jointly learning the distribution enables us to generate a more accurate graph representation of an image which leads to a better object detection performance. We demonstrate the benefits of our context-likelihood graph formulation and the energy-based graph refinement via experiments on the Visual Genome and MS-COCO datasets where we achieve a consistent improvement over object detectors like DETR and Faster-RCNN, as well as alternative methods modeling object interrelationships separately. Our method is detector agnostic, end-to-end trainable, and especially beneficial for rare object classes.

Classical models of memory in psychology and neuroscience rely on similarity-based retrieval of stored patterns, where similarity is a function of retrieval cues and the stored patterns. While parsimonious, these models do not allow distinct representations for storage and retrieval, despite their distinct computational demands. Key-value memory systems, in contrast, distinguish representations used for storage (values) and those used for retrieval (keys). This allows key-value memory systems to optimize simultaneously for fidelity in storage and discriminability in retrieval. We review the computational foundations of key-value memory, its role in modern machine learning systems, related ideas from psychology and neuroscience, applications to a number of empirical puzzles, and possible biological implementations.

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

Learning structured representations of the visual world in terms of objects promises to significantly improve the generalization abilities of current machine learning models. While recent efforts to this end have shown promising empirical progress, a theoretical account of when unsupervised object-centric representation learning is possible is still lacking. Consequently, understanding the reasons for the success of existing object-centric methods as well as designing new theoretically grounded methods remains challenging. In the present work, we analyze when object-centric representations can provably be learned without supervision. To this end, we first introduce two assumptions on the generative process for scenes comprised of several objects, which we call compositionality and irreducibility. Under this generative process, we prove that the ground-truth object representations can be identified by an invertible and compositional inference model, even in the presence of dependencies between objects. We empirically validate our results through experiments on synthetic data. Finally, we provide evidence that our theory holds predictive power for existing object-centric models by showing a close correspondence between models' compositionality and invertibility and their empirical identifiability.

Understanding objects is a central building block of artificial intelligence, especially for embodied AI. Even though object recognition excels with deep learning, current machines still struggle to learn higher-level knowledge, e.g., what attributes an object has, and what can we do with an object. In this work, we propose a challenging Object Concept Learning (OCL) task to push the envelope of object understanding. It requires machines to reason out object affordances and simultaneously give the reason: what attributes make an object possesses these affordances. To support OCL, we build a densely annotated knowledge base including extensive labels for three levels of object concept (category, attribute, affordance), and the causal relations of three levels. By analyzing the causal structure of OCL, we present a baseline, Object Concept Reasoning Network (OCRN). It leverages causal intervention and concept instantiation to infer the three levels following their causal relations. In experiments, OCRN effectively infers the object knowledge while following the causalities well. Our data and code are available at https://mvig-rhos.com/ocl.

Neural implicit representation has attracted attention in 3D reconstruction through various success cases. For further applications such as scene understanding or editing, several works have shown progress towards object compositional reconstruction. Despite their superior performance in observed regions, their performance is still limited in reconstructing objects that are partially observed. To better treat this problem, we introduce category-level neural fields that learn meaningful common 3D information among objects belonging to the same category present in the scene. Our key idea is to subcategorize objects based on their observed shape for better training of the category-level model. Then we take advantage of the neural field to conduct the challenging task of registering partially observed objects by selecting and aligning against representative objects selected by ray-based uncertainty. Experiments on both simulation and real-world datasets demonstrate that our method improves the reconstruction of unobserved parts for several categories.

For humans, language production and comprehension is sensitive to the hierarchical structure of sentences. In natural language processing, past work has questioned how effectively neural sequence models like transformers capture this hierarchical structure when generalizing to structurally novel inputs. We show that transformer language models can learn to generalize hierarchically after training for extremely long periods -- far beyond the point when in-domain accuracy has saturated. We call this phenomenon structural grokking. On multiple datasets, structural grokking exhibits inverted U-shaped scaling in model depth: intermediate-depth models generalize better than both very deep and very shallow transformers. When analyzing the relationship between model-internal properties and grokking, we find that optimal depth for grokking can be identified using the tree-structuredness metric of murty2023projections. Overall, our work provides strong evidence that, with extended training, vanilla transformers discover and use hierarchical structure.

Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and function. As a comparative tool here we apply hierarchical ontology logs (olog) that follow a rigorous mathematical formulation based on category theory to provide an insightful system representation by expressing knowledge in a conceptual map. We explain the process of analogy creation, draw connections at several levels of hierarchy and identify similar patterns that govern the structure of the hierarchical systems silk and music and discuss the impact of the derived analogy for nanotechnology.

In recent years supervised representation learning has provided state of the art or close to the state of the art results in semantic analysis tasks including ranking and information retrieval. The core idea is to learn how to embed items into a latent space such that they optimize a supervised objective in that latent space. The dimensions of the latent space have no clear semantics, and this reduces the interpretability of the system. For example, in personalization models, it is hard to explain why a particular item is ranked high for a given user profile. We propose a novel model of representation learning called Supervised Explicit Semantic Analysis (SESA) that is trained in a supervised fashion to embed items to a set of dimensions with explicit semantics. The model learns to compare two objects by representing them in this explicit space, where each dimension corresponds to a concept from a knowledge base. This work extends Explicit Semantic Analysis (ESA) with a supervised model for ranking problems. We apply this model to the task of Job-Profile relevance in LinkedIn in which a set of skills defines our explicit dimensions of the space. Every profile and job are encoded to this set of skills their similarity is calculated in this space. We use RNNs to embed text input into this space. In addition to interpretability, our model makes use of the web-scale collaborative skills data that is provided by users for each LinkedIn profile. Our model provides state of the art result while it remains interpretable.

People can categorize the same entity at multiple taxonomic levels, such as basic (bear), superordinate (animal), and subordinate (grizzly bear). While prior research has focused on basic-level categories, this study is the first attempt to examine the organization of categories by analyzing exemplars produced at the subordinate level. We present a new Italian psycholinguistic dataset of human-generated exemplars for 187 concrete words. We then use these data to evaluate whether textual and vision LLMs produce meaningful exemplars that align with human category organization across three key tasks: exemplar generation, category induction, and typicality judgment. Our findings show a low alignment between humans and LLMs, consistent with previous studies. However, their performance varies notably across different semantic domains. Ultimately, this study highlights both the promises and the constraints of using AI-generated exemplars to support psychological and linguistic research.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell can reflect the history memories of multiple child cells or multiple descendant cells in a recursive process. We call the model S-LSTM, which provides a principled way of considering long-distance interaction over hierarchies, e.g., language or image parse structures. We leverage the models for semantic composition to understand the meaning of text, a fundamental problem in natural language understanding, and show that it outperforms a state-of-the-art recursive model by replacing its composition layers with the S-LSTM memory blocks. We also show that utilizing the given structures is helpful in achieving a performance better than that without considering the structures.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

Deformable image registration is crucial for aligning medical images in a non-linear fashion across different modalities, allowing for precise spatial correspondence between varying anatomical structures. This paper presents NestedMorph, a novel network utilizing a Nested Attention Fusion approach to improve intra-subject deformable registration between T1-weighted (T1w) MRI and diffusion MRI (dMRI) data. NestedMorph integrates high-resolution spatial details from an encoder with semantic information from a decoder using a multi-scale framework, enhancing both local and global feature extraction. Our model notably outperforms existing methods, including CNN-based approaches like VoxelMorph, MIDIR, and CycleMorph, as well as Transformer-based models such as TransMorph and ViT-V-Net, and traditional techniques like NiftyReg and SyN. Evaluations on the HCP dataset demonstrate that NestedMorph achieves superior performance across key metrics, including SSIM, HD95, and SDlogJ, with the highest SSIM of 0.89, and the lowest HD95 of 2.5 and SDlogJ of 0.22. These results highlight NestedMorph's ability to capture both local and global image features effectively, leading to superior registration performance. The promising outcomes of this study underscore NestedMorph's potential to significantly advance deformable medical image registration, providing a robust framework for future research and clinical applications. The source code and our implementation are available at: https://bit.ly/3zdVqcg

We introduce a method to generate 3D scenes that are disentangled into their component objects. This disentanglement is unsupervised, relying only on the knowledge of a large pretrained text-to-image model. Our key insight is that objects can be discovered by finding parts of a 3D scene that, when rearranged spatially, still produce valid configurations of the same scene. Concretely, our method jointly optimizes multiple NeRFs from scratch - each representing its own object - along with a set of layouts that composite these objects into scenes. We then encourage these composited scenes to be in-distribution according to the image generator. We show that despite its simplicity, our approach successfully generates 3D scenes decomposed into individual objects, enabling new capabilities in text-to-3D content creation. For results and an interactive demo, see our project page at https://dave.ml/layoutlearning/

Massive data corpora like WebText, Wikipedia, Conceptual Captions, WebImageText, and LAION have propelled recent dramatic progress in AI. Large neural models trained on such datasets produce impressive results and top many of today's benchmarks. A notable omission within this family of large-scale datasets is 3D data. Despite considerable interest and potential applications in 3D vision, datasets of high-fidelity 3D models continue to be mid-sized with limited diversity of object categories. Addressing this gap, we present Objaverse 1.0, a large dataset of objects with 800K+ (and growing) 3D models with descriptive captions, tags, and animations. Objaverse improves upon present day 3D repositories in terms of scale, number of categories, and in the visual diversity of instances within a category. We demonstrate the large potential of Objaverse via four diverse applications: training generative 3D models, improving tail category segmentation on the LVIS benchmark, training open-vocabulary object-navigation models for Embodied AI, and creating a new benchmark for robustness analysis of vision models. Objaverse can open new directions for research and enable new applications across the field of AI.

Capsule networks (see e.g. Hinton et al., 2018) aim to encode knowledge of and reason about the relationship between an object and its parts. In this paper we specify a generative model for such data, and derive a variational algorithm for inferring the transformation of each model object in a scene, and the assignments of observed parts to the objects. We derive a learning algorithm for the object models, based on variational expectation maximization (Jordan et al., 1999). We also study an alternative inference algorithm based on the RANSAC method of Fischler and Bolles (1981). We apply these inference methods to (i) data generated from multiple geometric objects like squares and triangles ("constellations"), and (ii) data from a parts-based model of faces. Recent work by Kosiorek et al. (2019) has used amortized inference via stacked capsule autoencoders (SCAEs) to tackle this problem -- our results show that we significantly outperform them where we can make comparisons (on the constellations data).

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

Understanding how humans conceptualize and categorize natural objects offers critical insights into perception and cognition. With the advent of Large Language Models (LLMs), a key question arises: can these models develop human-like object representations from linguistic and multimodal data? In this study, we combined behavioral and neuroimaging analyses to explore the relationship between object concept representations in LLMs and human cognition. We collected 4.7 million triplet judgments from LLMs and Multimodal LLMs (MLLMs) to derive low-dimensional embeddings that capture the similarity structure of 1,854 natural objects. The resulting 66-dimensional embeddings were stable, predictive, and exhibited semantic clustering similar to human mental representations. Remarkably, the dimensions underlying these embeddings were interpretable, suggesting that LLMs and MLLMs develop human-like conceptual representations of objects. Further analysis showed strong alignment between model embeddings and neural activity patterns in brain regions such as EBA, PPA, RSC, and FFA. This provides compelling evidence that the object representations in LLMs, while not identical to human ones, share fundamental similarities that reflect key aspects of human conceptual knowledge. Our findings advance the understanding of machine intelligence and inform the development of more human-like artificial cognitive systems.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

We define the bicategory of Graph Convolutional Neural Networks GCNN_n for an arbitrary graph with n nodes. We show it can be factored through the already existing categorical constructions for deep learning called Para and Lens with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor GCNN_n to Para(CoKl(R^{n times n} times -)). We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.

How multimodal large language models (MLLMs) perceive the visual world remains a mystery. To one extreme, object and relation modeling may be implicitly implemented with inductive biases, for example by treating objects as tokens. To the other extreme, empirical results reveal the surprising finding that simply performing visual captioning, which tends to ignore spatial configuration of the objects, serves as a strong baseline for video understanding. We aim to answer the question: how can objects help video-language understanding in MLLMs? We tackle the question from the object representation and adaptation perspectives. Specifically, we investigate the trade-off between representation expressiveness (e.g., distributed versus symbolic) and integration difficulty (e.g., data-efficiency when learning the adapters). Through extensive evaluations on five video question answering datasets, we confirm that explicit integration of object-centric representation remains necessary, and the symbolic objects can be most easily integrated while being performant for question answering. We hope our findings can encourage the community to explore the explicit integration of perception modules into MLLM design. Our code and models will be publicly released.

While large language models (LLMs) appear to be increasingly capable of solving compositional tasks, it is an open question whether they do so using compositional mechanisms. In this work, we investigate how feedforward LLMs solve two-hop factual recall tasks, which can be expressed compositionally as g(f(x)). We first confirm that modern LLMs continue to suffer from the "compositionality gap": i.e. their ability to compute both z = f(x) and y = g(z) does not entail their ability to compute the composition y = g(f(x)). Then, using logit lens on their residual stream activations, we identify two processing mechanisms, one which solves tasks compositionally, computing f(x) along the way to computing g(f(x)), and one which solves them directly, without any detectable signature of the intermediate variable f(x). Finally, we find that which mechanism is employed appears to be related to the embedding space geometry, with the idiomatic mechanism being dominant in cases where there exists a linear mapping from x to g(f(x)) in the embedding spaces. We fully release our data and code at: https://github.com/apoorvkh/composing-functions .

We survey left 3-Engel elements in groups.

The question of whether there exists a finite group of order at least three in which every element except one is a commutator has remained unresolved in group theory. In this article, we address this open problem by developing an algorithmic approach that leverages several group theoretic properties of such groups. Specifically, we utilize a result of Frobenius and various necessary properties of such groups, combined with Plesken and Holt's extensive enumeration of finite perfect groups, to systematically examine all finite groups up to a certain order for the desired property. The computational core of our work is implemented using the computer system GAP (Groups, Algorithms, and Programming). We discover two nonisomorphic groups of order 368,640 that exhibit the desired property. Our investigation also establishes that this order is the minimum order for such a group to exist. As a result, this study provides a positive answer to Problem 17.76 in the Kourovka Notebook. In addition to the algorithmic framework, this paper provides a structural description of one of the two groups found.

Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding objective, while the compositionality is implicitly imposed by the architectural or algorithmic bias in the encoder. This misalignment between auto-encoding objective and learning compositionality often results in failure of capturing meaningful object representations. In this study, we propose a novel objective that explicitly encourages compositionality of the representations. Built upon the existing object-centric learning framework (e.g., slot attention), our method incorporates additional constraints that an arbitrary mixture of object representations from two images should be valid by maximizing the likelihood of the composite data. We demonstrate that incorporating our objective to the existing framework consistently improves the objective-centric learning and enhances the robustness to the architectural choices.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the combinatorial space of possible inputs, raising the question of what structure representations must have to support generalization to unseen combinations. We formalize three desiderata for compositional generalization under standard training (divisibility, transferability, stability) and show they impose necessary geometric constraints: representations must decompose linearly into per-concept components, and these components must be orthogonal across concepts. This provides theoretical grounding for the Linear Representation Hypothesis: the linear structure widely observed in neural representations is a necessary consequence of compositional generalization. We further derive dimension bounds linking the number of composable concepts to the embedding geometry. Empirically, we evaluate these predictions across modern vision models (CLIP, SigLIP, DINO) and find that representations exhibit partial linear factorization with low-rank, near-orthogonal per-concept factors, and that the degree of this structure correlates with compositional generalization on unseen combinations. As models continue to scale, these conditions predict the representational geometry they may converge to. Code is available at https://github.com/oshapio/necessary-compositionality.

In the last decade, several organizations have produced documents intended to standardize, in the normative sense, and promote guidance to our recent and rapid AI development. However, the full spectrum of ideas presented in these documents has not yet been analyzed, except for a few meta-analyses and critical reviews of the field. In this work, we seek to expand on the work done by past researchers and create a tool for better data visualization of the contents and nature of these documents, to understand whether there is consensus or similarity between the principles espoused by various institutions, which may inspire debates on future regulations. We also provide some preliminary thoughts and questions that could guide the continuity of the research through a critical analysis of the results acquired by our methodology into a sample size of 200 documents.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Prior to the deep learning era, shape was commonly used to describe the objects. Nowadays, state-of-the-art (SOTA) algorithms in medical imaging are predominantly diverging from computer vision, where voxel grids, meshes, point clouds, and implicit surface models are used. This is seen from numerous shape-related publications in premier vision conferences as well as the growing popularity of ShapeNet (about 51,300 models) and Princeton ModelNet (127,915 models). For the medical domain, we present a large collection of anatomical shapes (e.g., bones, organs, vessels) and 3D models of surgical instrument, called MedShapeNet, created to facilitate the translation of data-driven vision algorithms to medical applications and to adapt SOTA vision algorithms to medical problems. As a unique feature, we directly model the majority of shapes on the imaging data of real patients. As of today, MedShapeNet includes 23 dataset with more than 100,000 shapes that are paired with annotations (ground truth). Our data is freely accessible via a web interface and a Python application programming interface (API) and can be used for discriminative, reconstructive, and variational benchmarks as well as various applications in virtual, augmented, or mixed reality, and 3D printing. Exemplary, we present use cases in the fields of classification of brain tumors, facial and skull reconstructions, multi-class anatomy completion, education, and 3D printing. In future, we will extend the data and improve the interfaces. The project pages are: https://medshapenet.ikim.nrw/ and https://github.com/Jianningli/medshapenet-feedback

Detecting objects in real-world scenes is a complex task due to various challenges, including the vast range of object categories, and potential encounters with previously unknown or unseen objects. The challenges necessitate the development of public benchmarks and challenges to advance the field of object detection. Inspired by the success of previous COCO and LVIS Challenges, we organize the V3Det Challenge 2024 in conjunction with the 4th Open World Vision Workshop: Visual Perception via Learning in an Open World (VPLOW) at CVPR 2024, Seattle, US. This challenge aims to push the boundaries of object detection research and encourage innovation in this field. The V3Det Challenge 2024 consists of two tracks: 1) Vast Vocabulary Object Detection: This track focuses on detecting objects from a large set of 13204 categories, testing the detection algorithm's ability to recognize and locate diverse objects. 2) Open Vocabulary Object Detection: This track goes a step further, requiring algorithms to detect objects from an open set of categories, including unknown objects. In the following sections, we will provide a comprehensive summary and analysis of the solutions submitted by participants. By analyzing the methods and solutions presented, we aim to inspire future research directions in vast vocabulary and open-vocabulary object detection, driving progress in this field. Challenge homepage: https://v3det.openxlab.org.cn/challenge

We present an open-vocabulary and zero-shot method for arbitrary referring expression segmentation (RES), targeting input expressions that are more general than what prior works were designed to handle. Specifically, our inputs encompass both object- and part-level labels as well as implicit references pointing to properties or qualities of object/part function, design, style, material, etc. Our model, coined RESAnything, leverages Chain-of-Thoughts (CoT) reasoning, where the key idea is attribute prompting. We generate detailed descriptions of object/part attributes including shape, color, and location for potential segment proposals through systematic prompting of a large language model (LLM), where the proposals are produced by a foundational image segmentation model. Our approach encourages deep reasoning about object or part attributes related to function, style, design, etc., enabling the system to handle implicit queries without any part annotations for training or fine-tuning. As the first zero-shot and LLM-based RES method, RESAnything achieves clearly superior performance among zero-shot methods on traditional RES benchmarks and significantly outperforms existing methods on challenging scenarios involving implicit queries and complex part-level relations. Finally, we contribute a new benchmark dataset to offer ~3K carefully curated RES instances to assess part-level, arbitrary RES solutions.

Engineering efficient implementations of compact and succinct structures is a time-consuming and challenging task, since there is no standard library of easy-to- use, highly optimized, and composable components. One consequence is that measuring the practical impact of new theoretical proposals is a difficult task, since older base- line implementations may not rely on the same basic components, and reimplementing from scratch can be very time-consuming. In this paper we present a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements. We demonstrate the functionality of the framework by recomposing succinct solutions for document retrieval.

We describe new datasets for studying generalization from easy to hard examples.

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy "graph tracing" task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

How can a robot efficiently extract a desired object from a shelf when it is fully occluded by other objects? Prior works propose geometric approaches for this problem but do not consider object semantics. Shelves in pharmacies, restaurant kitchens, and grocery stores are often organized such that semantically similar objects are placed close to one another. Can large language models (LLMs) serve as semantic knowledge sources to accelerate robotic mechanical search in semantically arranged environments? With Semantic Spatial Search on Shelves (S^4), we use LLMs to generate affinity matrices, where entries correspond to semantic likelihood of physical proximity between objects. We derive semantic spatial distributions by synthesizing semantics with learned geometric constraints. S^4 incorporates Optical Character Recognition (OCR) and semantic refinement with predictions from ViLD, an open-vocabulary object detection model. Simulation experiments suggest that semantic spatial search reduces the search time relative to pure spatial search by an average of 24% across three domains: pharmacy, kitchen, and office shelves. A manually collected dataset of 100 semantic scenes suggests that OCR and semantic refinement improve object detection accuracy by 35%. Lastly, physical experiments in a pharmacy shelf suggest 47.1% improvement over pure spatial search. Supplementary material can be found at https://sites.google.com/view/s4-rss/home.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

3D dense captioning is a task involving the localization of objects and the generation of descriptions for each object in a 3D scene. Recent approaches have attempted to incorporate contextual information by modeling relationships with object pairs or aggregating the nearest neighbor features of an object. However, the contextual information constructed in these scenarios is limited in two aspects: first, objects have multiple positional relationships that exist across the entire global scene, not only near the object itself. Second, it faces with contradicting objectives--where localization and attribute descriptions are generated better with tight localization, while descriptions involving global positional relations are generated better with contextualized features of the global scene. To overcome this challenge, we introduce BiCA, a transformer encoder-decoder pipeline that engages in 3D dense captioning for each object with Bi-directional Contextual Attention. Leveraging parallelly decoded instance queries for objects and context queries for non-object contexts, BiCA generates object-aware contexts, where the contexts relevant to each object is summarized, and context-aware objects, where the objects relevant to the summarized object-aware contexts are aggregated. This extension relieves previous methods from the contradicting objectives, enhancing both localization performance and enabling the aggregation of contextual features throughout the global scene; thus improving caption generation performance simultaneously. Extensive experiments on two of the most widely-used 3D dense captioning datasets demonstrate that our proposed method achieves a significant improvement over prior methods.

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of R^{n} for the groups S_n, O(n), Sp(n), and SO(n). By using category theoretic constructions, we build a richer structure that is not seen in the original formulation of these neural networks, leading to new insights. In particular, we outline the development of an algorithm for quickly computing the result of a vector that is passed through an equivariant, linear layer for each group in question. The success of our approach suggests that category theory could be beneficial for other areas of deep learning.

We introduce the first metric for evaluating disentanglement at individual hierarchy levels of a structured latent representation. Applied to object-centric generative models, this offers a systematic, unified approach to evaluating (i) object separation between latent slots (ii) disentanglement of object properties inside individual slots (iii) disentanglement of intrinsic and extrinsic object properties. We theoretically show that for structured representations, our framework gives stronger guarantees of selecting a good model than previous disentanglement metrics. Experimentally, we demonstrate that viewing object compositionality as a disentanglement problem addresses several issues with prior visual metrics of object separation. As a core technical component, we present the first representation probing algorithm handling slot permutation invariance.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Human perception is structured around objects which form the basis for our higher-level cognition and impressive systematic generalization abilities. Yet most work on representation learning focuses on feature learning without even considering multiple objects, or treats segmentation as an (often supervised) preprocessing step. Instead, we argue for the importance of learning to segment and represent objects jointly. We demonstrate that, starting from the simple assumption that a scene is composed of multiple entities, it is possible to learn to segment images into interpretable objects with disentangled representations. Our method learns -- without supervision -- to inpaint occluded parts, and extrapolates to scenes with more objects and to unseen objects with novel feature combinations. We also show that, due to the use of iterative variational inference, our system is able to learn multi-modal posteriors for ambiguous inputs and extends naturally to sequences.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Imitation learning with visual observations is notoriously inefficient when addressed with end-to-end behavioural cloning methods. In this paper, we explore an alternative paradigm which decomposes reasoning into three phases. First, a retrieval phase, which informs the robot what it can do with an object. Second, an alignment phase, which informs the robot where to interact with the object. And third, a replay phase, which informs the robot how to interact with the object. Through a series of real-world experiments on everyday tasks, such as grasping, pouring, and inserting objects, we show that this decomposition brings unprecedented learning efficiency, and effective inter- and intra-class generalisation. Videos are available at https://www.robot-learning.uk/retrieval-alignment-replay.

There is an analogy that is often made between deep neural networks and actual brains, suggested by the nomenclature itself: the "neurons" in deep neural networks should correspond to neurons (or nerve cells, to avoid confusion) in the brain. We claim, however, that this analogy doesn't even type check: it is structurally flawed. In agreement with the slightly glib summary of Hebbian learning as "cells that fire together wire together", this article makes the case that the analogy should be different. Since the "neurons" in deep neural networks are managing the changing weights, they are more akin to the synapses in the brain; instead, it is the wires in deep neural networks that are more like nerve cells, in that they are what cause the information to flow. An intuition that nerve cells seem like more than mere wires is exactly right, and is justified by a precise category-theoretic analogy which we will explore in this article. Throughout, we will continue to highlight the error in equating artificial neurons with nerve cells by leaving "neuron" in quotes or by calling them artificial neurons. We will first explain how to view deep neural networks as nested dynamical systems with a very restricted sort of interaction pattern, and then explain a more general sort of interaction for dynamical systems that is useful throughout engineering, but which fails to adapt to changing circumstances. As mentioned, an analogy is then forced upon us by the mathematical formalism in which they are both embedded. We call the resulting encompassing generalization deeply interacting learning systems: they have complex interaction as in control theory, but adaptation to circumstances as in deep neural networks.

In this paper we introduce a new, high-quality, dataset of images containing fruits. We also present the results of some numerical experiment for training a neural network to detect fruits. We discuss the reason why we chose to use fruits in this project by proposing a few applications that could use this kind of neural network.

Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and reviewers in recomender systems, queries and URLs in search engines, users and posts in social networks. The size and the dynamic nature of such graphs generate the need for more efficient ranking methods. In this thesis, at first we present the fundamental mathematical backround that we use subsequently and we describe the basic principles of the Perron-Frobebius theory for non negative matrices as well as the the basic principles of the Markov chain theory. Then, we propose a novel algorithm named BipartiteRank, which is suitable to rank scenarios, that can be represented as a bipartite graph. This algorithm is based on the random surfer model and inherits the basic mathematical characteristics of PageRank. What makes it different, is the fact that it introduces an alternative type of teleportation, based on the block structure of the bipartite graph in order to achieve more efficient ranking. Finally, we support this opinion with mathematical arguments and then we confirm it experimentally through a series of tests on real data.

Patent examiners need to solve a complex information retrieval task when they assess the novelty and inventive step of claims made in a patent application. Given a claim, they search for prior art, which comprises all relevant publicly available information. This time-consuming task requires a deep understanding of the respective technical domain and the patent-domain-specific language. For these reasons, we address the computer-assisted search for prior art by creating a training dataset for supervised machine learning called PatentMatch. It contains pairs of claims from patent applications and semantically corresponding text passages of different degrees from cited patent documents. Each pair has been labeled by technically-skilled patent examiners from the European Patent Office. Accordingly, the label indicates the degree of semantic correspondence (matching), i.e., whether the text passage is prejudicial to the novelty of the claimed invention or not. Preliminary experiments using a baseline system show that PatentMatch can indeed be used for training a binary text pair classifier on this challenging information retrieval task. The dataset is available online: https://hpi.de/naumann/s/patentmatch.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

As the size of deep learning models continues to grow, finding optimal models under memory and computation constraints becomes increasingly more important. Although usually the architecture and constituent building blocks of neural networks allow them to be used in a modular way, their training process is not aware of this modularity. Consequently, conventional neural network training lacks the flexibility to adapt the computational load of the model during inference. This paper proposes SortedNet, a generalized and scalable solution to harness the inherent modularity of deep neural networks across various dimensions for efficient dynamic inference. Our training considers a nested architecture for the sub-models with shared parameters and trains them together with the main model in a sorted and probabilistic manner. This sorted training of sub-networks enables us to scale the number of sub-networks to hundreds using a single round of training. We utilize a novel updating scheme during training that combines random sampling of sub-networks with gradient accumulation to improve training efficiency. Furthermore, the sorted nature of our training leads to a search-free sub-network selection at inference time; and the nested architecture of the resulting sub-networks leads to minimal storage requirement and efficient switching between sub-networks at inference. Our general dynamic training approach is demonstrated across various architectures and tasks, including large language models and pre-trained vision models. Experimental results show the efficacy of the proposed approach in achieving efficient sub-networks while outperforming state-of-the-art dynamic training approaches. Our findings demonstrate the feasibility of training up to 160 different sub-models simultaneously, showcasing the extensive scalability of our proposed method while maintaining 96% of the model performance.

We release a realistic, diverse, and challenging dataset for object detection on images. The data was recorded at a beer tent in Germany and consists of 15 different categories of food and drink items. We created more than 2,500 object annotations by hand for 1,110 images captured by a video camera above the checkout. We further make available the remaining 600GB of (unlabeled) data containing days of footage. Additionally, we provide our trained models as a benchmark. Possible applications include automated checkout systems which could significantly speed up the process.

Language places subtle constraints on how we make inductive inferences. Developmental evidence by Gelman et al. (2002) has shown children (4 years and older) to differentiate among generic statements ("Bears are daxable"), universally quantified NPs ("all bears are daxable") and indefinite plural NPs ("some bears are daxable") in extending novel properties to a specific member (all > generics > some), suggesting that they represent these types of propositions differently. We test if these subtle differences arise in general purpose statistical learners like Vision Language Models, by replicating the original experiment. On tasking them through a series of precondition tests (robust identification of categories in images and sensitivities to all and some), followed by the original experiment, we find behavioral alignment between models and humans. Post-hoc analyses on their representations revealed that these differences are organized based on inductive constraints and not surface-form differences.

This explainer document aims to provide an overview of the current state of the rapidly expanding work on synthetic data technologies, with a particular focus on privacy. The article is intended for a non-technical audience, though some formal definitions have been given to provide clarity to specialists. This article is intended to enable the reader to quickly become familiar with the notion of synthetic data, as well as understand some of the subtle intricacies that come with it. We do believe that synthetic data is a very useful tool, and our hope is that this report highlights that, while drawing attention to nuances that can easily be overlooked in its deployment.

We analyse perception and memory, using mathematical models for knowledge graphs and tensors, to gain insights into the corresponding functionalities of the human mind. Our discussion is based on the concept of propositional sentences consisting of subject-predicate-object (SPO) triples for expressing elementary facts. SPO sentences are the basis for most natural languages but might also be important for explicit perception and declarative memories, as well as intra-brain communication and the ability to argue and reason. A set of SPO sentences can be described as a knowledge graph, which can be transformed into an adjacency tensor. We introduce tensor models, where concepts have dual representations as indices and associated embeddings, two constructs we believe are essential for the understanding of implicit and explicit perception and memory in the brain. We argue that a biological realization of perception and memory imposes constraints on information processing. In particular, we propose that explicit perception and declarative memories require a semantic decoder, which, in a simple realization, is based on four layers: First, a sensory memory layer, as a buffer for sensory input, second, an index layer representing concepts, third, a memoryless representation layer for the broadcasting of information ---the "blackboard", or the "canvas" of the brain--- and fourth, a working memory layer as a processing center and data buffer. We discuss the operations of the four layers and relate them to the global workspace theory. In a Bayesian brain interpretation, semantic memory defines the prior for observable triple statements. We propose that ---in evolution and during development--- semantic memory, episodic memory, and natural language evolved as emergent properties in agents' process to gain a deeper understanding of sensory information.

We present a meta-learning framework for learning new visual concepts quickly, from just one or a few examples, guided by multiple naturally occurring data streams: simultaneously looking at images, reading sentences that describe the objects in the scene, and interpreting supplemental sentences that relate the novel concept with other concepts. The learned concepts support downstream applications, such as answering questions by reasoning about unseen images. Our model, namely FALCON, represents individual visual concepts, such as colors and shapes, as axis-aligned boxes in a high-dimensional space (the "box embedding space"). Given an input image and its paired sentence, our model first resolves the referential expression in the sentence and associates the novel concept with particular objects in the scene. Next, our model interprets supplemental sentences to relate the novel concept with other known concepts, such as "X has property Y" or "X is a kind of Y". Finally, it infers an optimal box embedding for the novel concept that jointly 1) maximizes the likelihood of the observed instances in the image, and 2) satisfies the relationships between the novel concepts and the known ones. We demonstrate the effectiveness of our model on both synthetic and real-world datasets.

A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the entity exists and its orientation to represent the instantiation parameters. Active capsules at one level make predictions, via transformation matrices, for the instantiation parameters of higher-level capsules. When multiple predictions agree, a higher level capsule becomes active. We show that a discrimininatively trained, multi-layer capsule system achieves state-of-the-art performance on MNIST and is considerably better than a convolutional net at recognizing highly overlapping digits. To achieve these results we use an iterative routing-by-agreement mechanism: A lower-level capsule prefers to send its output to higher level capsules whose activity vectors have a big scalar product with the prediction coming from the lower-level capsule.

Humans refer to objects in their environments all the time, especially in dialogue with other people. We explore generating and comprehending natural language referring expressions for objects in images. In particular, we focus on incorporating better measures of visual context into referring expression models and find that visual comparison to other objects within an image helps improve performance significantly. We also develop methods to tie the language generation process together, so that we generate expressions for all objects of a particular category jointly. Evaluation on three recent datasets - RefCOCO, RefCOCO+, and RefCOCOg, shows the advantages of our methods for both referring expression generation and comprehension.

We report a series of robust empirical observations, demonstrating that deep Neural Networks learn the examples in both the training and test sets in a similar order. This phenomenon is observed in all the commonly used benchmarks we evaluated, including many image classification benchmarks, and one text classification benchmark. While this phenomenon is strongest for models of the same architecture, it also crosses architectural boundaries -- models of different architectures start by learning the same examples, after which the more powerful model may continue to learn additional examples. We further show that this pattern of results reflects the interplay between the way neural networks learn benchmark datasets. Thus, when fixing the architecture, we show synthetic datasets where this pattern ceases to exist. When fixing the dataset, we show that other learning paradigms may learn the data in a different order. We hypothesize that our results reflect how neural networks discover structure in natural datasets.

We present Manify, an open-source Python library for non-Euclidean representation learning. Leveraging manifold learning techniques, Manify provides tools for learning embeddings in (products of) non-Euclidean spaces, performing classification and regression with data that lives in such spaces, and estimating the curvature of a manifold. Manify aims to advance research and applications in machine learning by offering a comprehensive suite of tools for manifold-based data analysis. Our source code, examples, datasets, results, and documentation are available at https://github.com/pchlenski/manify

In this paper, we introduce Nested Low-Rank Adaptation (NoRA), a novel approach to parameter-efficient fine-tuning that extends the capabilities of Low-Rank Adaptation (LoRA) techniques. Vanilla LoRA overlooks pre-trained weight inheritance and still requires fine-tuning numerous parameters. To addresses these issues, our NoRA adopts a dual-layer nested structure with Singular Value Decomposition (SVD), effectively leveraging original matrix knowledge while reducing tunable parameters. Specifically, NoRA freezes the outer LoRA weights and utilizes an inner LoRA design, providing enhanced control over model optimization. This approach allows the model to more precisely adapt to specific tasks while maintaining a compact parameter space. By freezing outer LoRA weights and using an inner LoRA design, NoRA enables precise task adaptation with a compact parameter space. Evaluations on tasks including commonsense reasoning with large language models, fine-tuning vision-language models, and subject-driven generation demonstrate NoRA's superiority over LoRA and its variants. Code will be released upon acceptance.