kaushikreddyxyz/toybench-distributions

ToyBench Distributions

A benchmark suite of 8 feature distributions for evaluating sparse autoencoders and toy models of superposition. Generated using the [occhio] research library (docs).

Dataset Summary

Property	Value
Distributions	8
Samples per distribution	200,000
Features per sample	1,296
Dtype	torch.float32
Format	SafeTensors + JSON metadata
Total size	~8 GB
True L0	~8 (all distributions)
Generator seed	42 (all distributions)
License	CC BY 4.0

Distributions

1. Zipfian (zipfian)

The simplest distribution. Each feature fires independently with zipfian (power-law) activation probability: p_active[i] = high / (i+1)^alpha, decaying smoothly from high=0.5 to low=2/N. Purely captures frequency variation.

2. Correlated Pairs (correlated_pairs)

Features are grouped into pairs (2i, 2i+1). Each pair activates jointly with zipfian probability (high=0.63, low=2.70/N), then each feature within an active pair fires independently with p_individual ~ [0.5, 1.0]. Models co-occurring features like "peanut butter and jam".

3. Hierarchical Pairs (hierarchical_pairs)

Features form pairs (2i, 2i+1): the primary fires with zipfian p_active (high=0.6, low=2.39/N); the secondary fires conditionally with p_follow=0.6. The secondary's magnitude is coupled to the primary's via beta[i] ~ Uniform(0,1). Models parent-child feature relationships with magnitude inheritance.

4. Deep Hierarchy (deep_hierarchy)

Features are nodes of a randomly sampled DAG (p_edge=18/N). Each sample starts n_firings=2 random walks from uniformly chosen nodes upward to a root, activating all nodes along each path. beta=0.8 controls value decay per step (shrinking=True). Models deep hierarchical dependencies.

5. Preferential Attachment (preferential_attachment)

Features are nodes of a weighted directed graph with power-law in-degree (alpha=0.75). Sampling: each feature fires independently with p_active=4/N, then cascades to out-neighbors via Noisy-OR with edge weights from Uniform(0.2, 0.6). Edge density p_edge=4.5/N. Models one-step causal propagation in a sparse network.

6. Simplicial Complex (simplicial_complex)

Features are vertices of 7-dimensional simplices (648 faces, 8 vertices each). Faces are constructed to cover all 1,296 vertices, then padded with random faces. sampling_mode='single': one face fires per sample with p_active=1/648. Models features living on geometric simplices.

7. Spherical (spherical)

Features are placed approximately uniformly on S^4 (the 4-sphere). Each sample picks a random direction and magnitude m ~ Uniform(0.5, 1.0); features activate via a cosine bump with length_scale=0.276. Models features on manifolds (e.g., coordinates, pitch-yaw-roll).

8. Toric (toric)

Features are placed on a uniform 6x6x6x6 grid on T^4 (the 4-torus, N = 6^4 = 1296). Each sample picks a random point and magnitude m ~ Uniform(0.5, 1.0); features activate via a cosine bump with length_scale=0.752. Models periodic/cyclical features (e.g., seconds x minutes x hours).

File Structure

toybench-distributions/
  {distribution_name}/
    samples/
      samples.json          # Metadata (class, parameters, shapes)
      samples.safetensors   # Tensor data (200000 x 1296, float32)

Where {distribution_name} is one of: correlated_pairs, deep_hierarchy, hierarchical_pairs, preferential_attachment, simplicial_complex, zipfian, spherical, toric.

Usage

The easiest way to use these distributions is with occhio, which handles downloading, caching, and efficient GPU-buffered sampling:

from occhio.distributions import HuggingFaceDistribution

correlated_dist = HuggingFaceDistribution(
    repo_id="kaushikreddyxyz/toybench-distributions",
    filename="correlated_pairs/samples/samples.safetensors",
)

hierarchical_dist = HuggingFaceDistribution(
    repo_id="kaushikreddyxyz/toybench-distributions",
    filename="hierarchical_pairs/samples/samples.safetensors",
)

sample1 = hierarchical_dist.sample(64) # shape: (64, 1296)
sample2 = correlated_dist.sample(64)   # shape: (64, 1296)

Samples are memory-mapped from disk and transferred to device on demand, so the full dataset is never loaded into GPU memory at once.

Alternatively, load directly with huggingface_hub:

from huggingface_hub import hf_hub_download
from safetensors.torch import load_file

repo_id = "kaushikreddyxyz/toybench-distributions"
path = hf_hub_download(repo_id, "correlated_pairs/samples/samples.safetensors")
samples = load_file(path)["samples"]  # shape: (200000, 1296)

Citation

If you use this dataset, please cite:

@dataset{toybench,
  title={ToyBench Distributions},
  author={Kupper, Niclas and Siewke, Oliver and Reddy, Kaushik and Ayonrinde, Kola},
  year={2026},
  url={https://huggingface.co/datasets/kaushikreddyxyz/toybench-distributions},
  license={CC-BY-4.0}
}