---
license: cc-by-4.0
language:
  - en
tags:
  - interpretability
  - mechanistic-interpretability
  - reproduction
  - jacobian-lens
  - global-workspace
pretty_name: J-space Reproduction on Qwen2.5-0.5B
size_categories:
  - n<1K
---

# J-space Reproduction on Qwen2.5-0.5B

Per-probe measurements **reproducing Anthropic's "global workspace" / J-space finding on a small open
model** (Qwen2.5-0.5B-Instruct, 24 layers, 896 hidden dims), computed on CPU.

This is a **reproduction-measurements dataset**, not a training dataset. It exists so anyone can check the
central claim: *a language model does part of its reasoning in a tiny, causally-necessary subspace of its
activations, separate from the tokens it emits.*

- 📄 Original research: Anthropic, [A global workspace in language models](https://www.anthropic.com/research/global-workspace) · [full write-up](https://transformer-circuits.pub/2026/workspace/index.html)
- ✍️ The story of this reproduction: [bitácora post — "The tiny workspace where a small model does its thinking"](https://bitacora.utopiaia.com/posts/08-jspace.html)

## The headline result (12 reasoning probes, mean)

| quantity | value |
|---|---|
| reasoning workspace size (effective rank) | **1.5%** of hidden dims |
| future-influence energy in the top-8 SVD directions | **76%** |
| reasoning error, model intact | 2.83 nats |
| reasoning error, **random** 8-dim slice removed | 3.45 nats (+0.62) |
| reasoning error, **J-space** 8-dim subspace removed | 4.07 nats (+1.24) |
| **causal necessity** (extra damage from removing the J-space vs a random slice) | **+0.62 nats (≈2× the damage)** |

Removing the 8-dimensional J-space hurts reasoning roughly **twice** as much as removing a random slice of
the same size — the model genuinely leans on that tiny subspace.

## How it was measured (the Jacobian lens)

1. **Future-influence Jacobian** — back-propagate the loss on the model's own continuation to each layer's
   activations: `G_l = d(next-token NLL) / d(hidden_l)`. Each row is the direction that activation pushes
   future outputs.
2. **Subspace extraction** — SVD of `G_l`; keep the top-8 right-singular directions = the J-space at that
   layer. Report its effective-rank fraction and top-8 energy.
3. **Causal ablation** — project the J-space out of the residual stream mid-network and measure the
   reasoning-NLL increase, against a **random equal-rank subspace** control.

Full method code is included (`jspace_advanced.py`, `jspace_report.py`); it runs on CPU in a couple of
minutes. `python jspace_report.py` regenerates `jspace_measurements.jsonl` + `jspace_summary.json`.

## Files

- `jspace_measurements.jsonl` — one row per probe:
  - `prompt`, `base_nll`, `jspace_ablated_nll`, `random_ablated_nll`
  - `effrank_frac`, `energy_top8` (subspace stats)
  - `per_layer_influence` — future-influence norm per layer (24 values)
  - `workspace_concepts_by_depth` — logit-lens top tokens at the final position, by depth
- `jspace_summary.json` — the aggregate table above
- `jspace_advanced.py`, `jspace_report.py` — the exact measurement code

## Honest caveats

- **One small model, one subspace size, twelve prompts.** The *causal* claim (a tiny, load-bearing
  reasoning subspace exists) replicates cleanly and robustly. The **content** is hard to read on a 0.5B
  model — the logit-lens workspace concepts are noisy and only sharpen in the last layers.
- The original paper's **"planning" aspect** (future-relevant concepts activating *early*) is **weak here**:
  on this model reasoning mostly resolves in the last few layers.
- The J-space is a **diagnostic lens**, not an engineering knob — attempts to exploit it (e.g. mixed-
  precision quantization or as a data-free model-merge fitness) do **not** work; that's documented
  separately.

## Citation

If Anthropic's finding is what you're citing, cite their paper. If you use these reproduction measurements
or the method code, a link back to the bitácora post is appreciated.