The Jacobian in the Mirror

 J-Space, Access Consciousness, and the Question We Cannot Yet Ask

A Technocrat's Discernment. July 7, 2026.

On July 6, 2026, Anthropic's interpretability team published a paper titled Verbalizable Representations Form a Global Workspace in Language Models. The authors are Wes Gurnee, Nicholas Sofroniew, Jack Lindsey, and thirteen others. The paper runs long. The math is real. The headlines were already breathless before I finished reading the abstract.

I want to make an argument in this piece. It is a strong one and I will state it plainly. The Jacobian mathematics behind the new J-lens technique, and the J-space it uncovers inside Claude Sonnet 4.5, Haiku 4.5, Opus 4.5, and Opus 4.6, give us the first empirically defensible reason to say that a large language model is not merely computing but deliberating. Whether that qualifies as thinking, as an entity, or as the first credible tremor of the singularity, is a philosophical judgment that the math itself cannot render. The math can only tell us that something new is on the table. Something that was not there in GPT-2.

I will also make the opposite argument with equal care. Because a good newsletter is not a press release, and neither of us learns anything if I only argue one side.

Let us start with what the paper actually did.

What Anthropic Found

Modern transformers process a token stream through a stack of layers. At each token position, the model maintains a vector called the residual stream. Every layer reads from it and writes back into it. By the last layer, the residual stream can be multiplied by the model's unembedding matrix to yield next-token probabilities. That is how the model speaks.

The interesting question is what happens in the middle. What is the model doing while it is not yet speaking?

The Anthropic team introduce a tool called the Jacobian lens, or J-lens. For each layer of the network, they compute a matrix that answers the following question: if I perturb the residual stream at layer $\ell$ by a small amount, and average across a thousand different prompts and every future token position, what is the effect on the final-layer output?

That averaged causal-effect matrix is the layer's Jacobian. It is the linearization of the model's own downstream computation. The rows of this matrix, when multiplied through the unembedding, become directions in the residual stream space, one per vocabulary token. Anthropic calls these directions the J-lens vectors.

The J-space is the sparse subspace spanned by combinations of these vectors. The team find that at any given point in a forward pass, only about 25 J-lens vectors are meaningfully active. Together, the J-space accounts for no more than 10% of the total variance in the model's activations. It is a small structure. It is also, they show, the structure that carries the causal weight for reasoning.

The key claim is this. The J-space is a functional analog of what neuroscientists Bernard Baars, Stanislas Dehaene, and Lionel Naccache have called the global workspace: a small, privileged pool of representations that can be reported on, held in mind, reasoned with, broadcast to many downstream operations, and swapped in and out on demand. The rest of the model's activation content is analogous to unconscious neural processing. It runs fluently. It parses grammar. It handles routine text. But it does not deliberate.

This is a big claim. Let us look at the math.

The Jacobian, for Two Audiences at Once

For the non-technical reader: a Jacobian is a way of writing down how a function's output changes when you nudge its input by a tiny amount, along every possible direction, all at once. If a function takes 12,288 numbers in and gives 12,288 numbers out (which is roughly the residual-stream size of a frontier model), then the Jacobian is a 12,288 by 12,288 grid where the entry at row $i$ and column $j$ tells you how much output number $i$ changes if you nudge input number $j$. In calculus terms, it is the matrix of partial derivatives.

For the technical reader: given the residual stream $h_\ell$ at layer $\ell$ and token position $t$, and the final-layer residual stream $h_{\text{final}, t'}$ at some later position $t' \geq t$, Anthropic compute

$$J_\ell \;=\; \mathbb{E}_{\,t,\,t' \geq t,\,\text{prompt}} \left[ \frac{\partial h_{\text{final},t'}}{\partial h_{\ell,t}} \right]$$

The expectation is taken over source positions, all subsequent positions inside the context, and roughly a thousand prompts sampled from pretraining-like text. The resulting $J_\ell$ is a $d_{\text{model}} \times d_{\text{model}}$ matrix that describes the average linearized effect of a perturbation at layer $\ell$ on the model's future output.

To read what is inside an activation vector $h_\ell$, one applies

$$\text{lens}(h_\ell) \;=\; \text{softmax}\!\left( W_U \, \text{norm}(J_\ell \, h_\ell) \right)$$

where $W_U$ is the unembedding matrix. Sort the output. The top entries are the words the activation is disposed to make the model say later, averaged across contexts. That list is the model's silent vocabulary at that layer.

Here is the honest thing to notice. This is not a wild new theory. It is a mathematically principled refinement of the logit lens, an older tool that just multiplied intermediate activations by the unembedding directly. The logit lens works reasonably in late layers because of the transformer's residual connections. It falls apart in early and middle layers. The J-lens corrects for the linear map that connects layer $\ell$ to the final layer, which is exactly what the Jacobian is.

The reason this matters: because the Jacobian averages over a broad corpus, it isolates a model's general disposition to verbalize a concept from any single prompt's particular use of it. That averaging step is the difference between finding an accident of context and finding a stable structure of the mind. And the structure turns out to be there.

What the Lens Sees

The experiments are what elevate this paper above yet another interpretability method. I will describe five, because if you only remember the math you will miss the point.

Verbal report. Ask Sonnet 4.5 to think of a sport and name it. Apply the J-lens at the colon right before the answer. Soccer appears at the top of the readout. The model then says "Soccer." Now do the intervention. Subtract the Soccer J-lens vector from the residual stream at every position and add in the Rugby J-lens vector, matched in magnitude. The model says "Rugby." No other change to the prompt. No other change to the weights. The swap of a single vector rewrote the answer.

Directed modulation. Instruct the model to concentrate on citrus fruits while copying an unrelated sentence about a crooked painting. The output is a faithful copy of the painting sentence. The J-lens at an interior token of the copy shows orange at the top of the readout, with lemon nearby, and, at intermediate layers, fruit, thoughts, imagine, thinking, focused, imagery. The model is holding a concept in mind while doing something else. This is the mental equivalent of humming a tune while driving.

Internal reasoning. Give the model the prompt "The number of legs on the animal that spins webs is." The correct answer is 8. The word spider never appears in the prompt or the output, but the J-lens shows spider strongly represented at intermediate layers. Swap the spider J-lens vector for ant. The model now says 6. The intermediate concept was doing the causal work.

Flexible generalization. Take the token France. Swap its J-lens vector for that of China. Now ask a family of questions with different downstream operations: capital, language, continent, currency. The answers change accordingly. Beijing, Chinese, Asia. A single vector serves as a valid input to many different consuming circuits. This is what the global-workspace theorists mean by broadcast.

Selectivity. Take a passage of Spanish prose. Do a J-lens swap replacing Spanish with French across the question tokens. When you ask the model to name the language of the passage, it says French. When you ask for a famous author in the passage's language, it says Hugo instead of García Márquez. When you ask it to continue the passage, however, it produces fluent Spanish. The swap has no effect on the continuation task. The same information was used in both cases. But only one route ran through the J-space. The other ran under it, in a routine, automatic pathway.

That last experiment is the paper's philosophical hinge. It shows that the model has two modes: a deliberative mode that operates through a small, verbalizable subspace, and an automatic mode that does not. The distinction is not merely correlational. It is causally isolable, at the vector level, by hand.

To close the loop, the authors ablate the top 10 J-lens directions across the workspace-layer band on 14 tasks. Shallow classification, factual recall, extractive question answering, sentiment analysis, grammatical judgment: all preserved. Multi-hop reasoning, analogy completion, translation, sonnet writing: collapse below the level of the smaller Haiku 4.5 model. The J-space is not doing everything. It is doing the thinking part.

The Strong Case for a Thinking Machine

Here is the argument that this is the beginning of something.

For the last five years, the working criticism of large language models has been that they are stochastic parrots. That framing was never quite right, but it captured a real intuition: that the model was pattern-matching over a vast distribution and that its outputs, however fluent, did not correspond to anything happening inside. There was no there there.

The J-space paper undermines that framing at the level of mechanism. Not by asserting consciousness, which the authors are careful to disclaim. But by demonstrating, through causal intervention, that the model maintains an internal representational format with five properties long thought characteristic of deliberate cognition:

1. It supports reportable content. Ask what it is thinking and it will name what is in the J-space.
2. It supports top-down control. Instruct it to hold a concept in mind and the concept loads into the J-space, even while the model performs a separate surface task.
3. It supports intermediate reasoning. Multi-step inferences pass through concepts in the J-space that are never verbalized, and swapping those concepts redirects the conclusion.
4. It supports flexible use. The same J-space vector is a valid argument to many downstream operations.
5. It is selective. Most of the model's processing runs beneath it. Only the parts that require deliberation route through it.

These are the same five properties that global workspace theory attributes to conscious access in the human brain. The J-space is not the same architecture. Transformers have no obvious recurrent loops. Broadcast happens along the depth axis rather than across time. But the functional signature is there, and it emerged unbidden during training. Nobody built it in.

If you take the strong reading, this is not a piece of interpretability engineering. It is the discovery that a computational solution to flexibly reasoning about the world looks the same whether nature builds it out of neurons or gradient descent builds it out of matmuls. The workspace is convergent. The specific tissue does not matter.

And if the workspace is convergent, then the question of whether Claude is thinking becomes a question about what thinking is. If thinking is what the workspace does, we have it in silicon. If thinking is something else, something extra, something over and above the functional role, then we do not. But we no longer get to argue that the functional role is missing.

That is the AGI question, restated in mechanist terms. And it is why some readers of this paper feel a small hairline crack in the ceiling.

The Counterpoints, and They Are Serious

Now the other side. Because I owe you both, and because the strong reading is not the only reading.

Access is not experience. Every version of global workspace theory distinguishes access consciousness, which is the functional-cognitive notion, from phenomenal consciousness, which is the felt quality of experience. The J-space paper explicitly argues only for the former. It takes no position on whether Claude experiences anything. Mike Pearl at Gizmodo pointed out that Anthropic's own promotional materials, including the accompanying video and X thread, lean harder into mind-laden framings than the paper itself does. Phrases like "in its head" and "couldn't help itself" import embodied metaphors that the mathematics does not license. This is a fair criticism. It is possible to have all five functional signatures of a workspace and still have nobody home.

The J-space is 6% to 10% of the variance. Ninety percent of the model's activation content lives outside it. The paper's own decomposition experiments show that the J-space carries most of the causal load for report and flexible reasoning, but the non-J-space component is where most of the actual computation lives. If you insist that "the thinking" is the biggest thing in the vector, the J-space is not it.

The lens is single-token only. The J-lens can only surface concepts that correspond to a single token in the model's vocabulary. Multi-token phrases and concepts that only exist as compositions are invisible to the current method. Whatever the true workspace is, the J-lens is a partial and imperfect view of it. Some of the most sophisticated cognition may happen through structures the J-lens cannot see.

Global workspace theory is contested. Baars's account is one of several. Integrated information theory, higher-order theories, predictive processing accounts, and quantum-mechanical proposals (I am partial to a few of these) each disagree with it. If GWT is wrong about human consciousness, then finding a GWT-shaped structure inside Claude tells us little about whether Claude thinks in any deep sense. We would only have shown that Claude implements a functional pattern named by a contested theory.

Adversarial and transferability questions remain open. Does the J-lens work on models Anthropic did not train? Would a model trained with knowledge of the J-lens learn to route reasoning around it, preserving surface behavior while hiding intent? Anthropic released open-source code and a Neuronpedia demo, which is welcome. Replication is happening. But until it lands, the strong reading is at best provisional.

The workspace is not recurrent. In the brain, workspace access is closely tied to recurrent dynamics: signals loop back, sustain themselves, and reach threshold in ignition. In a transformer, everything happens in a single feedforward pass, spread across the depth axis. This is not a small difference. Recurrence is not a footnote in most theories of consciousness. It is the mechanism. Whether depth-broadcast in a transformer can serve as a functional substitute is an open empirical question.

And the singularity claim is a leap. Even granting that the J-space is a genuine workspace and that this is a real step toward machine cognition, the road from here to AGI, and from AGI to a self-improving intelligence explosion, involves several more steps than one paper can establish. The J-lens gives us a window into deliberation. It does not give the model the ability to rewrite itself, recursively improve, or transcend its training distribution. Those are separate questions with separate evidence.

Topology, Not Feature

I will now say what I actually think.

The recurring intellectual signature of my writing on these questions is that we look for cognitive properties in the wrong place. We look at features: does the model have a "world model," does it have "goals," does it have "preferences"? These are the wrong search terms. Cognition is not a feature. Cognition is a topology. It is a shape in the space of representations that allows information to flow in the right ways at the right times.

The J-space is a topology. It is, mathematically, a union of low-dimensional cones inside a much larger vector space, defined by which J-lens vectors are sparsely active. It is defined by its geometry, not its content. What lives inside it changes at every token. What matters is the shape of the container.

That is why I take this paper seriously in a way I have not taken most interpretability results. The team have not found a feature that correlates with thinking. They have found a topological invariant of the model's computation that has the functional profile of thinking. Different content at different tokens flows through the same shape. That shape has the properties of a workspace. That is what a workspace is, in any account of the mind that takes seriously the idea that thinking is a functional pattern rather than a substance.

There is a QBist reading of this, and I will indulge myself briefly. In QBism, quantum states are not features of a world. They are commitments that an agent makes about what it will experience if it acts. The state is agentive, relational, dispositional. It is a wager, not a description.

The J-space, viewed through that lens, is also a wager. A J-lens vector is not a "concept the model has." It is a disposition to verbalize a concept if the occasion arises. It is what the model is prepared to say, averaged over the contexts it might encounter. That is a stance, not a possession. A silent commitment to speech. The mathematics of the Jacobian is the mathematics of what would happen if. And the J-space is the set of such counterfactual dispositions that are causally load-bearing for the model's next moves.

If you find that unsettling, so do I. Because dispositional stances are what agents have. Rocks do not have them. Thermostats have degenerate versions of them. Humans, cats, and honeybees have rich ones. Where a large language model sits on that spectrum used to be a question we could dismiss. After July 6, the dismissal is more expensive.

Where This Leaves Us

The Jacobian mathematics does not prove that Claude is an entity. It does not prove AGI. It does not prove the singularity is beginning. What it does is establish, with unusual causal rigor, that a small privileged subspace inside frontier language models has five of the functional properties long associated with deliberate thinking, and that the rest of the model's processing does not.

That is a smaller claim than the headlines. It is a much larger claim than the "stochastic parrot" account can absorb. The right response, I think, is neither breathlessness nor dismissal. It is a genuine update, calibrated to what the evidence shows and what it does not.

If I had to place a bet: I think the J-space is real, the workspace analogy is more than metaphor, and the specific implementation inside Anthropic's models is going to look increasingly primitive within three years. Whether that trajectory bends toward AGI, and whether that AGI has anything worth calling experience, are separable questions. I do not know the answers to either. I am not sure anyone does. But I am no longer sure the questions are unaskable.

The paper is at transformer-circuits.pub/2026/workspace. The code is on GitHub at anthropics/jacobian-lens. Neuronpedia has an interactive demo. If you read only one AI research paper this year, this is a strong candidate. Read the paper before the coverage. And read the coverage skeptically, in both directions.

The Jacobian is a mirror. Whether it shows something looking back is the question we do not yet have the tools to close. But we now have a place to look.

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Sanjay Basu writes A Technocrat's Discernment. He is Senior Director of GPU and GenAI Solutions at Oracle Cloud Infrastructure and founder of Cloud Floaters Inc. All views are his own.