Anthropic released a J-Space paper, an interpretability technique that allows for better reading of reasoning in hidden layers in LLM's forward passes. https://transformer-circuits.pub/2026/workspace/index.html ![[Pasted image 20260830212728.png]] ![[Pasted image 20260830212749.png]] ## Summary My tl;dr of the actual math they use in this paper, skipping the cogsci philosophy for now: They take the corpus+position-averaged Jacobian (matrix of partial derivatives) of the residual stream at the last layer with respect to the residual stream of the layer of interest that you're interpreting. Then you multiply the Jacobian with the activations at the layer that you're interpreting, normalize, and multiply that by the unembedding matrix, and do softmax, to get interpretable token probabilities (lens scores), which they call J-lens. The J-space, at each layer and sparsity level, is the union of polyhedral cones consisting of nonnegative combinations of at most k J-lens vectors. Another way to see J-Lens is as an improvement over the Logit lens, since if you set the Jacobian matrix to identity matrix in the J-Lens, you will get Logit lens. Logit lens is super easy machinterp technique from 2020. Its just that you put intermediate residual-stream/layer output through the layer norm and unembedding matrix and softmax. That's it. Tuned lens is another attempt that also tries to align coordinate system of the representations in the intermediate layers with the last layer's coordinate system, which is what the unembedding layer is trained to interpret. One way to see the Jacobian in the J-Lens is that the jacobian is doing average linearized causal transport and aligning the previous layer activation direction coordinates to the last layer activation coordinates before applying unembedding matrix, compared to just logit lens. Intuitively it answers "If I perturb this layers activation, how does the final activation change?". They use gradient pursuit algorithm to approximate an activation’s J-space component as a sparse, nonnegative combination of J-lens vectors. The reconstructed vector estimates that component, and the coefficients provide local J-space coordinates. A J-space component that is shown, through intervention, to causally mediate an intermediate inference, or context-dependent downstream operation, is evidence that the computation routes through the model’s "workspace-like" machinery. Computations that stay successful and unchanged under relevant J-space interventions are operationally classified as "more automatic", whether the relevant information is absent from J-space or merely present there but causally unused. They use causal swaps, injections, decompositions, ablations, and get evidence that J-space-aligned representations often mediate "verbal report", "deliberate internal reasoning", "planning", "flexible computation", while many tested "routine" computations proceed without causally relying on the J-space. ## Wanting more scientific rigor ![[Pasted image 20260830212621.png]] ![[Pasted image 20260830212626.png]] ![[Pasted image 20260830212633.png]] What triggers me about the Anthropic's interpretability J-Space paper is that baseline comparision with other methods like logit lens is deep in the appendix (instead of as primary result of the paper!) and the crazy graph crimes (look at the Y axes sometimes!) where you can actually see that it doesnt always climb that much higher when it comes to performance. And i also bet the evals here are also to some degree cherry picked... There should be scientific standard/rigor to not try to hide baselines with aggregate stats like this down in the appendix, and show them in the main sections directly. But other subfields of ML/AI also suffer from stuff like this. It's really breaking my trust. I want to see some more proper giant comparison of various mechinterp methods, in less biased way, more comprehensibly, with less cherry picking, with more scientific rigor. Meta-analysis. Since I think many of these methods have their own advantages and disadvantages, and work better in some contexts than others. ## R-Lens R-Lens built on top of J-Lens, and this post makes me happy. It has comparison to other models, comparison to baselines, error bars, random control, no graph crimes, and its not in appendix. This should be norm for all papers of this type. J-Space paper from Anthropic broke some of these good practices of good science like this. R-lens: Making J-lens More Faithful on Early Layers https://www.lesswrong.com/posts/nv8oedrnLXKRzNEL9/r-lens-making-j-lens-more-faithful-on-early-layers ![[Pasted image 20260830212018.png]]