Filtering noisy gradients lifts the J++ Lens to 55% recall on models' hidden variables

The J-Lens, introduced by Gurnee et al. (2026), returns the tokens a model is most disposed to verbalise given a single activation ^[3]. It gets there through a Jacobian averaged over many activations ^[4]. Kola Ayonrinde of Anthropic Fellows and Jack Lindsey of Anthropic found that noisy gradients pile up in that average and corrupt it [c17, c6]. Their fix has three parts: Jacobians from activations that give poor readouts are down-weighted, Layer-wise Relevance Propagation is applied to the backward pass when the Jacobians are computed, and non-semantic tokens are removed from the readout ^[7]. Only the first two act on the Jacobian. The third filters the token list the lens returns, so the gradient-filtering label also covers a cleanup of the output ^[7].

The order of the work is the part I would copy. Before touching the tool, the authors set out four reasons the J-Lens might miss an intermediate variable: the workspace hypothesis is a poor model of language model cognition, the workspace lacks a linear representation of the variable, the model does not represent it at all, or the lens is imperfect ^[8]. They then showed that a substantial fraction of intermediate variables can be extracted linearly ^[9]. That evidence points at the lens. Next they showed that filtering out the Jacobians from a subset of activations raises lens performance ^[10].

The workspace is worth reading because Gurnee et al. tied it to behaviour. Given the prompt "Fact: The number of legs on the animal that spins webs is", the J-Lens surfaced "spider" and "legs" at intermediate layers before the model predicted 8 ^[11]. Patching in the J-Lens vector for "ant" in place of "spider" flipped the answer to 6, the right count for an ant ^[11].

On the authors' extraction tasks, J++ beats the J-Lens by 19.5 points and the R-Lens by 17.5 [d1, d2]. The metric is recall@10, so the correct intermediate has to appear among the top ten readout tokens ^[1]. The targets are known in advance. In one example the intended path runs from the prompt to "heart" to "four chambers" ^[17]. A monitor watching for eval awareness has no known target to check against. For the score to carry over, the concept would have to sit in the workspace the way a multi-hop intermediate does. Someone would also have to spot it in a ten-token list without knowing what to look for.

Ayonrinde and Lindsey wrote, "We believe that more faithful lenses can be useful in monitoring for eval awareness and unverbalised scheming." ^[21] The results in the post come from the latent variable extraction tasks ^[1]. The post does not say how a poor readout is scored for down-weighting, or how the 55.2% splits across the three changes and the range of model sizes [c7, c14].