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Language Model Circuits Are Sparse in the Neuron Basis

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The paper claims that MLP neurons—specifically the pre-down-projection activations—are as sparse and faithful a feature basis for circuit tracing as sparse autoencoders, and that a single-backward-pass attribution method (RelP) makes this p

desk verdict Genuinely useful empirical result: MLP activations plus RelP give SAE-level sparse circuits on SVA; the central claim is real but the title outruns the evidence. read the letter →

arxiv 2601.22594 v2 pith:RLL4NQFV submitted 2026-01-30 cs.CL cs.AI

Aryaman Arora , Zhengxuan Wu , Jacob Steinhardt , Sarah Schwettmann This is my paper · ORCID
classification cs.CLcs.AI
keywords MLPactivationscircuittracingsparseautoencodersRelPattributionneuronbasismechanisticinterpretabilitysubject-verbagreementmulti-hopreasoning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Interpretability research has largely assumed that individual neurons are too entangled to serve as units for circuit tracing, motivating sparse autoencoders and other learned feature dictionaries. This paper argues the opposite: the pre-down-projection MLP activations are a privileged basis, and circuits expressed directly in that basis are about as sparse and faithful as circuits expressed in learned SAE features. The key technical moves are to attribute to MLP activations rather than MLP outputs and to replace Integrated Gradients with RelP, a single-backward-pass attribution built on a locally linearised copy of the model. On a subject–verb agreement benchmark, roughly 200 neurons suffice to almost fully control the behaviour; on a multi-hop capitals task, small groups of neurons encode each reasoning hop and can be steered to change the answer. The paper's intended consequence is that scalable automated interpretability can proceed without training additional dictionaries.

What carries the argument

The key object is the MLP activation vector h^(i)_j in the residual stream: the pre-down-projection hidden activations, whose coordinates are made a privileged basis by the elementwise SiLU nonlinearity. The argument is carried by this choice of basis together with RelP attribution, which replaces all nonlinearities on the backward pass by their local linearisations (detached or frozen RMSNorm scales, SiLU gates, and attention weights) plus a half-rule that divides gradients by two through the gated MLP's elementwise product, preserving a completeness property. RelP on MLP activations yields attribution scores in a single backward pass and, when extended to edges with stop-gradients on inter

What would settle it

Run the neuron-vs-SAE circuit comparison on a transformer with a non-gated MLP (e.g. GELU, no multiplicative gate). If, at equal circuit size, the neuron-basis circuit's faithfulness on subject-verb agreement is materially below the SAE-basis circuit's—or if RelP's top-200 neurons share little overlap with the top-200 by brute-force single-neuron ablation—the central claim fails outside gated-MLP architectures.

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Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that MLP neurons are as sparse a feature basis as SAEs for circuit tracing: for the first time, they empirically show that circuits of about 10^2 MLP neurons can control model behaviour on a standard benchmark, with near-perfect faithfulness and completeness, matching SAE-based circuits. The sparsity appears specifically when the nodes are the MLP hidden activations (before the down projection) rather than the MLP outputs, because the elementwise nonlinearity makes the activation coordinates a privileged basis. The gap that remained under Integrated Gradients is closed by RelP, which attributes via a locally linearised replacement model

Load-bearing premise

The load-bearing premise is that RelP's local linearisation of the network—freezing normalization scales, SiLU gates, and attention weights, and halving gradients through gated MLPs—preserves the true relative causal importance of individual neurons, a premise the authors validate only on a handful of templatic tasks and the MIB benchmark.

Editorial extensions

If this is right

  • Neuron-level circuits can be obtained with no extra training cost: no SAE needs to be trained or loaded, making circuit tracing more tractable for large models.
  • Circuit tracing no longer requires paired counterfactual inputs: RelP's unpaired variant finds sparse circuits from zero baselines, extending the approach to non-templatic settings.
  • The neuron basis is more faithful than learned bases because it avoids SAE reconstruction errors, feature splitting and absorption, and the need to maintain dictionaries throughout training.
  • The recovered circuits are actionable: steering a single 'say a capital' neuron flips the model's top output from the correct capital to the state in a majority of cases, and steering neuron clusters changes the output in line with their hypothesised roles.
  • RelP also improves attribution at coarser granularity, achieving the best or second-best CMD scores on the circuit-localisation track of the Mechanistic Interpretability Benchmark for node and edge attribution.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The sparsity result is demonstrated on gated-MLP transformers; a natural stress test is whether plain-GELU or non-gated architectures also show MLP-activation sparsity, or whether gated MLPs are what manufacture the privileged basis.
  • Because RelP attribution is computed on a locally linearised replacement model, the neuron rankings are only as faithful as that linearisation; comparing RelP's top-k sets against exhaustive single-neuron ablation on naturalistic inputs would quantify the risk.
  • If MLP activations are indeed a privileged basis, the architectural trend toward sparsity—gated MLPs, mixture-of-experts routing—may be making future models more transparent in the neuron basis, an implication the authors gesture at but do not test.
  • The user-modelling case study hints that neuron circuits can surface demographic inferences from prefilled infobox outputs, but whether such circuits generalise beyond contrived prompts remains open.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper argues that MLP activation neurons are as sparse a feature basis for circuit tracing as SAE features, contrary to the common assumption that neurons are too distributed to be useful. It proposes using MLP activations as the representation and RelP, a gradient-based attribution method that linearizes nonlinearities, for selecting neuron-level circuits. The empirical core is on the SVA benchmark, where the authors report that ~10^2 MLP neurons achieve near-perfect faithfulness/completeness, closing the gap with SAE features, with supporting experiments on unpaired data, Gemma-2 models, the MIB benchmark, and case studies on multi-hop reasoning, arithmetic, multilingual antonyms, and user modeling. The paper also includes steering experiments showing that individual neurons can change model outputs in interpretable ways.

Significance. If the central claim holds, the result is significant: it challenges the prevailing assumption that SAEs or transcoders are necessary for sparse, interpretable circuit discovery, and it offers a cheaper neuron-based alternative with no additional training cost. The paper has real strengths: selection is performed on training data and evaluation on held-out inputs with the original model, which avoids the most obvious circularity; the comparison spans multiple representations, two attribution methods, several tasks, and two model families; and the case studies include concrete steering interventions. The proof in Appendix B that the half-rule preserves completeness for gated MLPs is a useful formal contribution. However, the paper's quantitative claims currently rest on a metric-definition error and on attribution-fidelity evidence that is largely at module level rather than neuron level, so the headline claim is not yet secured.

major comments (4)
  1. [§3.2, Eqs. (3)–(4)] The equations defining Faithfulness and Completeness are identical: both are E[m(C,x)-m(∅,x)] / E[m(M,x)-m(∅,x)]. If C(x) in Eq. (1) means running the model with the circuit's complement ablated, then Eq. (3) is a reasonable faithfulness measure, but Completeness should ablate the circuit itself and compare to full-model ablation, e.g. E[m(C_ablated,x)-m(∅,x)] / E[m(M,x)-m(∅,x)]. As written, the two metrics are the same quantity, and all plots reporting both 'Faithfulness' and 'Completeness' (Figs. 1–5) become ambiguous. Please correct the definitions and confirm that the experiments use the intended distinct ablations.
  2. [§5.2, Eq. (11), Table 3] The central 'as sparse as SAEs' claim depends on RelP correctly ranking individual MLP neurons. RelP uses a replacement model with frozen RMSNorm, SiLU, and attention coefficients and the LRP half-rule; final evaluations are on the original model, but node selection is made with the replacement model. The direct evidence for neuron-level ranking fidelity is limited to the four templatic SVA tasks. The MIB validation in Table 3 operates at module level (attention heads/MLPs), not at the individual-neuron level asserted in §5.2. If the frozen-coefficient model over-credits neurons whose causal effects are mediated by nonlinear interactions, the top-neuron set could be much less faithful on non-templatic or out-of-distribution inputs. Please add neuron-level validation, e.g., by comparing RelP rankings to actual activation-patching ground truth on a sample of non-templatic inputs, or by rep
  3. [§G.1 and Table 13] The paper manually excludes 12 neurons because they are 'always activated' and uninformative (§G.1). However, Table 13 in the user-modeling case study reports six of these filtered neurons—L9/N4255, L6/N5866, L11/N11321, L7/N6673, L5/N7012, L2/N4786—as high-additional-information neurons for the non-binary class. This inconsistency suggests the filtering was applied unevenly across case studies or that the table includes neurons that were supposed to be removed. Please clarify whether the manual exclusion was applied to every case study, and report results with and without the filtered set so readers can assess the impact on the qualitative conclusions.
  4. [Figs. 1–5, §5.1] The main quantitative comparisons—especially the headline claim that ~200 MLP neurons are as sparse as SAE features—are presented as curves without error bars, confidence intervals, or multiple seeds. The MIB table says results are averaged over three seeds, but no variance is reported. No code is released. For a claim that is explicitly quantitative and comparative, this makes it difficult to judge whether the observed gap between MLP activations and SAEs is robust. Please include variability estimates (e.g., over seeds or task subsets), or release code so the curves can be reproduced.
minor comments (6)
  1. [§5.4] The text says RelP achieves 'over 80% faithfulness while maintaining high completeness.' Given Eqs. (3)–(4), lower completeness is better, so this should read 'low completeness.'
  2. [§5.2] The sentence 'We discovered RelP at the same time Jafari et al. (2025) did' is not verifiable from the manuscript and is unrelated to the technical content. Consider removing it or providing a dated preprint/artifact.
  3. [§4] For SAE circuits, the error term is allowed as a node if its attribution score passes the threshold. This is a standard choice, but it means the SAE circuits are not purely in the learned feature basis. Please report an additional comparison with SAE circuits that exclude the error term, since the headline comparison is about basis sparsity.
  4. [Table 3] The caption says results are averaged across three seeds, but no standard deviations or per-seed values are shown. Please add them, particularly for the RelP row.
  5. [§6.1] The case study manually selects 23 of 257 traced neurons for detailed discussion. This is acceptable as an exploratory illustration, but the manuscript should state more clearly that the qualitative circuit interpretation is based on a hand-picked subset, not on the full automatically traced circuit.
  6. [§B, Eq. (34)] In the bilinearized MLP equation, it would help to explicitly define s = Freeze(σ(W_gate x)), since the notation 'detach the SiLU nonlinearity's effect' is ambiguous and the subsequent degree-2 homogeneity argument depends on that interpretation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: circuit selection and evaluation are decoupled, and the central claim is checked on held-out data with the original model.

full rationale

The paper's central claim is that MLP-neuron circuits are as sparse and faithful as SAE circuits. The derivation chain is: (1) choose a set of neurons/features by attribution (IG or RelP) on a training subset; (2) evaluate the resulting circuit by mean-ablating the complement on the original model and measuring faithfulness/completeness on a held-out validation subset. Selection and evaluation therefore use different instances and different models (the replacement model for gradients vs. the original model for evaluation). Equation (1) defines evaluation on the original model M with mean ablation, while Equations (10)-(11) define RelP attribution on a replacement model; the latter is only used to rank nodes, not to define the success metric. Thus the 'as sparse as SAEs' result is not forced by construction: a random or poorly chosen neuron set would score worse, as the paper's own baselines show. RelP itself originates externally (Jafari et al., 2025), and its external validation on MIB compares against published baselines from the original MIB paper, providing independent evidence for the attribution method. The self-citations present in the paper (e.g., Choi et al. for neuron descriptions, Wu et al. for SAE baselines) are not load-bearing for the main sparsity claim. The local linearization in Table 2 and the half-rule in Appendix B are approximations whose faithfulness is an empirical correctness concern, not a circularity: they do not encode the conclusion that neurons are as sparse as SAEs. No equation in the paper reduces to its own input, no fitted parameter is renamed as a prediction, and no uniqueness theorem is imported to forbid alternatives. The paper is therefore self-contained against external evaluation for the purposes of circularity.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

No fundamentally new entities are introduced. The main load-bearing assumptions are the validity of mean ablation and the faithfulness of RelP's local linearisation.

free parameters (4)
  • attribution threshold τ = 0.005
    Set in §6 to filter neurons on the capitals task; not optimized and may not generalize.
  • IG integration steps n = 10
    Used for Integrated Gradients in §5; 10 backward passes, a hyperparameter.
  • edge candidate pool = top 10^3 neurons
    In §5.4, restricts edge computation to top 1000 neurons; arbitrary threshold affecting edge results.
  • steering multiplier α = selected from {−4,−2,−1,0,2,4}
    Chosen manually in §6 to show steering effects; not systematic.
assumptions (3)
  • domain assumption Mean ablation is a valid intervention for circuit evaluation
    Standard in the field (Marks et al., Wang et al.), but the faithfulness/completeness scores depend on this choice.
  • ad hoc to paper Local linearisation of nonlinearities preserves causal attribution ordering
    RelP freezes RMSNorm, SiLU, and attention weights (Table 2). The paper assumes this approximation is faithful enough, validated only on a few tasks.
  • domain assumption Automatic neuron descriptions from Choi et al. (2024) reliably reflect neuron function
    Used to interpret the multi-hop circuit; descriptions are simulator-based and may be noisy.

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Pith. "Pith review of Language Model Circuits Are Sparse in the Neuron Basis." pith.science (2026). https://pith.science/paper/RLL4NQFV

@misc{pith2026260122594,
  author       = {Pith},
  title        = {Pith review of: Language Model Circuits Are Sparse in the Neuron Basis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RLL4NQFV}},
  note         = {Machine review of arXiv:2601.22594}
}
abstract

The high-level concepts that a neural network uses to perform computation need not be aligned to individual neurons (Smolensky, 1986). Language model interpretability research has thus turned to techniques which decompose the neuron basis into more interpretable units of model computation, such as sparse autoencoders (SAEs). However, not all neuron-based representations are uninterpretable. For the first time, we empirically show that MLP neurons are as sparse a feature basis as SAEs. We use this finding to develop an end-to-end gradient-based attribution pipeline for circuit tracing on the MLP neuron basis, which surfaces causally effective neurons on a variety of tasks. On a standard subject-verb agreement benchmark (Marks et al., 2025), a circuit of $\approx 10^2$ MLP neurons is enough to control model behaviour. On the multi-hop city-state-capital task from (Lindsey et al., 2025), we find a circuit in which small sets of neurons encode specific latent reasoning steps (e.g. mapping a city to its state), and can be steered to change the model's output. This work thus advances automated interpretability of language models without imposing additional training costs.

Figures

Figures reproduced from arXiv: 2601.22594 by the authors.

Figure 1
Figure 1. Faithfulness and completeness for different choices of representation in the model (residual stream, attention, MLP activations, or MLP outputs) and basis (neurons or SAE) when applying Integrated Gradients, averaged over the 4 SVA tasks with paired data. evaluate the faithfulness and completeness of the circuits, av￾eraged over the evaluation set. We plot these values against k and identify methods that achieve the… view at source ↗
Figure 3
Figure 3. Faithfulness and completeness for different choices of representation and basis when applying Integrated Gradients, averaged over the 4 SVA tasks with unpaired data. and RelP for each circuit component, we use a zero baseline. Formally, this gives us: IGActv(x) = v(x) Z 1 α=0 ∂m(M, x; do v = αv(x))) ∂v(x) dα ≈ v(x) 1 n Xn i=1 ∂m(M, x; do v = i n v(x))) ∂v(x) (12) RelPv(x) = v(x) ∂ m(Mreplacement, x) ∂ v(x) (13) We k… view at source ↗
Figure 5
Figure 5. Faithfulness and completeness for edge-based circuit evaluation on the SVA benchmark. All methods use MLP activa￾tions as the neuron basis. Circuits are pruned by removing edges based on attribution scores, with neurons removed when all incom￾ing or outgoing edges are pruned. 5 · 105 potential edges per example. For each pair of neu￾rons in our filtered set, we compute edge weights using the attribution flows define… view at source ↗
Figures from the paper (10 more)
Figure 6
Figure 6. Figure 6: The ‘Texas’ circuit. not present in the main text since they only add additional evidence to the same claims we make here. Lindsey et al. (2025) use cross-layer transcoders (CLTs) to trace circuits for three of those tasks. We aim to show that we can find comparably in…
Figure 7
Figure 7. Figure 7: Effect of steering L23/N8079- on the capitals dataset. to check whether the resulting effect on the model’s out￾puts corresponds with the hypothesised role of each cluster (e.g. steering the “say a capital” cluster negatively should cause the model to not output capita…
Figure 8
Figure 8. Figure 8: SVA unpaired with zero-ablation. E. Paired SVA results with Gemma-2 models We apply the same evaluation framework described in the main text to the Gemma-2 model family to validate that MLP activations form strong bases for constructing sparse circuits across different…
Figure 9
Figure 9. Figure 9: Faithfulness and completeness for Gemma-2-2B. MLP activations provide significantly sparser circuits than MLP outputs and approach SAE-based performance across both SAE widths. 16k Width SAEs. The Gemma-2-9B model with 16k width SAEs shows consistent patterns with the …
Figure 10
Figure 10. Figure 10: Faithfulness and completeness for Gemma-2-9B with 16k width SAEs. MLP activations deliver significantly sparser circuits than MLP outputs and remain competitive with SAE-based approaches. E.3. Summary The results on Gemma-2 models validate our main findings: MLP activ…
Figure 11
Figure 11. Figure 11: Analysis of attribution patterns on each of the SVA subsets. MLP activation attributions have greater spread and more outliers. In Figure 11a, we plot the histogram of attribution scores Attr(v) for each node v ∈ V (recall that these scores are averaged over the train…
Figure 12
Figure 12. Figure 12: Attribution heatmaps of the top-AUROC neuron for mod-10 features. The axes are the addends in the addition prompt. 8Recall that an AUROC of 0.5 corresponds to random performance; AUROCs far from 0.5 mean the neuron gives signal about the feature of interest (where AUR…
Figure 13
Figure 13. Figure 13: Mod-n neuron search results. As a robustness check, we also look for mod-n features for values of n other than 10; this checks for false positive noise in our analysis; e.g. we don’t generally expect to find mod-3 neurons for base-10 addition. We repeat the procedure …
Figure 14
Figure 14. Figure 14: Attribution heatmaps of the top-AUROC neuron for tens digit features. The axes are the addends in the addition prompt. Finally, we look for tens-digit neurons. We find a substantial number of neurons with high AUROCs for each outcome, but their attribution matrices ar…
Figure 15
Figure 15. Figure 15: Multilingual antonyms task results. H.2.1. LANGUAGE The language-specific neurons are numerous and often have relevant descriptions, such as L31/N4787- which has the description “activation on Arabic grammatical forms and prefixes...within religious or formal Arabic c…

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