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arxiv: 2605.09438 · v1 · submitted 2026-05-10 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

fmxcoders: Factorized Masked Crosscoders for Cross-Layer Feature Discovery

Andreas D. Demou , Panagiotis Koromilas , James Oldfield , Yannis Panagakis , Mihalis A. Nicolaou
Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:49 UTC · model grok-4.3

classification 💻 cs.LG
keywords crosscoderssparse autoencoderscross-layer featurestransformer interpretabilityfactorized modelsfeature discoverymechanistic interpretabilityLLM evaluation
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The pith

Factorized masked crosscoders recover 3-13 times more cross-layer features than standard crosscoders in transformers.

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

Many features in pretrained transformers emerge or persist across multiple layers, yet standard crosscoders trained jointly on all layers mostly learn latents driven by only one or two layers. The paper shows this happens because the encoder and decoder weights can vary freely per layer and because nothing penalizes a latent for ignoring most layers. fmxcoders replace the weights with low-rank tensor factorizations that draw every latent's per-layer components from one shared cross-layer basis, then add stochastic layer masking during training so that a latent loses its signal if any single layer is removed. Across GPT-2 Small, Pythia-410M, Pythia-1.4B, and Gemma-2-2B, the resulting latents show 10-30 point gains in probing F1, 25-50% lower reconstruction error, roughly double the functional coherence, and 3-13 times more latents judged semantically coherent by an LLM.

Core claim

Standard crosscoders fail to recover cross-layer features because their per-layer weights are unconstrained and cross-layer dependence is unregularized, so most latents collapse to surface patterns in a single layer. fmxcoders address both problems by replacing the encoder and decoder with low-rank tensor factorizations whose per-layer slices come from a shared basis, and by training with stochastic layer masking that penalizes any latent whose activation collapses when one layer is masked. The resulting shared latents act as better concept detectors and yield large gains in probing accuracy, reconstruction quality, and semantic coherence across four different base models.

What carries the argument

Low-rank tensor factorization of the encoder and decoder weights that forces every latent to draw its per-layer contributions from one shared cross-layer basis, combined with stochastic layer masking that penalizes latents for depending on only one or two layers.

Load-bearing premise

The functional coherence metric and the LLM-as-a-judge scores truly reflect genuine cross-layer semantic meaning rather than simply rewarding the factorized architecture.

What would settle it

An ablation that removes either the tensor factorization or the layer masking and finds that functional coherence and probing F1 gains disappear, or a human annotation study in which the new latents do not receive higher semantic coherence ratings than those from standard crosscoders.

Figures

Figures reproduced from arXiv: 2605.09438 by Andreas D. Demou, James Oldfield, Mihalis A. Nicolaou, Panagiotis Koromilas, Yannis Panagakis.

Figure 1
Figure 1. Figure 1: Standard crosscoders (top) parameterize the encoder and decoder as L independent per￾layer matrices and recover latents whose functional dependence collapses onto a few layers, capturing surface-level patterns. fmxcoders (bottom) replace these with low-rank tensor factorizations that share a cross-layer basis across all latents, and add stochastic layer masking as a denoising regularizer along the layer ax… view at source ↗
Figure 2
Figure 2. Figure 2: Norm coherence c n (blue) and functional coherence c f (green) latent distributions for crosscoders (top row) and fmxcoder (bottom row) variants trained on Pythia-410M. The average value and standard deviation of each coherence distribution are also shown in red color. 4.3 Qualitative and LLM-Judge Analysis of Features [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Heat maps for MSE, mean F1 and mean functional coherence [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Similar to Figure 3, for CP [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
read the original abstract

Many features in pretrained Transformers span multiple layers: they emerge through stages of inference, persist in the residual stream, or are built jointly by parallel MLPs. Crosscoders (namely, sparse dictionaries trained jointly across layers) aim to recover these cross-layer features in a single shared latent space. We show that standard crosscoders largely fail at this purpose. Although their decoder weight norms spread evenly across layers, a functional coherence metric we introduce reveals that each latent's activation is effectively driven by only one or two layers on average. While functionally coherent latents act as human-interpretable concept detectors (e.g., US states and cities), the layer-localized latents that crosscoders predominantly learn collapse onto surface-level patterns such as digit detectors. We trace this failure to two structural limitations: unconstrained cross-layer parameterization and unregularized cross-layer dependence. We address both by introducing fmxcoders, which (i) replace the encoder and decoder with low-rank tensor factorizations that draw every latent's per-layer weights from a shared cross-layer basis, and (ii) apply stochastic layer masking, a denoising regularizer along the layer axis that penalizes latents whose contribution collapses when a single layer is masked. Across GPT2-Small, Pythia-410M, Pythia-1.4B, and Gemma2-2B, fmxcoders lift mean probing F1 by 10-30 points, surpassing per-layer SAE baselines that standard crosscoders fail to reach, reduce reconstruction MSE by 25-50%, and roughly double mean functional coherence. An LLM-as-a-judge evaluation further shows that fmxcoders recover 3-13$\times$ more semantically coherent latents than standard crosscoders across all four base LLMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The paper claims that standard crosscoders for sparse dictionary learning across transformer layers largely fail to recover truly cross-layer features, as their latents are predominantly driven by only one or two layers despite even decoder weight norms; it introduces fmxcoders using low-rank tensor factorizations for shared cross-layer bases in encoder and decoder plus stochastic layer masking as a regularizer, and reports that this yields 10-30 point gains in mean probing F1 (surpassing per-layer SAE baselines), 25-50% lower reconstruction MSE, roughly doubled mean functional coherence, and 3-13× more semantically coherent latents (via LLM-as-a-judge) across GPT2-Small, Pythia-410M, Pythia-1.4B, and Gemma2-2B.

Significance. If the newly introduced functional coherence metric and LLM judge evaluations prove to be architecture-agnostic measures of genuine cross-layer semantics, the work would meaningfully advance mechanistic interpretability by providing a practical method to extract features that emerge or persist across layers rather than collapsing to surface patterns. The multi-model scale of the evaluation and direct comparison against both standard crosscoders and per-layer SAEs are clear strengths; the introduction of a denoising regularizer along the layer dimension is a technically clean idea.

major comments (3)
  1. [Abstract and §3] Abstract and §3 (functional coherence metric definition): The metric is defined to penalize latents whose activations are driven by few layers on average. Because fmxcoders explicitly optimize against single-layer collapse via stochastic masking, reported doublings of mean functional coherence risk being partly tautological rather than evidence of superior feature discovery; an ablation isolating the masking term from the factorization (or an external validation set of known cross-layer concepts) is needed to establish that the metric adds independent information.
  2. [Abstract and §4] Abstract and §4 (LLM-as-a-judge evaluation): The claim of recovering 3-13× more semantically coherent latents rests on an LLM judge whose prompts and scoring rubric are not shown to be invariant to the structural differences (low-rank shared bases) introduced by fmxcoders. If the judge implicitly rewards more factorized or less surface-level activations, the multiplier cannot be attributed cleanly to better cross-layer discovery; a blinded human evaluation on a held-out subset or comparison against an architecture-agnostic coherence probe would strengthen the result.
  3. [§5] §5 (experimental results): The reported probing F1 and MSE gains are presented without error bars, standard deviations across random seeds, or statistical significance tests. Given that the central empirical claim is consistent improvement across four models and multiple metrics, the absence of variability estimates makes it difficult to assess whether the 10-30 point F1 lift and 25-50% MSE reduction are robust or sensitive to hyperparameter choices such as factorization rank.
minor comments (3)
  1. [Methods] The paper should report the chosen factorization rank for each model and any sensitivity analysis, as this is listed among the free parameters and directly affects the low-rank assumption.
  2. [Figures] Figure captions and axis labels in the results section would benefit from explicit mention of the number of latents and the exact masking probability used, to aid reproducibility.
  3. [§5] A brief discussion of how the per-layer SAE baselines were trained (same sparsity, same dictionary size) would clarify that the comparison is fair.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful and constructive feedback on our manuscript. We have carefully reviewed each major comment and provide detailed point-by-point responses below. We outline the specific revisions we will make to address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (functional coherence metric definition): The metric is defined to penalize latents whose activations are driven by few layers on average. Because fmxcoders explicitly optimize against single-layer collapse via stochastic masking, reported doublings of mean functional coherence risk being partly tautological rather than evidence of superior feature discovery; an ablation isolating the masking term from the factorization (or an external validation set of known cross-layer concepts) is needed to establish that the metric adds independent information.

    Authors: We acknowledge the close relationship between the stochastic layer masking regularizer and the functional coherence metric, as the former is explicitly designed to discourage single-layer collapse. However, the metric itself is an independent, post-hoc measure of the average number of layers that meaningfully contribute to each latent's activations, and it is not part of the training loss. To demonstrate that the reported gains reflect genuine improvements in cross-layer feature discovery rather than a tautology, we will add an ablation study in the revised manuscript. This ablation will train factorized models both with and without the masking term and report the resulting differences in functional coherence, probing F1, MSE, and the number of coherent latents. We will also include concrete examples of known cross-layer concepts (e.g., entity tracking and syntactic features) recovered by fmxcoders to provide external validation of the metric. revision: yes

  2. Referee: [Abstract and §4] Abstract and §4 (LLM-as-a-judge evaluation): The claim of recovering 3-13× more semantically coherent latents rests on an LLM judge whose prompts and scoring rubric are not shown to be invariant to the structural differences (low-rank shared bases) introduced by fmxcoders. If the judge implicitly rewards more factorized or less surface-level activations, the multiplier cannot be attributed cleanly to better cross-layer discovery; a blinded human evaluation on a held-out subset or comparison against an architecture-agnostic coherence probe would strengthen the result.

    Authors: We agree that transparency and validation of the LLM-as-a-judge protocol are essential to rule out bias from the low-rank factorization. In the revised manuscript, we will include the complete prompts and scoring rubric in the appendix. To further strengthen the claim, we will add a blinded human evaluation on a held-out subset of 100 latents per model, where human evaluators (unaware of the source method) rate semantic coherence based on top activating examples and tokens. We will report inter-rater agreement and correlation with the LLM scores. While a full-scale human study across all models and latents is not feasible, this targeted evaluation will provide independent corroboration that the 3-13× increase corresponds to improved cross-layer semantic coherence. revision: partial

  3. Referee: [§5] §5 (experimental results): The reported probing F1 and MSE gains are presented without error bars, standard deviations across random seeds, or statistical significance tests. Given that the central empirical claim is consistent improvement across four models and multiple metrics, the absence of variability estimates makes it difficult to assess whether the 10-30 point F1 lift and 25-50% MSE reduction are robust or sensitive to hyperparameter choices such as factorization rank.

    Authors: We thank the referee for highlighting this important presentation issue. In the revised §5, we will report all key metrics (probing F1, MSE, functional coherence) with error bars indicating standard deviation across at least three independent random seeds per configuration. We will also include statistical significance tests (paired t-tests with p-values) for the primary comparisons against standard crosscoders and per-layer SAEs. Additionally, we will add a sensitivity analysis varying the factorization rank and reporting its effect on performance to address robustness to hyperparameter choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity in fmxcoders empirical claims

full rationale

The paper introduces a new architecture (low-rank factorized encoder/decoder plus stochastic layer masking) and a new functional coherence metric to diagnose standard crosscoders. Reported gains in probing F1 (10-30 points) and reconstruction MSE (25-50%) are measured on independent tasks across multiple models and are not reducible to quantities defined inside the training objective or metric by construction. The coherence improvement is expected from the explicit regularizer but does not render the other metrics tautological. No self-citations, uniqueness theorems, ansatzes smuggled via prior work, or renamings of known results appear as load-bearing steps. This is the normal non-circular outcome for an empirical architecture paper.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach rests on standard assumptions from sparse dictionary learning plus two new architectural choices; no new physical entities are postulated.

free parameters (2)
  • factorization rank
    The shared basis dimension in the low-rank tensor factorization is a hyperparameter that must be chosen.
  • masking probability
    The probability used for stochastic layer masking is a design choice that affects regularization strength.
axioms (1)
  • domain assumption Features in pretrained transformers can be usefully represented as sparse activations of dictionary elements that are consistent across layers.
    This is the core premise that justifies training any crosscoder.

pith-pipeline@v0.9.0 · 5647 in / 1325 out tokens · 59962 ms · 2026-05-12T04:49:41.685858+00:00 · methodology

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Reference graph

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