fmxcoders: Factorized Masked Crosscoders for Cross-Layer Feature Discovery
Authors: Andreas D. Demou, Panagiotis Koromilas, James Oldfield, Yannis Panagakis, Mihalis A. Nicolaou
Organizations: 1The Cyprus Institute · University of Athens · 4Archimedes AI/Athena Research Center · University of Oxford · University of Cyprus
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× more semantically coherent latents than standard crosscoders across all four base LLMs.
Dictionary learning methods like Sparse Autoencoders (SAEs) and crosscoders attempt to explain a model by decomposing its activations into independent features. Interactions between features hence induce errors in the reconstruction. We formalize this intuition via compact proofs and make five contributions. First, we show how, \textit{in principle}, a compact proof of model performance can be constructed using a crosscoder. Second, we show that an error term arising in this proof can naturally be interpreted as a measure of interaction between crosscoder features and provide an explicit expression for the interaction term in the Multi-Layer Perceptron (MLP) layers. We then provide three applications of this new interaction measure. In our third contribution we show that the interaction term itself can be used as a differentiable loss penalty. Applying this penalty, we can achieve ``computationally sparse'' crosscoders that retain 60% of MLP performance when only keeping a single feature at each datapoint and neuron, compared to 10% in standard crosscoders. We then show that clustering according to our interaction measure provides semantically meaningful feature clusters, and finally that sleeper agents have significant interactions. Code is available at https://github.com/chainik1125/crosscoders-feature-interactions/tree/arxiv.
Recent methods in language model interpretability employ techniques such as sparse autoencoders to decompose residual stream contributions into linear, semantically meaningful features. Such methods are commonly interpreted as identifying features that persist in the residual stream and that subsequent layers build upon. We challenge this view by identifying the Transformer Layer Correction Mechanism (TLCM), wherein adjacent transformer layers systematically counteract portions of each other's contributions. TLCM appears in 5 out of 7 major open-source model families and activates across nearly all tokens in diverse texts. We show that TLCM emerges during pretraining, operates most strongly on contextually dependent tokens, and adaptively calibrates its correction strength based on the preceding layer's output. Using the layer Jacobian, we further show that TLCM selectively corrects specific subspaces while reinforcing others, which we interpret through a ``propose-and-reject'' framework in which layers propose candidate features and subsequent layers selectively remove inappropriate ones. This dynamic suggests that the residual stream at any layer contains transient proposals alongside persistent features, helping explain why SAE feature descriptions often have low specificity, why effective model steering requires extreme feature amplification, and why transcoders hold a theoretical advantage over SAEs.
We give a novel logical characterization of encoder-decoder transformers, the foundational architecture for LLMs that also sees use in various settings that benefit from cross-attention. We study such transformers over text in the practical setting of floating-point numbers and soft-attention, characterizing them with a new temporal logic. This logic extends propositional logic with a counting global modality over the encoder input and a past modality over the decoder input. We also give an additional characterization of such transformers via a type of distributed automata, and show that our results are not limited to the specific choices in the architecture and can account for changes in, e.g., masking. Finally, we discuss encoder-decoder transformers in the autoregressive setting.