Crosscoders: Sparse Dictionary Architectures

• Crosscoders are sparse dictionary learning architectures that discover and track interpretable latent feature evolution across models, checkpoints, and tasks.
• They use paired encoder/decoder mechanisms and shared dictionaries to align features, enabling causal attribution of concept emergence and transformation.
• Extensions include symmetry detection, fine-tuning diffing, and activation steering, which enhance model control, safety auditing, and interpretability.

Crosscoders are sparse dictionary learning architectures designed to discover, track, and interpret latent feature evolution across models, checkpoints, and tasks. In their most common instantiations, crosscoders learn a unified sparse, interpretable feature space aligned across different models, training snapshots, or input transformations, via paired encoder/decoder weights. Their primary utility is in mechanistic model analysis: by aligning semantically meaningful features and quantifying feature shifts, crosscoders enable causal attribution of concept emergence, transformation, or discontinuation. Recent works extend crosscoders to continuous pretraining analysis, fine-tuning behavioral diffing, symmetry discovery in neural networks, and sparse activation steering for model control.

1. Architecture and Principles

Crosscoders generalize sparse autoencoders (SAEs) by leveraging a shared dictionary of latent concept vectors, with snapshot‐ or model‐specific encoders and decoders (Bayazit et al., 5 Sep 2025, Ge et al., 21 Sep 2025). For a set of activations $a^\theta(x)$ from models indexed by $\theta$, the crosscoder encoder $\mathrm{Enc}_\theta$ maps activations onto a sparse feature vector $f(x)$ via

$$f(x) = \sigma\left( \sum_{\theta\in\Theta} W^{\theta}_{enc}\cdot a^\theta(x) + b_{enc} \right)$$

with $\sigma(\cdot)$ denoting a sparsity-promoting nonlinearity, typically JumpReLU. Reconstructions for each model/checkpoint use decoder weights $W^{\theta}_{dec}$:

$$\hat{a}^\theta(x) = W^{\theta}_{dec}\cdot f(x) + b^{\theta}_{dec}$$

The loss jointly optimizes the reconstruction error across all checkpoints, plus a sparsity term:

$$L = \sum_{c \in C} \| a^c(x) - \hat{a}^c(x)\|^2_2 + \lambda\sum_{c \in C}\sum_i f_i(x)\|W_{dec,i}\|_2$$

This framework allows interpretable, cross-snapshot alignment of feature directions. Advanced variants include BatchTopK selection for enforcing a competitive representation and avoiding shrinkage/decoupling artifacts (Minder et al., 3 Apr 2025), and segmented steering for activation-level control (Chang et al., 28 May 2025).

2. Tracking Concept Emergence During Pretraining

Crosscoders have recently been used to analyze the temporal emergence and consolidation of linguistic features in LLMs at concept granularity (Bayazit et al., 5 Sep 2025, Ge et al., 21 Sep 2025). By training on triplets or sets of checkpoints, one can trace when morphological, syntactic, or semantic features arise, persist, or disappear. Feature emergence is detected by changes in decoder norms $\|W_{dec,i}^\theta\|$ for feature $i$ at checkpoint $\theta$; features typically begin to form at a "phase transition" around step 1000 for major Transformers.

Feature-level attribution—using metrics such as indirect effect (IE):

$$\mathrm{IE}(m;\mathbf{a};x) = m(x|\operatorname{do}(\mathbf{a}=\mathbf{a}_{patch})) - m(x)$$

and relative indirect effect (RelIE):

$$\mathrm{RelIE}_{2\!-\!way,i} = \frac{|\mathrm{IE}_i^{(c_2)}|}{|\mathrm{IE}_i^{(c_1)}| + |\mathrm{IE}_i^{(c_2)}|}$$

is used to establish causal links between features and downstream behavior, e.g., grammatical agreement or error handling. Crosscoders can further distinguish features formed by pretraining statistics ("statistical learning phase") versus those emerging in later "feature learning phase" (Ge et al., 21 Sep 2025).

3. Model Diffing and Fine-Tuning Interpretability

Crosscoders are foundational to model diffing: uncovering mechanistic changes during LLM fine-tuning (e.g., chat tuning or safety enhancement) by tracking latent concept shifts between model variants (Boughorbel et al., 23 Sep 2025, Minder et al., 3 Apr 2025). The key procedure is:

1. Train a crosscoder on activations from both models (base and fine-tuned).
2. For each latent, compute decoder strength differences:

$$\Delta_{norm}(j) = \frac{1}{2} \left( \frac{\|d_j^{(M_2)}\|_2 - \|d_j^{(M_1)}\|_2}{\max(\|d_j^{(M_2)}\|_2, \|d_j^{(M_1)}\|_2)} + 1 \right)$$

1. Use BatchTopK loss to prevent artifacts; apply latent scaling (ratios $\nu^\epsilon$ and $\nu^r$) to filter shrinkage/decoupling.
2. Annotate differential latents to capability categories.

Research shows that enhanced latent classes (safety, multilinguality, instruction-following) correspond to concrete performance jumps after targeted fine-tuning (Boughorbel et al., 23 Sep 2025), while reductions in self-referential and hallucination-management latents mark trade-offs.

4. Extensions: Symmetry, Segmented Control, Activation Steering

Group crosscoders introduce transforms under finite symmetry groups $G$, learning feature families that are equivariant or invariant to rotations, reflections, or other group operations (Gorton, 31 Oct 2024). The encoder works on untransformed activations, while the decoder reconstructs the whole orbit of activations $[a^l(gI): g\in G]$, identifying mechanistic patterns. Cosine similarity between dictionary blocks for group actions reveals geometric invariances inherent in learned features.

Sparse crosscoders are also used in activation steering (Fusion Steering), providing a framework for interpretable, dynamic modulations of sparse neuron features per prompt (Chang et al., 28 May 2025). Segmented steering is accomplished by tuning fusion weights $\alpha$ and injection strengths $\gamma$ separately for each layer group, targeting high-level corrections in output factuality and style. Optuna-based hyperparameter selection optimizes token overlap and perplexity, providing prompt-specific control in scalable, interpretable architectures.

5. Practical Use Cases and Implications

• Representation Learning Analysis: Crosscoders allow fine-grained, snapshot-by-snapshot inspection of concept evolution, critical for debugging and understanding pretraining phases in LLMs (Bayazit et al., 5 Sep 2025, Ge et al., 21 Sep 2025).
• Model Behavior Attribution: By tracking feature causality and direction, crosscoders attribute macroscopic metric changes to microscopic concept shifts, including emergence of new functionalities or trade-offs due to fine-tuning (Boughorbel et al., 23 Sep 2025, Minder et al., 3 Apr 2025).
• Safety and Ethics Auditing: Detection of refusal, content moderation, and hallucination management features aids in operationalizing the safety and compliance of AI systems.
• Symmetry and Mechanistic Interpretability: Automatic discovery and clustering of symmetry-related features in vision networks (e.g., InceptionV1 mixed3b layer) clarifies geometric equivariances in neural representations (Gorton, 31 Oct 2024).
• Activation Steering: Sparse crosscoders serve as natural substrates for interpretability-driven activation-level interventions, offering modular, scalable prompt-specific tuning (Chang et al., 28 May 2025).

6. Limitations, Artifacts, and Best Practices

Training crosscoders with naive L1 sparsity loss can induce artifacts such as complete shrinkage (falsely identifying latents as model-specific) and latent decoupling (splitting single concepts across multiple latents). BatchTopK loss mitigates these effects by enforcing competitive selection, and latent scaling provides diagnostic ratios for more accurate attribution (Minder et al., 3 Apr 2025). For model diffing, it is advised to combine these practices with causal intervention and norm-based metrics (while calibrating effective $L_0$ sparsity).

Latent interpretation is best grounded by high-activation example annotation and clustering, establishing mappings between latent feature shifts and concrete capabilities (e.g., safety, multilinguality, format control). Continuous tracking and benchmark validation across architectures enhances reliability of insights into pretraining and fine-tuning effects.

7. Future Research Directions

Crosscoders are being extended along multiple axes:

• Deeper circuit tracing and subnetwork alignment across pretraining/fine-tuning stages.
• Continuous feature tracking for real-time model debugging and dynamic concept emergence analysis.
• Integration with segmented Fusion Steering and sparse Neuronpedia architectures for targeted, interpretable in-context control.
• Refinements for explainable, robust cross-domain deployment, safety auditing, and causal editing of LLMs.

Further generalization to other modalities, richer symmetry groups, and multi-agent or multi-task setups is ongoing. Their architecture-agnostic design, scalability, and capability for causal mechanistic attribution make crosscoders increasingly essential for principled interpretability in modern AI systems.