Model Diffing via Crosscoders

• Model diffing via crosscoders is a methodology that systematically identifies, quantifies, and interprets differences between complex computational models using sparse, interpretable feature representations.
• It employs crosscoders that align and decompose latent feature spaces across neural checkpoints, architectures, and programming languages for precise model auditing.
• The approach enhances model explainability and safety in applications like language model pretraining and software product lines by providing actionable, quantitative metrics.

Model diffing via crosscoders is a methodology that addresses the challenge of systematically identifying, quantifying, and interpreting the differences between complex computational models, particularly in the context of neural networks, software product lines, and LLMs. Crosscoders—techniques grounded in sparse autoencoder and dictionary learning frameworks—enable the alignment, decomposition, and comparison of model representations across different checkpoints, architectures, modalities, or even programming languages. The approach has proved critical for mechanistically dissecting how features, concepts, and capabilities emerge, shift, or vanish during processes such as pre-training, fine-tuning, or cross-language adaptation.

1. Conceptual Foundations and Need for Model Diffing

Model diffing is an essential capability in several domains where multiple versions or variants of the same artifact must coexist or be audited for changes. In software product lines, this arises due to the need to customize models for different geographic, legal, or product contexts, with different teams concurrently editing or extending large-scale models (Kuhn et al., 2012). Traditional text-based diff tools are inadequate for models with complex, spatial or multidimensional structures, as they lack a clear linear reading order and can lead to incomplete or missed change detection. Engineers have thus resorted to workarounds—annotating models with unique identifiers, diffing auto-generated code, or visually highlighting changes in documentation—underscoring the need for scalable and accurate diffing approaches tuned for model artifacts.

Crosscoders fulfill this need by learning structured, often sparse, representations (“dictionaries”) that can translate, align, or compare activations and features across models. Conceptually, if two model versions $M_1$ and $M_2$ are to be compared, a crosscoder aims to represent the differences as:

$$\text{diff}(M_1, M_2) = \{\Delta_i \mid \Delta_i \text{ denotes a change between } M_1 \text{ and } M_2\}$$

with each $\Delta_i$ ideally corresponding to an interpretable or causally meaningful feature difference.

2. Crosscoder Architectures and Methodologies

At the technical core, crosscoders extend sparse autoencoders by training a shared dictionary (or latent feature space) with source-specific encoder/decoder weights for each model variant or checkpoint:

• For two models $A$ and $B$, the encoder map $E^A$, $E^B$ and the decoder map $D^A$, $D^B$ transform activations into and out of a joint feature space. Each latent direction in the dictionary can be traced for its relative prominence (“decoder norm”) in each model.
• Crosscoders are trained by minimizing reconstruction loss plus sparsity penalties, with dictionary vectors aligning feature sets to enable direct, quantitative diffing.

Advanced variants address artifacts arising from simplistic $L_1$ loss penalties, such as “complete shrinkage” and “latent decoupling,” which can spuriously mark features as unique to only one model. Solutions include:

• Latent Scaling, in which least-squares scaling factors provide more accurate quantification of each latent’s true presence across models (Minder et al., 3 Apr 2025).
• BatchTopK training, which enforces competitive sparsity and reduces redundancy in latent allocation.

Architecture extensions incorporate group structure (group crosscoders), enabling analysis across symmetry transformations and equivariant feature spaces (Gorton, 31 Oct 2024); or adapt to time-evolving checkpoints to align features throughout pretraining (Bayazit et al., 5 Sep 2025, Ge et al., 21 Sep 2025).

3. Application Domains: Model Diffing in Practice

Crosscoders and their analogs have been deployed in a range of settings:

• Software Model-Driven Development: Translating visual, spatial models into linear, diffable representations allows for robust versioning, auditing, and regression validation (Kuhn et al., 2012).
• Deep Neural Network Comparative Analysis: Behavioral probing approaches such as ModelDiff use decision distance vectors (DDVs) and cosine similarity to assess degree of knowledge reuse, enabling black-box similarity detection even in the absence of shared architectures (Li et al., 2021).
• Cross-Language and Cross-Framework Analyses: Transcompiler-based methods harmonize code across programming languages, while embedding- or intermediate-representation-based approaches (e.g., XLIR) enable robust clone and model diffing across modalities (Pinku et al., 2023, Gui et al., 2022).
• LLM Pretraining and Fine-Tuning: Sparse crosscoders quantify emergence, maintenance, and decline of linguistic or conceptual features across pretraining steps; metrics such as Relative Indirect Effect (RelIE) track causal impact on downstream performance (Bayazit et al., 5 Sep 2025, Ge et al., 21 Sep 2025). Fine-tuning analysis isolates directions (“persona features”) whose changes correspond to emergent misalignment, instruction following, or safety mechanisms (Minder et al., 3 Apr 2025, Wang et al., 24 Jun 2025, Boughorbel et al., 23 Sep 2025).

4. Technical Metrics and Evaluation

Crosscoders output interpretable statistics for model diffing:

• Decoder Norm Difference: For latent $j$ with decoder weights $d_j^\mathrm{base}$ and $d_j^\mathrm{chat}$ (for base and fine-tuned models):

$$\text{norm}(j) = \frac{1}{2}\left(\frac{||d_j^\mathrm{chat}||_2 - ||d_j^\mathrm{base}||_2}{\max(||d_j^\mathrm{chat}||_2, ||d_j^\mathrm{base}||_2)} + 1\right)$$

This metric partitions latents into model-specific or shared.

• Latent Scaling Ratios ($\nu^r$, $\nu^\epsilon$): Quantify how much of a latent’s causal or reconstructive energy is captured in each model (Minder et al., 3 Apr 2025).
• Relative Indirect Effect (RelIE): Given an attribution score $\mathrm{IE}_i^{(c)}$ for a feature $i$ in checkpoint $c$, the two-way RelIE is:

$$\mathrm{RelIE}_i = \frac{|\mathrm{IE}_i^{(c_2)}|}{|\mathrm{IE}_i^{(c_1)}| + |\mathrm{IE}_i^{(c_2)}|}$$

Higher values indicate later checkpoint reliance (Bayazit et al., 5 Sep 2025).

• Performance Metrics: Standard domain metrics such as F1 score for code clone detection, precision and recall for JIT defect prediction (Nam et al., 11 Sep 2025), and statistical comparisons (e.g., two-way ANOVA, paired t-tests) to assess effect sizes and robustness.

5. Representative Findings and Case Studies

Model diffing via crosscoders yields insights unattainable by traditional evaluation:

• In LLMs, fine-tuning can sharply increase the prevalence of latent concepts related to safety, instruction following, or template adherence, while diminishing capacities related to self-reference or hallucination detection. For example, SimPO-enhanced Gemma-2-9b-it exhibited a +151.7% increase in instruction-following features but a –68.5% decrease in hallucination management (Boughorbel et al., 23 Sep 2025).
• During pretraining, linguistically meaningful features emerge in abrupt or gradual transitions corresponding to distinct training phases—statistical learning and feature learning. Emergent features persist, rotate, or vanish, with direct causal linkage to downstream task performance (Ge et al., 21 Sep 2025, Bayazit et al., 5 Sep 2025).
• In cross-language code analysis, methods that align isomorphic representations (e.g., cycle-consistent, contrastive learning objectives) greatly improve zero-shot clone detection and suggest that cross-LLM diffing should emphasize functional alignment over syntactic matching (Li et al., 2023).
• In software engineering, diff-style encoding formats amplify the effectiveness of model diffing, while model robustness to counterfactual tests often reveals reliance on superficial cues rather than true semantic understanding, highlighting a current limitation of defect prediction PLMs (Nam et al., 11 Sep 2025).

6. Challenges, Limitations, and Future Directions

Despite their utility, model diffing via crosscoders faces several limitations:

• Interpretability: While joint sparse dictionaries expose feature alignments, early snapshot features may be less interpretable, and automated interpretation remains an open problem (Bayazit et al., 5 Sep 2025).
• Computational Demand: Training crosscoders across many checkpoints or modalities is resource-intensive, though joint training is more efficient than per-snapshot autoencoders (Bayazit et al., 5 Sep 2025).
• Spurious Artifacts: Loss function design (e.g., $L_1$ sparsity) can induce artifacts such as falsely chat-only latents. Techniques like BatchTopK and latent scaling are recommended to mitigate these effects (Minder et al., 3 Apr 2025).
• Benchmark Sensitivity: Analysis is sensitive to the choice of models, checkpoints, and input distributions. Comparing models with different input shapes, modalities, or label sets still presents open challenges (Li et al., 2021).
• Semantic Diffing: Particularly in software and code, current approaches tend to rely on surface cues rather than true edit semantics, suggesting a need for models that integrate more semantic or structural knowledge (Nam et al., 11 Sep 2025).

Research continues into scaling crosscoders to richer forms of circuit analysis, extending symmetry-based group crosscoding beyond spatial domains, and integrating crosscoder-based diffing into automated toolchains for model auditing, training supervision, and explainability in AI safety contexts (Gorton, 31 Oct 2024, Wang et al., 24 Jun 2025).

7. Impact and Significance

Model diffing via crosscoders has shifted the paradigm of model comparison from surface-level benchmarking to latent, mechanistic examination. The methodology identifies the formation, consolidation, and regression of interpretable features governing critical behaviors, enabling fine-grained attribution of performance and safety differences. This capability is transforming model auditing, reproducibility, cross-system integration, and safety alignment in both machine learning and software engineering, offering a principled, interpretable, and scalable framework for comparing complex computational systems across time, domains, and architectures.