Behavior manifold analysis is introduced, which isolates behavior-specific geometry by selecting sparse behavior-associated coordinates and lifting them into low-dimensional local charts, and provides a unified framework for understanding the mechanistic distinction between the two objectives.
Abstract
Post-training can substantially alter language-model behavior, yet aggregate behavior rates do not reveal whether training removes an existing mechanism, creates a new one, or changes how an inherited mechanism is used. We study this question through two mechanistically distinct failures, repetition as a decoding-attractor pathology and sycophancy as a preference-related alignment failure. We introduce behavioral manifold analysis, which isolates behavior-specific geometry by selecting sparse behavior-associated coordinates and lifting them into low-dimensional local charts. We construct these charts in two complementary spaces. ACT captures runtime activation states, while NOC quantifies how strongly the model routes functional information flow through the shared behavior-associated subspace. Across multiple model families, the resulting charts are highly compressed and partially alignable across architectures. Contribution-space charts expose a more architecture-robust shared core, whereas activation-space charts retain stronger family-specific structure. Tracking these charts through controlled post-training reveals a consistent asymmetry. Supervised fine-tuning substantially alters the inherited behavioral geometry, whereas reward optimization changes behavior while largely preserving the underlying chart. This geometric perspective provides a unified framework for understanding the mechanistic distinction between the two objectives. SFT tends to rewrite behavioral geometry, whereas reward optimization primarily reweights it. Code is available at https://github.com/ronglingze/Manifold-Analysis
An architecture-agnostic sufficient condition is established linking behavioral similarity to inference-prompt coverage, small excess population log-loss, and similar effective target distributions---a possible training-side account rather than an empirical explanation of the observed trends.
Activation-based steering methods for large language models often induce broad, entangled changes in model behavior, inadvertently altering capabilities unrelated to the intended behavior, which limits their reliability for fine-grained behavioral control. We address this limitation by reframing behavioral intervention through a geometric information bottleneck (IB) perspective, in which effective steering corresponds to selectively modifying task-relevant information while preserving the geometric structure of orthogonal representational subspaces. Building on this view, we propose a disentanglement-based intervention framework, termed IB-ACT, that identifies both where and how to intervene by exploiting the layer-wise geometry of representation spaces to isolate behavior-relevant information without disturbing other dimensions. Our method introduces a layer-selection mechanism determined prior to intervention, rather than relying on post hoc sparsity or regularization losses, and applies geometrically constrained transformations that target behavior-relevant subspaces in activation space while preserving orthogonal structure. We provide theoretical justification showing that interventions at these layers reduce unintended information leakage under an IB-style objective. Empirically, we evaluate IB-ACT on toxicity control and hallucination reduction in large language models and demonstrate consistent improvements over recent baselines, while analyzing the spectral structure of behavior-relevant representations for jailbreak mitigation. Overall, our findings suggest that selectively intervening at structurally appropriate layers is critical for controllable and disentangled behavioral steering in large language models.
Toan Doan, Thin Nguyen, Sunil Gupta· Proceedings of the 32nd ACM...· 0 citations
Shani et al. (2026) show that LLM representations broadly recover human category boundaries, while failing to reflect fine-grained typicality structure. Their analysis uses cosine similarity over dense model representations. We revisit their approach using overlap over active sparse autoencoder (SAE) latent sets as a more interpretable similarity measure. We first verify that this set-level measure is meaningful: SAE latent sets can recover union-like compositional structure in controlled toy models and induce semantically coherent neighborhoods in natural text. Extending the human-concepts analysis to SAE set similarities, we find that SAE activation sets do not recover human category boundaries or within-category typicality more faithfully than dense embeddings or residual-stream states, but instead track model-internal similarity structure. To probe this gap further, we study active latent sets under well-controlled semantic modifications, revealing a substantial mismatch between human judgements of conceptual change and change in the SAE active set. We interpret this as evidence that, outside idealised settings, SAE features do not compose via simple bag-of-features semantics.
Nikolai Bolik, Lennart Stöpler, Artur Andrzejak· 0 citations
We uncover ELR collapse in language model pretraining: learning rate (LR) and parameter norm govern loss dynamics primarily through their ratio, the effective learning rate (ELR). When ELR is matched across runs, their loss trajectories collapse throughout training despite substantially different LRs and parameter norms. Across optimizers, architectures, datasets, and model scales, mean collapse errors are typically a few x 10^-3, below the seed-to-seed variation measured in a representative configuration. Systematic ablations identify normalization design and the timescale of LR-norm variation as key determinants of collapse precision. Controlled interventions further show that weight decay and Hyperball shape loss dynamics primarily through the ELR schedules they induce. Replacing LR with ELR enables a fitted functional scaling law (FSL) to transfer across norm-control methods. The resulting ELR-based FSL also explains delayed acceleration, a recurring effect of norm control. Together, these results establish ELR as a common coordinate linking LR scheduling, norm control, and loss dynamics.
Zihan Liu, Ruiheng Zheng, Shaobo Zhang et al.· 1 citation
Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge. Here, we show that concept geometry can be precisely characterized via Laguerre Geometry, in which a concept is defined as a region--a Laguerre-Voronoi cell or a union of cells--allowing us to strictly define, measure, and separate concepts. Building on this formulation, we show that finer-grained concept structures, such as inclusion and hierarchy, are naturally revealed by the Laguerre weights. We then push this geometry inside the transformer. Decomposing each layer into piecewise-linear operators, we show that a token's hidden trajectory is governed by two coupled mechanisms: a static tree of self-contained piecewise-linear flow, and a dynamic transport that hops the trajectory across trees when cross-token attention fires. This decomposition yields Geometric Lens, a training-free, hyperparameter-free method for reading out the exact concept a hidden vector encodes at any layer. We also develop Laguerre Autoencoder, a 2D visualizer that renders both the decision geometry and a model's full reasoning trajectory in one view. Finally, we move beyond explanatory geometry toward actionable interpretability, showing that Geometric Lens recovers the correct factual token when a model is prompted with in-context interference. The code is available on GitHub.
Joint-Embedding Predictive Architectures (JEPAs) are effective for images, video, and audio, yet deterministic JEPA-style latent prediction has not become a standard objective for text encoders. We argue that this gap reflects a mismatch between squared-error latent prediction and the conditional structure of language. The key requirement is conditional concentration: given a context and target location, the target representation should lie near a single meaningful point. Local image prediction often satisfies this through spatial continuity, whereas masked text can admit multiple valid token or span completions whose representations need not share a coherent center. We formalize this mismatch through three conditions---predictability, non-collapse, and low conditional variance---and show how their failure creates centroid degeneracy and collapse pressure in text. Matched I-JEPA and T-JEPA experiments reveal the predicted sequence: mutual-information saturation and elevated target variance precede train--validation instability, effective-rank degeneration, cosine collapse, and poor downstream transfer. The same pattern appears across five independent data seeds, indicating that it is not a sampling artifact. These results do not rule out predictive learning for language; they show that text-compatible JEPA objectives must preserve multiple plausible completions rather than compress them into a single latent point.