Representation Drift

Mixed-precision post-training quantization needs a per-module sensitivity signal; for a text embedder the obvious one -- the retrieval quality a module costs when quantized -- needs relevance labels that deployments rarely have. We measure a label-free substitute: quantization-induced representation drift, obtained by quantizing one module, re-encoding the corpus, and recording how far the output embeddings moved from their full-precision positions. What is specific is the observable: the deployed output representation a dense retriever ranks with. Across five development embedders, configuration-level drift orders sampled mixed-precision plans against held-out retrieval quality at a macro Spearman of 0.911, the sensitivity transports across calibration corpora and retrieval domains in the usable regime, module drifts compose rank-consistently but not numerically, and relevance-derived sensitivity adds no consistent value. The method is one additive allocation under a hard packed-byte budget, with no labels and no search. On three embedders held untouched until method, baselines and hypotheses were frozen and sealed, the pre-registered directional hypothesis against the prior LieQ criterion holds (3/3 at the main budget, no collapse) and drift scores above a two-sided LieQ steelman in 2/3; but at the main budget drift is numerically lower than same-budget uniform precision on all three (-0.99, -0.85, -1.01 points), having reduced module and whole-model drift as designed. Output drift is thus a robust coarse sensitivity signal, not a universally optimal allocation objective: it avoids the catastrophic failures of the transferred signed-geometry adaptation and can remain usable at stressed budgets where uniform collapses, but fine-grained redistribution around a strong uniform operating point remains unresolved.

Representations continually change as a network learns new tasks. We ask whether early representational changes naturally form a geometric structure that continues to shape later learning. We identify a low-dimensional subspace of early representation drift, which we call a scaffold, and test whether it is reused across subsequent tasks. Across four pretrained visual encoders and two datasets, later representational changes consistently favor this early-defined subspace over matched random alternatives. This reuse is history-dependent: when networks experience different early tasks but identical later training inputs, each network preferentially reuses the scaffold induced by its own learning history. The same preference appears in individual optimizer updates, even though the network's dominant local response directions shift away from the original scaffold. Finally, constraining motion within the scaffold slows new-task acquisition more than matched random constraints, while effects on old-task retention are less consistent. In summary, these results suggest that early experience leaves a persistent geometric imprint on how neural networks adapt to future tasks.Code is available at https://github.com/YuantaoDeng/latent-scaffold.

Continual learning must absorb new tasks without erasing old ones, and replay---mixing a small buffer of past examples into current training---is among the most effective remedies for catastrophic forgetting. Yet its generalization behavior is shaped by two coupled effects that existing analyses fold into a single hypothesis-level quantity: finite memory replaces each past distribution with an empirical proxy, and repeated reuse couples the buffer, the current data, and the final hypothesis through a shared optimization trajectory. We develop a layer-wise information-theoretic framework that separates these effects at every depth. Our main result decomposes the expected generalization gap into a replay-induced representation drift and an optimization-dependence term, the latter further resolved into stability, plasticity, interaction, and residual-coupling components. Two refinements make the framework operational. A Wasserstein relaxation of the drift term, valid under support mismatch, yields a depth-dependent drift--sensitivity trade-off whose minimizer identifies which interior layer to stabilize. An SGLD instantiation of the optimization term reduces it to a trajectory-level log-determinant budget, exposing a curvature-aware gradient-alignment statistic that serves as an online diagnostic of task-wise forgetting. Controlled and benchmark experiments confirm the predicted memory scaling, the interior funnel, and the alignment signal's link to forgetting.

Activation monitors -- lightweight probes trained on a language model's internal representations -- are an increasingly common layer in deployment safety stacks. Deployed models however are rarely static: they are quantized, fine-tuned, adapted with LoRA, or served with merged adapters while the monitor remains frozen. We present the first systematic test of whether this implicit contract holds: whether activation monitors trained on a base model remain reliable after these routine model updates. Across multiple safety-relevant monitors, model depths, update families, and open-weight models, we find a sharp split: quantization-style updates largely preserve frozen probe performance, while fine-tuning-style updates frequently make probes stale. Fragility is highly monitor-dependent, with privacy/PII probes most affected and refusal-compliance probes comparatively stable, showing that retraining a behavior need not stale its corresponding monitor. QLoRA is especially damaging despite NF4 quantization alone being relatively benign, suggesting that quantization becomes riskier when combined with adaptation. We further show that degradation is predictable from pre-deployment features, enabling revalidation budgets to be triaged toward the monitors most likely to fail. Finally, we test repair strategies and find that cheap label-free activation realignment repairs every repair-relevant stale cell, with none requiring score calibration, few-label heads, or labeled retraining. These results suggest that fine-tuning should trigger activation-monitor revalidation by default, with prediction triaging which monitors to check first and label-free realignment as the default repair.

Catastrophic forgetting is often viewed as the destruction of previously learned knowledge during sequential learning. Building on the Accessibility Collapse framework, we investigate the geometric structure of recoverability in continual learning. Using Split CIFAR-100 and a sequentially trained ResNet-18, we analyze recoverability, representational drift, and recovery complexity across ten tasks. We introduce Recovery Subspace Dimensionality (k_t), a measure of the minimum number of singular directions required to preserve 90 percent of full probe performance. Contrary to our Recoverability Diffusion hypothesis, recovery dimensionality remains stable throughout training (mean k_t = 8.0) despite substantial representational drift. Principal-angle drift strongly predicts recoverability (r = -0.862), and a simple geometric model explains 82.2 percent of recoverability variance. These findings support the Stable Recovery Manifold hypothesis, suggesting that forgotten knowledge remains compactly decodable despite representational reorganization. The results indicate that catastrophic forgetting is primarily an accessibility and manifold-alignment problem rather than information destruction.

Large audio language models (LALMs) process both speech and environmental acoustic cues, yet struggle to retain non-speech information across multi-turn interactions. The performance gap between semantic (speech) and acoustic (non-speech) understanding remains poorly understood, and the underlying mechanisms of representation and retrieval are still unclear. This work introduces EnvMem, a controlled multi-turn benchmark designed to study this gap and identify the root causes of failures at the representation (i.e., latent embeddings) and retrieval levels (i.e., attention allocation). We further conduct post-hoc interventions to probe representational structure and attention dynamics. Our results reveal representational trajectory drift as the key failure mode, while showing that attention allocation plays a limited role in explaining the observed degradation. Overall, we provide a systematic framework for analyzing and improving non-linguistic memory in long-context LALMs, shedding light on future data and training design for robust acoustic memory modeling.

Multimodal large language models (MLLMs) often fail to transfer safety capabilities learned in the text modality to semantically equivalent non-text inputs, revealing a persistent multimodal safety gap. We study this gap from a representation-geometric perspective by analyzing a text-aligned refusal direction and a modality-induced drift direction. We show that multimodal inputs compress the usable separation along the refusal direction, making it no longer reliable for identifying and refusing harmful inputs. We refer to this failure mode as Safety Geometry Collapse. We quantify it through conditional refusal separability and show that stronger modality-induced drift is consistently associated with weaker refusal separability and higher attack success rates. We then validate the causal role of modality-induced drift through a fixed-strength activation intervention: counteracting the estimated drift restores refusal separability and improves multimodal safety. After drift correction, we further observe self-rectification, where the model recovers its ability to recognize and refuse harmful multimodal inputs during forward dynamics. This effect also provides an internal signal of the model's perceived harmfulness of each input. Motivated by this signal, we propose ReGap, a training-free inference-time method that adaptively corrects modality drift using self-rectification. Experiments across multiple multimodal safety benchmarks and utility benchmarks demonstrate the effectiveness of ReGap, which significantly improves the safety of MLLMs without compromising general capabilities. Our findings highlight representation-level modality alignment as a crucial direction for real-time safety improvement and for building safer, more reliable MLLMs.

The cosine similarity between a large language model's hidden activations before and after Supervised Fine-Tuning (SFT) remains very high. This, at first glance, suggests that SFT leaves the model's activation geometry largely undisturbed. However, projecting both sets of activations through a Sparse Autoencoder (SAE) pretrained on the base model reveals that the underlying sparse latents diverge significantly. We introduce a novel investigative pipeline which utilizes these pretrained SAEs as a high-resolution diagnostic tool to mechanistically investigate the drivers of this representational divergence. Through our analytical pipeline, we discover task-specific and layer-specific distributions of the precise semantic features that are systematically altered during supervised fine-tuning. We additionally identify a layer-wise update profile specific to safety alignment. All code, experimental scripts, and analysis files associated with this work are publicly available at: https://github.com/ruhzi/sae-investigation.

Pre-trained models with parameter-efficient fine-tuning (PEFT) have demonstrated promising potential for class-incremental learning (CIL), yet catastrophic forgetting still persists when adapting models to new tasks. In this paper, we present a novel perspective on catastrophic forgetting through the analysis of inter-layer relation drift, i.e., the progressive disruption of relationships among layer-wise representations during the learning of new tasks. We theoretically show that the increase of such drift reduces the classification margins of previously learned tasks, thereby degrading overall model performance. To address this issue, we propose \underline{S}elf-\underline{R}ectifying inter-layer \underline{R}elation Low-Rank Adaptation~(SR$^2$-LoRA), a simple yet effective method that mitigates catastrophic forgetting by constraining inter-layer relation drift. Specifically, SR$^2$-LoRA constructs the relation matrices induced by the previous and current models on current-task samples, and aligns the corresponding singular values. We further theoretically show that this alignment exhibits greater robustness to estimation perturbations than direct entry-wise alignment. Extensive experiments on standard CIL benchmarks demonstrate that SR$^2$-LoRA effectively mitigates catastrophic forgetting, with its advantages becoming more pronounced as the number of tasks increases. Code is available in the repository.

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy ($ρ= 0.89$-$0.97$) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial $ρ= 0.62$-$0.76$). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks ($ρ\approx 0.10$), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly $2\times$ greater geometric change than CKA during post-training alignment (up to $5.23\times$ in Llama) while providing earlier warning in 73% of models and maintaining a $6\times$ lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.

Fine-tuning adapts pretrained networks to new objectives. Whether the resulting depth profile of representational change reflects an intrinsic property of the model or the magnitude of gradient flow has not been tested directly. We measure this profile across 240 fine-tuning runs spanning 15 models in four architecture families (encoder and decoder transformers, a state-space model, and an RNN) at scales from 125M to 6.9B parameters. Representational change concentrates in output-proximal layers in every standard-training run except one. We apply a per-layer control that equalizes $\|ΔW\|/\|W\|$ across layers after each optimizer step. Under this control, the profile persists in some conditions and collapses in others. At 125M--350M, sequential-block architectures (BERT, OPT, GPT-2) retain the slope across tested objectives while parallel-block architectures (Pythia, CodeGen) retain it only for causal-language-modeling objectives. This architectural distinction narrows at 1.3B--1.4B, where both block types show positive equal-step slopes for CausalLM. Under standard training, profile shape is described by two additional axes: steepness tracks a training-free objective distance at initialization, and profile width is dominated by architecture. We treat the locality gradient, the depthwise slope of representational change, as a composite phenomenon whose components are scale-dependent.