Source-Free Class Relearning: Diagnosing Forgetting in Class Unlearning

Class unlearning aims to remove a model's ability to recognize designated forget classes while preserving performance on retain classes. However, low forget accuracy after unlearning does not necessarily mean the class structure has been erased. Approximate unlearning methods can alter classifier decision boundaries while leaving recoverable structure in the representation. Prior work has shown that forget classes can be recovered, but existing approaches require real forget or retain samples, auxiliary data, or reference checkpoints. We study class relearning in a strictly source-free setting, asking whether a forget class can be recovered through a classifier-head update using only the unlearned model. Our approach rests on a theoretical analysis establishing a sufficient alignment condition under which a single gradient step on a synthetic probe set increases the expected logit margin of the forget class. Building on this, we propose a white-box Source-Free Relearning Audit (SFRA), which generates candidate embeddings in representation space and uses model-guided confidence filtering to construct high-confidence retain probes and low-confidence boundary-adjacent probes that are relabelled as the forget class. Gaussian sampling and Softmax confidence are used by default, while ablations with alternative proposal distributions and uncertainty criteria show that recoverability is not specific to these choices. To quantify recoverability, we introduce the Relearning Score (RS), which jointly measures forget-class recovery and retain-accuracy preservation, and report class-matched $Δ$RS relative to a retrained reference. Experiments on CIFAR-10, CIFAR-100, and TinyImageNet with ResNet-18, ViT-B/16, and Swin-T show that several unlearning methods exhibit substantial source-free recoverability, and that for a subset of methods this recoverability exceeds the matched retrained reference.

Are You Thinking What I am Thinking? : Examining Conceptual Separation in Neural Architectures

Neural networks are increasingly employed to identify both well-defined and ambiguous concepts, yet output-level metrics reveal little about how those concepts are represented internally. Our study asks if these networks exhibit \textit{conceptual separation}: if examples of the same concept form coherent representations, and whether related concepts lie closer together in the representation space. We examine this conceptual organisation in Convolutional Neural Networks (CNNs) and Large Language Models (LLMs) through geometric and distributional analysis of their internal activations. In CNNs, familiar ImageNet concepts form coherent and semantically ordered representations, while this coherence weakens for unseen concepts and suffers within-class domain shift. In LLMs, clearly distinct domains remain well separated, related subdomains move closer together, and the distinction between ambiguous topics collapses at both the mean and covariance level. These results suggest that conceptual separation can reveal structure that output accuracy alone cannot, and may serve as a useful diagnostic of how robustly a model represents the concepts it is asked to identify. Code and data available on \href{https://github.com/JaeeRoshniCapstoneProject/Are-You-Thinking-What-I-m-Thinking-Examining-Conceptual-Separation-in-Neural-Architectures}{GitHub}.

Where Do Multilingual Vision-Language Encoders Fail on Low-Resource Languages?

Recent multilingual vision--language encoders cover hundreds of languages in a single model, yet on two state-of-the-art instances retrieval on low-resource languages (LRL; e.g. Swahili) trails high-resource ones (HRL; e.g. English) by $30^+$\,pp. We ask where in the trained encoder this gap is located. Prior modality-gap and cross-lingual subspace work suggests a linear language direction at the output crowds out alignment-relevant geometry. We falsify this: LEACE drives the linear language classifier from $>99\%$ to near chance and iterated INLP to $37$--$50\%$ while LRL retrieval moves within $\pm 1.5$\,pp and all tier means within $2.2$\,pp, tracking random controls. The linear bias is a \emph{symptom}, not the cause. Instead, the alignment-causal factor lies along the encoder's forward path: the EOS (end-of-sequence) hidden state's per-language trajectory diverges with depth. Substituting the EOS with its parallel English value three blocks before the projector lifts Swahili from $22.1\%$ to $69.1\%$ on one encoder (and reproduces on the other); three controls rule out pooled-position tautology and English specificity. A front-layer trunk that pulls each language's projection toward the parallel-content centroid corroborates the diagnosis at training time, recovering $+9.6$ / $+17.1$\,pp on LRL XM3600 retrieval (1{,}000-image subset), with consistent gains across three further benchmarks while preserving HRL performance.

Do Medical Vision Models Reason About Anatomy? Probing the Spatial Inductive Biases of Learned Visual Representations

Interpreting a CT scan means comparing structures on either side, judging how far apart organs sit, and knowing where each one belongs. Medical vision encoders are evaluated on diagnostic accuracy, or through assembled multimodal systems where a failure is hard to attribute, so it remains unclear whether their representations support any of this. We construct SPAR-Bench, eight probes over multi-organ abdominal CT that separate coordinate localization, relational reasoning, and spatial queries, and apply them to five architectural configurations and three medical foundation models, frozen and finetuned. Probes that ask for a comparison within the slice stay at chance, and neither pretraining scale, finetuning, nor architecture closes the gap. Probes that appear solved in domain fall to chance under zero-shot transfer, indicating that their accuracy reflects recall of canonical anatomy rather than computation over the image. Reading the same frozen features with a pooled head rather than the full set of tokens moves relational recovery from 0.7% to 67.8%, so pooled probing understates what a representation holds. Questions the encoders answer well are answered at chance by four open-weight MLLMs. Our results suggest these encoders carry a map of where organs usually lie, and little of the machinery for comparing structures within a particular patient. Code and data will be available at https://spar-bench.github.io.

Cross-Lingual Alignment Without Joint Training: Do Monolingual Language Models Converge on Universal Representations?

Cross-lingual alignment in multilingual language models is typically attributed to joint training: shared parameters, mixed-language batches, or explicit alignment objectives. We ask whether monolingual models trained on non-parallel data learn alignable representations without joint training. By testing on strictly monolingual language models, such as the Goldfish model families and independently developed models from different research labs, we find three results. Correlation: these models develop alignable representational geometry across layers, with alignment strengthening as data scale, model scale, or linguistic proximity increases. Construction: a single Procrustes rotation fit on parallel sentences maps hidden states between models. Causation: the same rotation transfers functional content; patching a rotated English residual into a German model on a factual cloze flips the prediction to the donor's capital in most cases. We confirm that cross-lingual alignment can emerge from the structure of language and the information it carries rather than from joint training, and this points to practical future directions including model stitching, merging, and modular multilingual systems built from monolingual components.

Representation Measurements Under Function-Preserving Reparameterizations

Hidden coordinates are not uniquely determined by a language model's input--output function, so representation-derived measurements should be invariant to function-preserving changes of basis. This study shows that column-permutation parallel analysis violates function-preserving reparameterization invariance because its reference distribution and selected component count can change while the model function and observed covariance spectrum remain fixed. More generally, a data-internal reference procedure cannot simultaneously preserve every coordinate marginal, remain orthogonally equivariant, and remove cross-coordinate covariance. Empirically, across five models, three retrieval domains, and 75 transformations, median component-count disagreement is 0.79 and median fixed-threshold decision disagreement is 0.26. A centering-only control isolates the reference-driven effect, with 1,141 of 1,200 component counts changing despite an unchanged observed spectrum, whereas independent parallel analysis seeds change none of the corresponding decisions. By contrast, orthogonally invariant comparator scores remain numerically stable with similar held-out discrimination. Together, these results show that parallel analysis-derived component counts and decisions can reflect hidden-coordinate choice rather than a well-defined property of the model.

FRAME: separating sampling variation from representational cause in medical imaging fairness

Subgroup performance differences are the standard evidence for fairness bias in medical imaging, and the usual response removes the demographic information that a model encodes. Here we introduce Fair-model Reference And Mechanism Evaluation (FRAME), a two-step framework for auditing such a claim. The first step derives a fair-model reference, the distribution of the difference under exact fairness at the observed subgroup sizes. In the second step, we test the remainder with two operators in representation space. One operator cannot change a within-group ranking by construction. Across 702,206 images and 36 encoders, the reference accounts for a median 41% of the reported race difference and 22% of the age difference. Injecting demographic decodability leaves the remainder unchanged, while entangling the group with the disease direction raises the race difference from 0.077 to 0.118. No intervention we tested changes the remainder more than a change of random seed does. Those interventions reduce a difference at the operating point and leave the within-group ranking difference at a median of 0.000. Applied to 89 differences in 9 published studies across 6 medical imaging modalities, the reference accounts for a median 25% of a rate difference and 70% of a difference in the area under the receiver operating characteristic curve. Image-text pretraining instead raises worst-group performance by about 0.05. Applying FRAME before choosing an intervention could distinguish differences that need a mechanistic explanation from differences compatible with sampling variation at the current cohort sizes.

Output Dilution: Redundant but Fragile Representations in MoE Models

Mixture-of-Experts (MoE) models appear to encode moral content as robustly as dense models, yet prove far more fragile in their encoding. In OLMoE-1B-7B, linear probes recover moral valence from nearly every expert-layer combination, with mean peak-layer accuracy above 90%. But these representations collapse under levels of activation noise that a dense model of matched size easily tolerates, with a 4.2-fold difference in robustness. We trace this to output dilution. Because the MoE block averages across active experts before contributing to the residual stream, the feedforward signal reaching downstream layers is nearly two orders of magnitude smaller than in a dense MLP. Moral information, our interest, survives aggregation intact but at a scale trivially overwhelmed by perturbation. Routing itself remains stable under noise while the vulnerability originates entirely in the diluted aggregate. Checkpoint trajectories confirm this is architectural, not learned. Experts never specialize and accuracy saturates within the first few thousand steps. In sparse architectures, redundant encoding does not imply robust encoding.

Linear Probing Provides Robust and Efficient Detection of Machine-Generated Text

Distinguishing machine-generated text (MGT) from human-written text (HWT) becomes increasingly important due to potential misuse. However, most supervised detectors often degrade out-of-domain (OOD) and require large, diverse training sets. In this work, we analyze the linearity and quality of MGT representations and show that simple linear probes outperform a wide range of detectors while being substantially more sample-efficient. We first show that MGT and HWT latent representations are linearly separable in low-dimensional space, and provide a plausible explanation for this separability through systematic differences in their representation quality. Motivated by these insights, we train two variants of simple linear probes and evaluate them across 4 benchmarks against 16 baselines. Probes consistently improve OOD detection (+11 AUC), requiring solely ${<}100$ samples to reach near-peak performance. We show that this transferability arises because probes recover a shared latent MGT direction that generalizes across diverse settings. Finally, we demonstrate that probing vectors capture a continuous spectrum of ``machineness'', highlighting their potential for fine-grained estimation of AI-edited text. Overall, our work provides insights into latent-space differences between MGT and HWT and demonstrates the potential of linear probes as as robust and sample-efficient MGT detectors. We release our code on~\href{https://github.com/gerritq/mgt_probes}{github}.

What Reaches Expert Review? Representation, Structural Screening, and Candidate-Form Dependence in AI-Assisted Item Development

Between AI-assisted item generation and expert review sits a computational evaluator whose decisions are usually treated as technical preliminaries. Yet representation, structural reduction, and selection policy determine which items and evidence psychometricians ever receive. Across two linked in-silico studies of 32,000 selected Big Five items, we followed fixed source populations from semantic representation through structural evaluation and candidate-form construction. Broad agreement in semantic geometry concealed consequential local differences: identical wording acquired different construct evidence, different items survived, and intended attributes could disappear even as community correspondence improved. These sensitivities also differed across generated source populations. At the final review boundary, both eligibility policies filled every content cell in every evaluable form, yet they presented different wording. Across embedding configurations, inclusive primary forms shared a median of only 6 of 40 items, reflecting the total downstream consequence of changing representation across structural evidence and ranking. The apparent stability of global summaries and complete forms therefore concealed instability in the content reaching psychometricians. The computational evaluator is not neutral infrastructure between generation and expertise; it is an inspectable and revisable part of measurement design.

Mitigating Reasoning-Induced Misalignment via Safety-Direction Penalty

Reasoning-Induced Misalignment, where fine-tuning on reasoning data containing no harmful content, including mathematics, code, and problem-solving with chain-of-thought traces can induce harmful behaviors of LLM, posing a serious challenge to the safety of LLM reasoning. Cross-architecture, cross-scale, and cross-dataset checks show that RIM does not always emerge. Previous work attributed RIM to neuron-level entanglement, but did not identify the geometry of the representation space underlying this entanglement or propose a training-time fix. We provide both: a representation-space analysis of RIM and the Safety-Direction Penalty (SDP), which penalizes movement along a learned safety direction during reasoning fine-tuning. The analysis extracts two activation-space directions, one encoding reasoning ability and the other safety behavior. These directions are coupled: fine-tuning that improves reasoning shifts safety representations, and prompts with larger shifts show larger safety degradation. CKA distance ratios and probes locate the safety-decision layers where this shift is most relevant. These findings guide the design of SDP: the coupling motivates penalizing displacement along the safety direction, and the layer localization sets the initial scope. When the initial scope leaves compensatory shifts beyond the penalized layers, the same diagnostics guide iterative expansion. On Qwen2.5-3B and 7B, SDP restores safety while preserving benchmark reasoning performance.

Beyond Fixed Directions: Adaptive Representation Analysis of Reasoning and Memorization in LLMs

Recent work has proposed that reasoning and memorization in language models can be characterized by a single representation direction, including methods that keep this direction fixed during reinforcement learning. We test two assumptions behind this view. First, are reasoning-oriented and factual-recall task groups approximately single-direction separable? Second, does the resulting geometry remain stable after GRPO? Using Qwen3-0.6B and a controlled 400-example dataset, we find that a one-dimensional projection can match a full 1024-dimensional linear probe with AUROC = 1.00 on the studied task groups. However, after GRPO, the corresponding direction is substantially reorganized: mean-direction cosine averages 0.453, probe-direction cosine 0.445, while direct representation drift reaches 0.511 at the final layer. Probe AUROC nevertheless remains 1.00. The evidence therefore supports single-direction decodability for the studied task groups but challenges fixed-direction stability: the information persists while its geometric realization changes.

Structure, Association, and Decision Value: Representation-Based Difficulty Estimation for Adaptive Inference in African-Language NLI

We ask whether internal representation statistics can provide useful example-level difficulty signals for adaptive inference in multilingual African NLP, and find that they cannot in this setting. Studying natural language inference across 15 African languages with frozen off-the-shelf checkpoints, we report four results. First, AfriXNLI's English configuration shares 1,047 of its 1,050 examples verbatim with XNLI evaluation data, and one widely used NLI checkpoint scores 1.000 on that test split, consistent with XNLI test exposure. Because AfriXNLI is derived from XNLI, its English, French and Swahili configurations cannot serve as clean evaluations for XNLI-trained models. Second, parameter count does not reliably order capability across African languages: our larger checkpoint is better in seven languages and worse in eight, with no significant aggregate difference. Third, across three multilingual representation spaces, angular dispersion is consistently more language-determined than effective rank, so pooled correlations can inflate one and mask the other. Fourth, the association that survives language control depends on the target: effective rank predicts probability gain from escalation but not whether escalation changes the prediction, while cheap-model confidence shows the opposite pattern; the two targets correlate at only 0.655. Under the tested models, signals, and compute budgets, no evaluated signal makes adaptive routing preferable to always-expensive inference, although an oracle exceeds it by 11 accuracy points at 60% of the compute. Our central methodological finding is that a representation statistic can be statistically significant for one notion of computational benefit while being irrelevant to another, and therefore be a poor decision variable.

Emergent 3D Instance Segmentation from Self-Supervised Point Transformers

Unsupervised 3D instance segmentation of outdoor LiDAR scans has traditionally relied on handcrafted geometric priors such as density-based clustering, motion cues, or projected 2D detections. In this work, we investigate whether a frozen, self-supervised point transformer already contains the structural information required to isolate object instances without any handcrafted geometric prior. Using this transformer purely as a feature extractor, we probe its internal representations across the SemanticKITTI, nuScenes, and Waymo Perception datasets. Our analysis yields four core insights: (1) the instance signal concentrates in the attention queries and keys rather than in the values or final output features; (2) output features semantically collapse, merging adjacent same-class objects that the queries and keys keep distinct; (3) this instance signal is bimodal in depth, strongest at the shallowest and deepest encoder stages; and (4) this signal is driven predominantly by the rotary position encoding (RoPE), whose removal collapses its advantage. We put these findings into our method TokenGraph3D, a training-free segmenter that groups points via connected components on a key-similarity graph, using neither density-based clustering nor proximity priors. Under identical prior-free conditions, we substantially outperform output-feature baselines, making the emergent 3D instance structure visible.

Unsure but Certain: Uncovering the Representation-Confidence Gap in Diffusion Language Models

Diffusion language models use broad context to create text, suggesting they might handle input noise better than standard models. Testing reveals this is only partially true. Internally, diffusion models detect text errors highly accurately. Externally, their reported certainty ignores this signal. As accuracy drops due to noise, confidence stays near its maximum and the ability to correctly rank answers degrades toward random chance. We call this mismatch the representation confidence gap. The visible concentration of high certainty scores is a misleading surface symptom. Standard math adjustments remove this concentration but fail to fix the underlying loss of ranking order. This ranking deficit favors standard models under noisy conditions and resists common remedies. Matching training recovers accuracy but not ranking, while score recalibration and input level error signals cannot reorder the final answers. However, the information needed to properly evaluate an answer survives in the hidden states. A lightweight extraction tool uses this signal to improve ranking. This approach is highly efficient because it leaves the base model completely frozen and requires zero additional text generation steps. We present this tool to prove the signal exists, while clearly noting its limits. Ultimately, certainty reliability is a more pressing limit than overall accuracy under noisy conditions.

"Many Are My Names": The Anatomy of the Assistant and Its Personas via Sparse Autoencoders

How a language model internally represents who is speaking, the Assistant, an assigned roleplay persona, or a narrated story character, remains underexplored. We study speaker representations using a dataset of user-expressed emotional text and corresponding model responses. We decompose three generation settings (Assistant, Roleplay, and Story) into sparse autoencoder features extracted at turn-boundary and pronoun-token positions and selected through a filtering pipeline for different depths. We characterize each surviving feature through its steering effects and activation distribution. Our main finding is that the Assistant and roleplay personas are not independent alternatives: personas retain the Assistant-associated feature core while progressively differentiating from it across layers, starting from operational machinery towards behavioral and stylistic features. Meanwhile, generated story characters lack the Assistant-associated core. Both Story and Roleplay can be distinguished from the Assistant with Immersive Simulation Mode. However, the Assistant can sometimes enter or slowly drift into it even in the default setting.

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers

Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head. Muon groks modular addition faster, but its solutions do not hold. All nine configurations on $(a+b) \bmod 113$ grok and later lose generalization. Across five seeds the selected AdamW reference falls below threshold on four, reaching 27.59%. Instability persists across two moduli, two widths, two training fractions, subtraction, and depth. The failure arises at the representation-readout interface, identified only jointly up to an invertible map unselected by the loss. After solving the training set, the gradient falls to order $10^{-6}$ and the optimizers respond differently: step-size elasticity is -0.03 for Muon versus +1.5 for AdamW, and the Muon group moves 8.0 times faster per parameter. From bit-identical states, freezing either group prevents failure. Freezing embeddings/readout removes it in five runs over 451,400 post-grokking steps and five paired seeds: unfrozen arms record 137-321 sub-threshold evaluations, frozen arms none. Removing Muon's normalization and orthogonalization is no substitute: it collapses representation from 326 effective conjugate pairs to 4, shows no recurrent collapse, and fails terminally. Fourier filtering separates circuit failure from masking. Across 43 checkpoints over five seeds and three regimes, the task-aligned family reaches exactly 100% alone. In circuit failure it no longer solves the task; in masking it remains perfect while the full model reaches 45.85%, giving a positive margin on every example, including errors, but being outvoted by a near-equal adversarial remainder. Rescaling it restores 99.9%; grokking is the same condition resolving upward. The task selects the family, swapping $(k,k)$ for $(k,-k)$ under subtraction. Across an abrupt collapse, standard Fourier support is unchanged and the power-distribution cosine remains 0.9899.

Transformer Geometry Observatory TGO-IV: Developmental Topology Observatory

Transformers have had a profound impact on the world of language processing and computer vision. As efforts to answer the million-dollar question of ``How does a Transformer learn?" have been increasing, existing interpretability studies primarily analyze representations at isolated layers or the network as a whole, while the developmental evolution of individual representations and its manifolds across transformer layers remains underexplored. With this work, we aim at providing a comprehensive analysis of the evolution of representations as the representation point cloud transforms across the layers; thereby attempting to isolate layers or establish a trend which comes closer to justifying how and when raw input representations evolve into task-relevant feature representations. Thus, Transformer Geometry Observatory-TGO-IV introduces a topological framework for analysing the evolution of Transformer representations through the lens of Persistent Homology. Rather than studying local geometric properties alone, TGO-IV constructs Vietoris--Rips simplicial complexes from token-level representation point clouds and investigates the evolution of their persistent topological signatures across Transformer layers. The proposed framework comprises complementary topological observatories including Persistence Diagrams, Barcode Diagrams, Betti Curves, Persistence Landscapes, Bottleneck Distance, and Wasserstein Distance, enabling a comprehensive analysis of how the global topology of representation point clouds develops throughout the forward pass.

IRIS: A Visual Cortex-Inspired Framework for Analyzing Orientation Selectivity in Vision Transformers

Vision transformers (ViTs) have become the de facto standard for image encoding across many perception tasks. Despite their empirical success, it remains mechanistically unclear how they encode low-level features, given their lack of inductive biases: ViTs process information globally rather than relying on local structure. Biological visual systems, in contrast, build low-level features, such as orientation selectivity in the primary visual cortex, by combining information from small, localized regions of the visual field. These features are general-purpose representations, shared and required across multiple specialized neural pathways, unlike higher-level, task-specific semantic features. This raises the question if such biologically-grounded features arise in ViTs. In this work, we systematically study how orientation selectivity emerges in ViTs by introducing a suite of neuroscience-inspired metrics: representational similarity score (RSS), orientation recruitment score (ORS), and orientation tuning bandwidth to quantify how orientation is encoded in representational geometry and as a function of model depth. Through extensive analysis, we find that: (1) the training paradigm is the strongest determinant of orientation selectivity, with models sharing an objective, peaking at comparable relative depths regardless of scale (2) many units are orientation-selective early in training, with early-to-middle layers recruiting more such units over time, while deeper layers lose selectivity and broaden their tuning toward semantic encoding and (3) our metrics offer a mechanistic heuristic for how many layers to unfreeze for best downstream generalization. Our framework presents a way to track biologically-grounded features during ViT training, probes how desired properties are encoded in transformer representations, and builds a systematic understanding of how ViTs generalize across tasks.

Through the LENS: Local Geometric Decomposition of Vision-Language Model Representations

Vision-language models (VLMs) process image patches and text tokens in a shared residual stream, but the local geometry through which the two modalities interact remains poorly understood. Most interpretability methods identify global linear directions, which may miss representations that are globally high-dimensional but locally low-dimensional. We introduce LENS (Local Explanation of Neighborhood Subspaces), a method that decomposes VLM activations into local low-rank Gaussian neighborhoods using a Mixture of Factor Analyzers. Applied to LLaVA-1.5-7B and Qwen3-VL-8B, LENS reveals distinct depth-dependent fusion trajectories consistent with each model's fusion mechanism: LLaVA progressively mixes modalities at later layers, whereas Qwen3-VL mixes them early, partially re-segregates them, and recombines them near the output. An automated multimodal labeling pipeline assigns concise semantic descriptions to these neighborhoods. Interpolating activations toward neighborhood centroids causally redirects generation within and across modalities and outperforms difference-in-means and VL-SAE in most evaluated conditions; in one LLaVA vision-to-vision setting, MFA achieves 5.7 times the VL-SAE score. Human evaluation finds MFA steering competitive with prompting and substantially stronger than the other intervention baselines. Finally, the MFA coefficient space improves Qwen3-VL image-to-rendered-text retrieval at the deepest evaluated layer from 14.9% to 48.6% R@1. Ablations show that the reported fusion trajectories are stable across component counts, local ranks, and modality-purity thresholds. These results support local geometric neighborhoods as useful interpretable and causal units for analyzing cross-modal representations in the evaluated VLMs.

ECG-InterpBench: Benchmarking the Interpretability of ECG Foundation Models with Matched-Scale Sparse Autoencoders

Existing benchmarks for electrocardiogram foundation models primarily evaluate downstream predictive performance, providing limited insight into whether their internal representations can be faithfully decomposed, clinically interpreted, or reproduced across independent analyses. We introduce ECG-InterpBench, a benchmark designed to systematically evaluate the interpretability of ECG foundation-model representations. ECG-InterpBench uses sparse autoencoders as standardized measurement instruments and matches their capacity across models to enable controlled comparisons. We evaluate six frozen ECG foundation models across five standardized encoder depths, five matched dictionary widths, and three random seeds, producing a 450-cell interpretability atlas comprising 75 exactly matched six-model comparison blocks. The benchmark evaluates complementary dimensions of representation interpretability, including sparse reconstruction fidelity, single-feature accessibility and coverage of 49 clinically meaningful ECG measurements, and cross-seed feature reproducibility. The evaluation further quantifies patient-sampling uncertainty, depth- and seed-dependent variation, and sensitivity to the sparsity parameterization. The benchmark reveals that ECG foundation models exhibit distinct interpretability profiles. A matched replication on MIMIC-IV-ECG confirms that reconstruction fidelity and clinical accessibility identify different leading models. The benchmark is accompanied by executable evaluation code, standardized manifests, cell-level metrics, and reproducibility audits. ECG-InterpBench complements performance-centered ECG benchmarks by providing a capacity-controlled and reproducible framework for comparing ECG foundation models across distinct dimensions of representation interpretability.

Prior Directions: Why GUI Grounding Gets Locked in the Past

Vision-language models often use descriptions of earlier visual states to make decisions about the current scene. When the scene changes, stale language can redirect an otherwise correct visual judgment toward an outdated answer. We study this failure as visual lock-in in a controlled grounding setting where only the verbalized prior varies. Across models, stronger lock-in accompanies smaller changes in the model representation before the final answer. This reversal suggests that lock-in depends not on how far this representation moves, but on how that movement is organized. In models that are harder to correct, prior-induced changes concentrate along a compact set of directions that repeatedly appear across examples. We call these recurrent axes the Prior Directions. They recur on held-out examples, while a descriptive four-model comparison associates greater concentration with stronger lock-in. Controlled interventions show that removing the component aligned with the Prior Directions restores visual grounding, whereas removing an equally large orthogonal component has little effect. Prior control thus arises when prior-induced changes form a coherent and reusable pattern in the representation used to produce the answer. This account explains why the same prior remains revisable in one model yet becomes dominant in another.

Do Unified Multimodal Models Think in One Space? A Lens Through Cross-Branch Steering

Unified multimodal models (UMMs) aim to integrate understanding and generation within a single architecture, yet it remains unclear whether these capabilities share a unified and transferable semantic space. This question is fundamentally challenging, as the two branches operate over heterogeneous representations (text tokens vs.\ visual latents) and distinct training objectives, making direct comparison difficult. To address this, we introduce \emph{cross-branch semantic steering}, an intervention-based framework that extracts semantic directions from one branch and applies them to the other. We show that steering vectors learned from the understanding branch can transfer to generation, enabling controllable image synthesis and improved semantic faithfulness. In contrast, the reverse direction consistently shows limited effectiveness. Our analysis suggests that this asymmetry may be related to a practical representational mismatch: understanding-derived vectors capture transferable, object-centric semantics, while generation-derived vectors primarily encode low-level appearance features. Our results reveal that architectural unification does not guarantee semantic alignment, and establish cross-branch steering as a practical tool for probing multimodal representations.

Probing the Origins of Reasoning Performance: Representational Quality for Mathematical Problem-Solving in RL vs. SFT Fine-Tuned Models

Large reasoning models trained via reinforcement learning (RL) have been increasingly shown to outperform their supervised fine-tuned (SFT) counterparts on mathematical reasoning tasks; Yet the mechanistic basis for this advantage remains unclear. We therefore ask, what internal representational differences enable RL models' superior performance? Our work presents two converging lines of evidence: First, linear probes trained on layer-wise hidden states reveal that RL models tend to achieve higher accuracy in predicting answer correctness compared to SFT models, indicating more linearly separable and structured representations. Second, mean ablation studies show that RL models develop a hierarchical architecture where deeper layers become progressively more critical, whereas SFT models distribute importance uniformly across layers. Together, these findings demonstrate that RL training fundamentally restructures how models represent and process reasoning problems. Finally, we analyze token-count variability under repeated sampling across problems to assess adaptive compute allocation. While we observe higher variability in some RL-tuned models than in their SFT counterparts, we see strong consistency in others, suggesting that token allocation may depend more on the overall training pipeline than on RL versus SFT alone. We believe this token-allocation variability reveals the spread of plausible on-policy reasoning, highlighting which models exhibit stable policies versus those that are under-determined, potentially non-identifiable solution behaviour.

Hilbert Operator for Progressive Encoding (HOPE): A Mathematical Framework for Deconstructing Learned Representations in Deep Networks

Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge. Given the link between learning and compression, network compression offers a promising lens to analyze this knowledge. However, standard compression heuristics often suffer from scale symmetries and architectural biases. To resolve these, we introduce Hilbert Operator for Progressive Encoding (HOPE), a mathematical framework to gradually deconstruct the representations in trained network weights. HOPE shifts network compression from the discrete domain into a Hilbert space of continuous functions. By modeling individual neurons as rank-1 Hilbert-Schmidt operators, HOPE unifies pruning and neuron merging as low-rank subspace projection. Extending this formulation, HOPE introduces macro block eviction to encompass multi-layer structures like entire residual pathways under the same unified metric. This unified approach enables unbiased architectural decisions across layers with different types and sizes. HOPE is a data-free and hyperparameter-free framework. We present proof-of-concept experiments in model compression and fine-tuning to highlight the practical potential of our theory.

Geometric Configurations of Perturbed Jailbreak Prompts

Perturbation techniques that turn unsuccessful jailbreak prompts into successful ones are continuously evolving, constituting a major security threat to LLM safety. In this paper, we investigate the internal representations of such string-level perturbed jailbreak inputs in the small weight models of the Qwen-2.5-1.5B/-3B/-7B-Instruct and Llama-3.2-1B/-3B/-3.1-8B-Instruct families. We select two representation spaces: the last-layer-last-token embedding space and the top-50 next-token probability space. The former space separates prompts based on their spelling and format, while the latter space is effectively one-dimensional but appears more complex to cluster. Within our refusal-dominated answer set we find no behavioral hyperplane in either space. Only the next token "Sure" in the 1.5B Qwen model, and both tokens "," and "ĊĊ" in the 1$ Llama model, display a significant association with a compliant-labeled answer.

Norm or Direction? Decoding Vision Mambas for High-Resolution Vision

Vision Mamba models replace quadratic self-attention with linear complexity selective state space models (SSMs), emerging as efficient visual backbones. However, MambaOut demonstrates that a Gated CNN block can match or exceed VMamba on image classification, questioning the necessity of SSMs for vision. This raises a fundamental question: do VMamba and MambaOut encode visual information differently at the representation level? To investigate, we apply cross model centered kernel alignment (CKA) analysis and find that VMamba's final stage blocks form representations distinctly different from both MambaOut and its own preceding blocks. We therefore focus on the final block features, decomposing each spatial token into magnitude and direction. MambaOut concentrates class-discriminative information in high-norm foreground tokens that align with Grad-CAM attribution. VMamba, by contrast, produces high-norm tokens predominantly in background regions, misaligned with Grad-CAM, yet preserves discriminative signals primarily in token directions. These observations reveal that the two models rely on different encoding strategies. We connect this difference to high-resolution classification and semantic segmentation. VMamba distributes logit support broadly across object regions, whereas MambaOut relies on sparse dominant tokens, a strategy that becomes less stable as token counts grow. Under full fine-tuning for segmentation, VMamba consistently outperforms MambaOut. These results suggest that VMamba's advantage in dense prediction stems not merely from the SSM mechanism or sequence length, but from how semantic evidence is organized across token magnitude, direction. Ultimately, we conclude that token magnitude and directional structure serve as critical axes for improving visual backbones, particularly under dense supervision.

Verbalizable Representations Form a Global Workspace in Language Models

Out of everything the human brain processes, only a small fraction is consciously accessible, in the sense of being available for verbal report, deliberate control, and flexible reasoning. In this paper, we present evidence that an analogous functional distinction has emerged in large language models. Using a new interpretability technique, the Jacobian lens, we identify the representations a model is poised to verbalize at any point in its processing. These representations, which we collectively call the J-space, exhibit the functional properties characteristic of a global workspace: their contents can be reported, deliberately summoned and held, used to carry the intermediate steps of silent reasoning, and passed as arguments to arbitrary downstream computations, while automatic processing such as text parsing and routine inference proceeds without them. The J-space also has structural signatures that global workspace theory associates with conscious access: it carries coherent content only in an intermediate band of layers, holds on the order of tens of concepts at a time, and is broadcast by the model's weights more widely than other representations. These properties make it a practical window into a model's unspoken thinking. In alignment audits, it reveals strategic deliberation, evaluation awareness, and trained-in misaligned dispositions that never appear in the model's outputs. We find that post-training installs the Assistant's point of view in the workspace, and we introduce counterfactual reflection training, which improves behavior by training only what a model would say if interrupted and asked to reflect. These results indicate that language models maintain a small, privileged set of representations bearing some of the functional hallmarks of conscious access, and that decoding these representations sheds light on ongoing cognitive processes.

Causal-Adversarial Probing of Clinical Covariates for Prostate MRI Grading

Deep learning models for prostate MRI-based cancer grading may encode clinical covariates that either reflect useful disease-related signal or non-generalising shortcut information, but their role is usually assumed. We propose a causal-reasoning framework for probing covariate dependence in MRI-based International Society of Urological Pathology (ISUP) Grade Group prediction. Rather than treating mpMRI as a direct cause of grade, we model MRI appearance and ISUP grade as observations of latent tumour pathology, and test whether candidate clinical variables act as nuisance correlates, disease-related proxies, or irrelevant covariates in the learned representation. We implement this using an adversarial framework that suppresses the decodability of individual clinical covariate at a time while preserving MRI-based grade prediction. The approach is developed and evaluated on 2,903 prostate MRI examinations, with external validation on 576 patients. We report a set of interesting and previously under-explored imaging-to-clinical-variable interactions in the context of deep learning generalisation. For examples, in binary ISUP Grade Group $\geq2$ classification, suppressing age, BMI, and alcohol use improved AUC by 1.23%, 0.84%, and 1.42%, respectively (all p < 0.05), suggesting reduced non-generalising covariate information; In contrast, suppressing PSA and prostate volume degraded AUC by 1.91% and 7.61% (all p < 0.001), indicating that these variables carried task-relevant signal. These findings show that adversarial covariate suppression can provide a practical representation-level analysis for distinguishing potentially harmful dependence from informative signal in prostate MRI grading models.

Representation and Reference Selection in Training-Free Synthetic Image Attribution

Synthetic image attribution aims at identifying the generator responsible for a given AI-generated image. Training-free reference-based attribution methods are easily scalable, since newly emerging generators can be incorporated by adding source-specific references rather than retraining a task-specific classifier. Their performance depends on two coupled factors: the representation space used for comparison and the way source-specific references are constructed. However, the interaction between these two factors remains largely unexplored. In this paper, we provide a controlled analysis of this interaction using references and off-the-shelf pretrained representations. We study representations extracted from different layers of CLIP and DINOv2, along with three reference selection methods with varying semantic constraints: arbitrary, semantically aligned, and resynthesis-based references. Our results show that attribution accuracy consistently peaks at intermediate representation levels, indicating that source-discriminative cues are more accessible before strong semantic abstraction dominates. We further show that intermediate representations are not completely semantically neutral, making reference selection critical: semantically constrained references reduce query-reference mismatch and improve attribution, especially under limited reference budgets. Resynthesis is most useful in low-reference regimes, while semantically aligned references provide a better accuracy-cost trade-off when a moderate-sized reference pool is available. Our findings show that training-free reference-based attribution should be understood as the interaction between where images are compared, how the reference set is constructed, and how many references are available.