Daily Papers

Continual instruction tuning (CIT) requires multimodal large language models (MLLMs) to adapt to a stream of tasks without forgetting prior capabilities. A common strategy is to isolate updates by routing inputs to different LoRA experts. However, existing LoRA-based Mixture-of-Experts (MoE) methods often jointly update the router and experts in an indiscriminate way, causing the router's preferences to co-drift with experts' adaptation pathways and gradually deviate from early-stage input--expert specialization. We term this as Misaligned Co-drift, which blurs expert responsibilities and exacerbates forgetting. To address this, we introduce the pathway activation subspace (PASs), a LoRA-induced subspace that reflects which low-rank pathway directions an input activates in each expert, providing a capability-aligned coordinate system for routing and preservation. Based on PASs, we propose a fixed-capacity PASs-based MoE--LoRA method with two components: PAS-guided Reweighting, which calibrates routing using each expert's pathway activation signals, and PAS-aware Rank Stabilization, which selectively stabilizes rank directions important to previous tasks. Experiments on a CIT benchmark show that our approach consistently outperforms a range of conventional continual learning baselines and MoE--LoRA variants in both accuracy and resistance to forgetting, without increasing model parameters. Our code is publicly available at https://github.com/yueluoshuangtian/PASs-MoE.

Cross-entropy pretraining and preference alignment update the same transformer weights, but leave geometrically distinct traces. We characterise this asymmetry with a relative-subspace-fraction probe that tracks how weight deltas align with residual-stream activation subspaces and with the prediction subspace defined by the unembedding. Alignment deltas concentrate in the read pathway (W_Q, W_K), along principal directions of attention-input activations, while remaining near-isotropic in the write pathway (W_O, W_2) relative to the prediction subspace. We explain this pattern through anisotropic gradient accumulation: updates to a matrix W are sums of outer products δ_t a_t^top, and inherit directional structure from whichever side has concentrated covariance. For read-pathway matrices, this side is the input activation a_t, whose covariance is spiked in trained transformers and therefore produces objective-agnostic concentration. For write-pathway matrices, the relevant side is the upstream gradient δ_t, whose anisotropy depends on the loss. Cross-entropy supplies the canonical sharp per-sample signal, inducing write-pathway prediction geometry during pretraining; alignment objectives typically add little further write-side concentration. We support this explanation with a within-checkpoint trajectory, a graded contrastive-objective control, and a closed-form rank-1 intervention with matched direction controls, providing causal evidence for the proposed weight-space geometry.

Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace interventions (such as activation patching) as a way to simultaneously manipulate model behavior and attribute the features behind it to given subspaces. In this work, we demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability. Counterintuitively, even if a subspace intervention makes the model's output behave as if the value of a feature was changed, this effect may be achieved by activating a dormant parallel pathway leveraging another subspace that is causally disconnected from model outputs. We demonstrate this phenomenon in a distilled mathematical example, in two real-world domains (the indirect object identification task and factual recall), and present evidence for its prevalence in practice. In the context of factual recall, we further show a link to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localization. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (indirect object identification) where prior manual circuit analysis informs an understanding of the location of a feature. We explore the additional evidence needed to argue that a patched subspace is faithful.

Model merging aims to enable multi-task learning by integrating the capabilities of multiple models fine-tuned from the same pre-trained checkpoint into a single model. Its core challenge is inter-task interference among task-specific parameter updates. In this paper, we analyze the output shifts induced by task updates and observe that their energy is concentrated in a small number of principal directions. We call the subspace spanned by these directions the essential subspace. In contrast, most remaining directions carry little task-relevant energy, but their accumulation across multiple task updates can cause severe interference during merging. Motivated by this observation, we propose Essential Subspace Decomposition (ESD), which decomposes each task update according to the principal components of its activation shift. Based on ESD, we introduce Essential Subspace Merging (ESM), a training-free static merging method that orthogonalizes and fuses essential components into one compact multi-task model. We further extend ESM to ESM++, a training-free dynamic merging method that decomposes task-specific residuals into low-rank experts and selects the most relevant expert through prototype-based routing during forward inference. Extensive experiments across multiple task sets and model scales demonstrate that ESM and ESM++ effectively preserves task knowledge while reducing inter-task interference.

In language models, what a representation encodes is determined by the geometry of its representation space: distances, not activations, carry meaning. Existing tools characterize the shape of this geometry but do not ask what that shape is organized for. We introduce Subspace PGA, a metric that tests whether a layer's distance structure aligns with the readout subspace of the unembedding matrix W_U more than with random subspaces of equal size. Across seven Pythia models (70M--6.9B) and three cross-family models, intermediate geometry is significantly organized for prediction (peak z = 9--24), but the degree is scale-dependent: small models (d leq 1024) progressively lose it at late layers during training -- even as loss keeps improving -- while large models (d geq 2048) preserve it throughout. We trace this to a capacity trade-off: a few dominant directions migrate away from W_U's readout, masking rather than destroying the predictive structure beneath, and removing them restores alignment. Neither spectral metrics nor loss curves capture this distinction. Scale thus determines not only how well a model predicts, but how its representation geometry is organized to do so.

Low-Rank Adaptation (LoRA) merging can efficiently combine diverse generative capabilities from multiple trained LoRAs for a diffusion model. However, existing LoRA merging techniques often suffer from severe parameter interference, causing destructive collisions in the shared parameter space. To address this, we propose Subspace Signal Routing (SSR), which resolves interference by routing internal signals instead of performing parameter-space merge. Specifically, SSR first constructs a unified subspace by concatenating candidate LoRAs along the rank dimension. Next, SSR employs an inverse correlation matrix to decorrelate mixed signals within this space. Finally, a directional guide matrix steers these purified signals into their respective task-specific subspaces. We provide a rigorous theoretical analysis proving that SSR aligns with the Ordinary Least Squares (OLS) solution, thereby ensuring mathematical optimality. We utilize the additivity of sufficient statistics to design a streaming algorithm. This enables on-the-fly updates that significantly reduce memory overhead and computation time. Extensive experiments validate that SSR significantly outperforms state-of-the-art methods while maintaining comparable efficiency. Code is available at https://github.com/nagara214/SSR-Merge.

Biologically-informed neural networks typically leverage pathway annotations to enhance performance in biomedical applications. We hypothesized that the benefits of pathway integration does not arise from its biological relevance, but rather from the sparsity it introduces. We conducted a comprehensive analysis of all relevant pathway-based neural network models for predictive tasks, critically evaluating each study's contributions. From this review, we curated a subset of methods for which the source code was publicly available. The comparison of the biologically informed state-of-the-art deep learning models and their randomized counterparts showed that models based on randomized information performed equally well as biologically informed ones across different metrics and datasets. Notably, in 3 out of the 15 analyzed models, the randomized versions even outperformed their biologically informed counterparts. Moreover, pathway-informed models did not show any clear advantage in interpretability, as randomized models were still able to identify relevant disease biomarkers despite lacking explicit pathway information. Our findings suggest that pathway annotations may be too noisy or inadequately explored by current methods. Therefore, we propose a methodology that can be applied to different domains and can serve as a robust benchmark for systematically comparing novel pathway-informed models against their randomized counterparts. This approach enables researchers to rigorously determine whether observed performance improvements can be attributed to biological insights.

Vision-Language Models require efficient adaptation to continually emerging downstream tasks. While Parameter-Efficient Fine-Tuning mitigates catastrophic forgetting, assigning isolated modules per task leads to parameter explosion. Conversely, recent similarity-driven sharing mechanisms falsely equate superficial visual similarity with underlying alignment consistency. This fundamental mismatch triggers severe negative transfer between visually similar but logically distinct tasks and fails to exploit alignment reuse across visually diverse ones. We argue thatalignment sharing is fundamentally a geometric problem of overlapping optimization trajectories within shared low-rank subspaces. Grounded in this insight, we propose iGSP, a novel framework that achieves efficient adaptation via implicit gradient subspace projection. Leveraging the early convergence of MoE routers to establish the subspace basis, iGSP bifurcates the adaptation process into two phases. First, the Subspace Identification phase introduces candidate experts via basis pre-expansion, applies a novel subspace-constrained regularization to implicitly project new task gradients onto the historical subspace, and precisely prunes redundant dimensions by treating routing probabilities as gradient flow indicators, ultimately to maximize knowledge reuse. Second, the Orthogonal Subspace Fine-Tuning phase fixes this structural basis and removes the regularization to rapidly fit the task-specific residual loss. Extensive experiments on the MTIL benchmark demonstrate that iGSP achieves state-of-the-art accuracy while significantly improving training efficiency, reducing the average trainable parameters by 42.7\% compared to current SOTA methods, and decreasing the final total parameters by 86.9\% relative to counterparts. The source code is available at https://github.com/GeoX-Lab/iGSP.

Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.

Mixture-of-Experts (MoE) scales model capacity efficiently by selectively routing inputs to a specialized subset of experts. However, input-expert specialization, the core motivation of MoE, critically depends on whether the router is actually aware of input structure. In practice, MoE routing is typically implemented as a shallow linear projection with limited awareness of input representation, which often leads to unstable routing. We propose STAR, a Structure Aware Routing that rethinks MoE routing as a subspace learning problem by augmenting standard learnable routing with an evolving principal subspace that tracks dominant input structure via Generalized Hebbian Algorithm (GHA). By aligning routing decisions directly with input structure, STAR enables stable expert specialization. We evaluate STAR on controlled synthetic setup and large-scale language and vision tasks, where it consistently improves routing quality and downstream performance over strong MoE baselines. Moreover, optional test-time subspace updates further enhance routing robustness and generalization under input distribution shifts.

Large Language Models (LLMs) rely on safety alignment to produce socially acceptable responses. This is typically achieved through instruction tuning and reinforcement learning from human feedback. However, this alignment is known to be brittle: further fine-tuning, even on benign or lightly contaminated data, can degrade safety and reintroduce harmful behaviors. A growing body of work suggests that alignment may correspond to identifiable geometric directions in weight space, forming subspaces that could, in principle, be isolated or preserved to defend against misalignment. In this work, we conduct a comprehensive empirical study of this geometric perspective. We examine whether safety-relevant behavior is concentrated in specific subspaces, whether it can be separated from general-purpose learning, and whether harmfulness arises from distinguishable patterns in internal representations. Across both parameter and activation space, our findings are consistent: subspaces that amplify safe behaviors also amplify unsafe ones, and prompts with different safety implications activate overlapping representations. We find no evidence of a subspace that selectively governs safety. These results challenge the assumption that alignment is geometrically localized. Rather than residing in distinct directions, safety appears to emerge from entangled, high-impact components of the model's broader learning dynamics. This suggests that subspace-based defenses may face fundamental limitations and underscores the need for alternative strategies to preserve alignment under continued training. We corroborate these findings through multiple experiments on five open-source LLMs. Our code is publicly available at: https://github.com/CERT-Lab/safety-subspaces.

Current unlearning and safety training methods consistently fail to remove dangerous knowledge from language models. We identify the root cause - unlearning targets representations which are too general - and develop a highly selective technique that unlearns robustly while preserving general performance. Our method performs PCA on activations and module-output gradients to identify subspaces containing common representations, then collapses these subspaces before computing unlearning updates, a technique we term Collapse of Irrelevant Representations (CIR). This avoids unlearning general knowledge and targets only representations specific to the facts being unlearned. When unlearning bio- and cyber-hazardous facts from Llama-3.1-8B, we achieve over 30x greater reduction in post-attack accuracy than the best baseline (Circuit Breakers), while disrupting general performance 30x less, and using less than 3 GPU-seconds per fact. Thus, by disentangling harmful and benign capabilities at the level of representations, CIR enables robust and non-disruptive unlearning.

Sparse mixture-of-experts (MoE) language models route each token to multiple experts, suggesting a geometric account of their benefit: co-selected experts should contribute distinct representation directions. Existing evidence often conflates route coherence, candidate quality, and candidate-by-context interaction. We distinguish these quantities using an Expert Subspace Separation Index (ESSI), matched-route residuals, and a prefix-controlled 2times2 factorial; frozen-route interventions and a controlled Top-k study assess functional value. Three paired contrasts organize the findings. First, across six MoE architectures, expert subspaces overlap substantially, yet actual routes explain token representations better than matched alternatives. Second, across the 39 factorial cells in OLMoE, Mixtral, and DeepSeek, the selected candidate explains more of the residual representation than the strongest unselected rival in every cell, yet the actual prefix narrows this advantage throughout: all interactions are negative, and every 95% confidence interval lies below zero. Third, this geometric narrowing does not imply functional redundancy: adding later experts improves next-token prediction in 24 of 39 frozen-route comparisons, while the other 15 estimates are inconclusive; a controlled training study also favors Top-2 over Top-1 in all three seeds. We call this joint pattern coherent overlap: routing selects token-relevant experts from a shared geometric neighborhood, while useful multi-expert computation persists without disjoint linear coverage. Separating these quantities clarifies why geometric similarity alone cannot determine redundancy or pruning value.

Training large language models (LLMs) is constrained by memory requirements, with activations accounting for a substantial fraction of the total footprint. Existing approaches reduce memory using low-rank weight parameterizations or low-rank gradient subspaces for optimizer states, while activation memory is addressed through architectural modifications or compression schemes based on periodically updated projections. We propose OASIS, an online activation subspace learning algorithm for memory-efficient training that tracks and continuously updates a low-dimensional activation subspace during training. Intermediate activations are projected onto this evolving subspace, reducing memory without modifying forward-pass computations. The evolving activation subspace induces low-rank gradient representations, enabling both gradients and optimizer states to be maintained directly in this subspace, while a projection-aware optimizer consistently transports optimizer states across subspace updates for stable training. Across various finetuning and pretraining tasks, OASIS achieves up to 2times lower peak memory than full fine-tuning while matching its performance and outperforming prior low-rank methods.

Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33\% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3\times speedup over 16-bit baseline. Code is available at https://github.com/utkarsh-dmx/project-resq.

Activation steering offers a promising approach to controlling the behavior of Large Language Models by directly manipulating their internal activations. However, most existing methods struggle to jointly steer multiple attributes, often resulting in interference and undesirable trade-offs. To address this challenge, we propose Multi-Subspace Representation Steering (MSRS), a novel framework for effective multi-attribute steering via subspace representation fine-tuning. MSRS reduces inter-attribute interference by allocating orthogonal subspaces to each attribute, isolating their influence within the model's representation space. MSRS also incorporates a hybrid subspace composition strategy: it combines attribute-specific subspaces for unique steering directions with a shared subspace for common steering directions. A dynamic weighting function learns to efficiently integrate these components for precise control. During inference, MSRS introduces a token-level steering mechanism that dynamically identifies and intervenes on the most semantically relevant tokens, enabling fine-grained behavioral modulation. Experimental results show that MSRS significantly reduces attribute conflicts, surpasses existing methods across a range of attributes, and generalizes effectively to diverse downstream tasks.

Model merging aims to integrate multiple task-specific fine-tuned models derived from a shared pre-trained checkpoint into a single multi-task model without additional training. Despite extensive research, task interference remains a major obstacle that often undermines the performance of merged models. In this paper, we propose ESM (Essential Subspace Merging) , a robust framework for effective model merging. We begin by performing Principal Component Analysis (PCA) on feature shifts induced by parameter updates. The resulting principal directions span an essential subspace that dominantly influences feature representations. Each task's parameter update matrix is projected onto its respective essential subspace for low-rank decomposition before merging. This methodology mitigates inter-task interference while preserving core task-specific functionality. Furthermore, we introduce a multi-level polarized scaling strategy that amplifies parameters containing critical knowledge and suppresses redundant ones, preventing essential knowledge from being overwhelmed during fusion. Extensive experiments across multiple task sets and model scales demonstrate that our method achieves state-of-the-art performance in multi-task model merging.

Mixture-of-Experts (MoE) architectures achieve parameter efficiency through conditional computation, yet contemporary designs suffer from two fundamental limitations: structural parameter isolation that causes catastrophic forgetting, and instruction-overfitting that degrades performance in instruction-free scenarios. We propose CDSP-MoE (Conflict-Driven Subspace Pruning MoE), a framework that addresses these issues through a paradigm shift from isolated expert containers to dynamic expert instantiation within a shared physical subspace. Grounded in the Universal Weight Subspace Hypothesis, CDSP-MoE maintains a super-complete parameter backbone where logical experts are carved out via learnable topology masks. Unlike prior work that uses gradient conflict for token reassignment or optimization surgery, we leverage it as a structural supervisory signal: a Lagged Gradient Game penalizes interfering connections in the shared manifold, enabling the topology to spontaneously prune conflicting pathways and evolve interpretable modular structures. Experimental results demonstrate that CDSP-MoE achieves robust content-driven routing without human-defined task labels, maintaining semantic specialization even under strict blind inference protocols where explicit instructions are absent. Code is available at: https://github.com/konodiodaaaaa1/Conflict-Driven-Subspace-Pruning-Mixture-of-Experts

Activation decomposition methods in language models are tightly coupled to geometric assumptions on how concepts are realized in activation space. Existing approaches search for individual global directions, implicitly assuming linear separability, which overlooks concepts with nonlinear or multi-dimensional structure. In this work, we leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space as a collection of Gaussian regions with their local covariance structure. MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid. We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space. Moreover, evaluations on localization and steering benchmarks show that MFA outperforms unsupervised baselines, is competitive with supervised localization methods, and often achieves stronger steering performance than sparse autoencoders. Together, our findings position local geometry, expressed through subspaces, as a promising unit of analysis for scalable concept discovery and model control, accounting for complex structures that isolated directions fail to capture.

Mechanistic interpretability aims to understand the behavior of neural networks by reverse-engineering their internal computations. However, current methods struggle to find clear interpretations of neural network activations because a decomposition of activations into computational features is missing. Individual neurons or model components do not cleanly correspond to distinct features or functions. We present a novel interpretability method that aims to overcome this limitation by transforming the activations of the network into a new basis - the Local Interaction Basis (LIB). LIB aims to identify computational features by removing irrelevant activations and interactions. Our method drops irrelevant activation directions and aligns the basis with the singular vectors of the Jacobian matrix between adjacent layers. It also scales features based on their importance for downstream computation, producing an interaction graph that shows all computationally-relevant features and interactions in a model. We evaluate the effectiveness of LIB on modular addition and CIFAR-10 models, finding that it identifies more computationally-relevant features that interact more sparsely, compared to principal component analysis. However, LIB does not yield substantial improvements in interpretability or interaction sparsity when applied to language models. We conclude that LIB is a promising theory-driven approach for analyzing neural networks, but in its current form is not applicable to large language models.

We generalize the class vectors found in neural networks to linear subspaces (i.e.~points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables the simultaneous improvement in accuracy and feature transferability. In GCR, each class is a subspace and the logit is defined as the norm of the projection of a feature onto the class subspace. We integrate Riemannian SGD into deep learning frameworks such that class subspaces in a Grassmannian are jointly optimized with the rest model parameters. Compared to the vector form, the representative capability of subspaces is more powerful. We show that on ImageNet-1K, the top-1 error of ResNet50-D, ResNeXt50, Swin-T and Deit3-S are reduced by 5.6%, 4.5%, 3.0% and 3.5%, respectively. Subspaces also provide freedom for features to vary and we observed that the intra-class feature variability grows when the subspace dimension increases. Consequently, we found the quality of GCR features is better for downstream tasks. For ResNet50-D, the average linear transfer accuracy across 6 datasets improves from 77.98% to 79.70% compared to the strong baseline of vanilla softmax. For Swin-T, it improves from 81.5% to 83.4% and for Deit3, it improves from 73.8% to 81.4%. With these encouraging results, we believe that more applications could benefit from the Grassmann class representation. Code is released at https://github.com/innerlee/GCR.

Predicting spatial gene expression from H&E histology offers a scalable and clinically accessible alternative to sequencing, but realizing clinical impact requires models that generalize across cancer types and capture biologically coherent signals. Prior work is often limited to per-cancer settings and variance-based evaluation, leaving functional relevance underexplored. We introduce HistoPrism, an efficient transformer-based architecture for pan-cancer prediction of gene expression from histology. To evaluate biological meaning, we introduce a pathway-level benchmark, shifting assessment from isolated gene-level variance to coherent functional pathways. HistoPrism not only surpasses prior state-of-the-art models on highly variable genes , but also more importantly, achieves substantial gains on pathway-level prediction, demonstrating its ability to recover biologically coherent transcriptomic patterns. With strong pan-cancer generalization and improved efficiency, HistoPrism establishes a new standard for clinically relevant transcriptomic modeling from routinely available histology.

The integration of histology images and gene profiles has shown great promise for improving survival prediction in cancer. However, current approaches often struggle to model intra- and inter-modal interactions efficiently and effectively due to the high dimensionality and complexity of the inputs. A major challenge is capturing critical prognostic events that, though few, underlie the complexity of the observed inputs and largely determine patient outcomes. These events, manifested as high-level structural signals such as spatial histologic patterns or pathway co-activations, are typically sparse, patient-specific, and unannotated, making them inherently difficult to uncover. To address this, we propose SlotSPE, a slot-based framework for structural prognostic event modeling. Specifically, inspired by the principle of factorial coding, we compress each patient's multimodal inputs into compact, modality-specific sets of mutually distinctive slots using slot attention. By leveraging these slot representations as encodings for prognostic events, our framework enables both efficient and effective modeling of complex intra- and inter-modal interactions, while also facilitating seamless incorporation of biological priors that enhance prognostic relevance. Extensive experiments on ten cancer benchmarks show that SlotSPE outperforms existing methods in 8 out of 10 cohorts, achieving an overall improvement of 2.9%. It remains robust under missing genomic data and delivers markedly improved interpretability through structured event decomposition.

We introduce ProtoPathway, an interpretable-by-design multimodal framework for cancer survival prediction that unifies whole slide imaging and transcriptomics through encoders producing biologically grounded representations on both sides of the fusion. On the histopathology side, K learnable morphological prototypes, trained end-to-end with the survival objective, serve as the slide representation itself: patches flow into prototype tokens via soft assignment, compressing variable-length patch sets into fixed task-adaptive tokens. On the genomic side, a bipartite graph neural network encodes gene expression within the Reactome pathway hierarchy, producing pathway embeddings that reflect both constituent genes and their broader biological context through bidirectional message passing over a shared gene--pathway graph. Cross-modal attention then operates over a compact prototype times pathway matrix in which prototypes query pathways, modeling the biological direction in which molecular programs give rise to tissue morphology. Because both axes carry stable task-learned identity, the attention matrix is itself an interpretability output, yielding native inference-time attribution across the full biological hierarchy, from genes through pathways and prototypes to spatial tissue maps. We evaluate on five TCGA cancer cohorts, demonstrating competitive or superior survival prediction with substantially improved biological interpretability and reduced computational cost, with interpretability claims validated through fold-stratified rank-based population-level analysis. Our source code, model weights, and Reactome pathways, together with a unified codebase reimplementing all multimodal survival baselines under identical preprocessing and evaluation, are available at: https://github.com/AmayaGS/ProtoPathway.

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

We introduce Exemplar Partitioning (EP), an unsupervised method for constructing interpretable feature dictionaries from large language model activations with sim 10^3times fewer tokens than comparable sparse autoencoders (SAEs). An EP dictionary is a Voronoi partition of activation space, built by leader-clustering streamed activations within a distance threshold. Each region is anchored by an observed exemplar that serves as both its membership criterion and intervention direction; dictionary size is not prespecified, but determined by the activation geometry at that threshold. Because exemplars are observed rather than learned, dictionaries built from the same data stream are directly comparable across layers, models, and training checkpoints. We characterise EP as an interpretability object via targeted demonstrations of properties newly accessible through this construction, plus one head-to-head benchmark. In Gemma-2-2B, EP dictionary regions are interpretable and support causal interventions: refusal in instruction-tuned Gemma concentrates in a region whose exemplar ablation can collapse held-out refusal. Cross-checkpoint matching between base and instruction-tuned dictionaries separates the directions preserved through finetuning from those introduced by it. EP regions and Gemma Scope SAE features decompose activation space differently but agree on a shared core: sim20% of EP regions match an SAE feature at F_1 > 0.5, and EP one-hot probes retain sim97% of raw-activation probe accuracy at ell_0 = 1. Nearest-exemplar distance provides a free out-of-distribution signal at inference. On AxBench latent concept detection at Gemma-2-2B-it L20, EP at p_1 reaches mean AUROC 0.881, +0.126 over the canonical GemmaScope SAE leaderboard entry and within 0.030 of SAE-A's 0.911, at sim 10^3times less build compute.

Detecting visual anomalies in industrial inspection often requires training with only a few normal images per category. Recent few-shot methods achieve strong results employing foundation-model features, but typically rely on memory banks, auxiliary datasets, or multi-modal tuning of vision-language models. We therefore question whether such complexity is necessary given the feature representations of vision foundation models. To answer this question, we introduce SubspaceAD, a training-free method, that operates in two simple stages. First, patch-level features are extracted from a small set of normal images by a frozen DINOv2 backbone. Second, a Principal Component Analysis (PCA) model is fit to these features to estimate the low-dimensional subspace of normal variations. At inference, anomalies are detected via the reconstruction residual with respect to this subspace, producing interpretable and statistically grounded anomaly scores. Despite its simplicity, SubspaceAD achieves state-of-the-art performance across one-shot and few-shot settings without training, prompt tuning, or memory banks. In the one-shot anomaly detection setting, SubspaceAD achieves image-level and pixel-level AUROC of 97.1% and 97.5% on the MVTec-AD dataset, and 93.4% and 98.2% on the VisA dataset, respectively, surpassing prior state-of-the-art results. Code and demo are available at https://github.com/CLendering/SubspaceAD.

Traditional white-box methods for creating adversarial perturbations against LLMs typically rely only on gradient computation from the targeted model, ignoring the internal mechanisms responsible for attack success or failure. Conversely, interpretability studies that analyze these internal mechanisms lack practical applications beyond runtime interventions. We bridge this gap by introducing a novel white-box approach that leverages mechanistic interpretability techniques to craft practical adversarial inputs. Specifically, we first identify acceptance subspaces - sets of feature vectors that do not trigger the model's refusal mechanisms - then use gradient-based optimization to reroute embeddings from refusal subspaces to acceptance subspaces, effectively achieving jailbreaks. This targeted approach significantly reduces computation cost, achieving attack success rates of 80-95\% on state-of-the-art models including Gemma2, Llama3.2, and Qwen2.5 within minutes or even seconds, compared to existing techniques that often fail or require hours of computation. We believe this approach opens a new direction for both attack research and defense development. Furthermore, it showcases a practical application of mechanistic interpretability where other methods are less efficient, which highlights its utility. The code and generated datasets are available at https://github.com/Sckathach/subspace-rerouting.

Artificial Intelligence Virtual Cells (AIVCs) aim to learn executable, decision-relevant models of cell state from multimodal, multiscale measurements. Recent studies have introduced single-cell and spatial foundation models, improved cross-modality alignment, scaled perturbation atlases, and explored pathway-level readouts. Nevertheless, although held-out validation is standard practice, evaluations remain predominantly within single datasets and settings; evidence indicates that transport across laboratories and platforms is often limited, that some data splits are vulnerable to leakage and coverage bias, and that dose, time and combination effects are not yet systematically handled. Cross-scale coupling also remains constrained, as anchors linking molecular, cellular and tissue levels are sparse, and alignment to scientific or clinical readouts varies across studies. We propose a model-agnostic Cell-State Latent (CSL) perspective that organizes learning via an operator grammar: measurement, lift/project for cross-scale coupling, and intervention for dosing and scheduling. This view motivates a decision-aligned evaluation blueprint across modality, scale, context and intervention, and emphasizes function-space readouts such as pathway activity, spatial neighborhoods and clinically relevant endpoints. We recommend operator-aware data design, leakage-resistant partitions, and transparent calibration and reporting to enable reproducible, like-for-like comparisons.

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

Synthetic gene expression data is increasingly proposed as a privacy-preserving substitute for controlled-access genomic repositories, but its safety depends on empirical auditing. Membership inference attacks (MIAs) provide that audit by testing whether a patient's gene expression profile was used to train a generative model. We report a red-team study on synthetic gene expression data derived from bulk RNA-seq profiles in The Cancer Genome Atlas, released by the ELSA Health 2026 Challenge. We unify five no-box attacks under a single weighted-distance framework in which each variant differs only in how it weights genes: uniformly (baseline), by variance, by synthetic-versus-reference KL divergence, by spectral residualization removing dominant principal components, and by curated pathway membership. Against a conditional variational autoencoder, spectral residualization raises AUC from 0.8251 to 0.8951 and TPR at 1% FPR from 0.3842 to 0.5970 on pan-cancer TCGA. Biological pathway priors did not transfer across targets.

Sparse Autoencoders (SAEs) are widely used for mechanistic interpretability in large language models, yet their formulation assigns each latent feature a single decoder direction, implicitly assuming features to be one-dimensional. We show that this assumption mismatches with the multi-dimensional structure of model features, provably inducing feature splitting through two distinct mechanisms. Geometrically, reconstructing a feature of intrinsic dimension d_i ge 2 to error varepsilon with single-direction decoders forces a number of atoms that is exponential in d_i. From an end-to-end optimization perspective, this splitting is not merely possible but actively preferred. We prove that there exists a continuous path from the true d_i-dimensional basis to a strictly lower risk of the ell_1-regularized SAE objective, whose descent directions drive any trained dictionary into that exponential regime. A single coherent feature is therefore fragmented across many near-collinear latents, producing spurious multiplicity and obscuring the intrinsic geometry. Motivated by this, we introduce Subspace-Aware Sparse Autoencoders (SASA), which replace single-vector decoders with learned decoder subspaces, enforce block sparsity via Top-s group gating, and adapt each group's effective rank with a nuclear-norm regularizer. We then show that once the block size satisfies r ge d_i, a single group not only can represent the entire feature slice but is the global minimizer of the SASA objective. This consolidation yields a sample complexity polynomial in d_i rather than exponential -- a decisive advantage given that every training activation costs an LLM forward pass. Empirically, on GPT-2 and Mistral-7B, SASA reduces feature splitting and absorption, improves monosemanticity and interpretability, and matches or exceeds standard SAEs while training on roughly half the token budget.

Diffusion and flow-matching schedules control the signal and noise coefficients that mix data and noise along affine probability paths. Minimizing a kinetic action defined on coefficient paths, motivated by optimal transport, helps explain strong baselines but remains model-agnostic and ignores prediction error. Here we introduce a model-aware schedule construction based on fiberwise optimal transport. At a fixed time and state on the probability path, compatible signal/noise decompositions form an affine fiber. We define a fiberwise prediction risk by averaging optimal-transport costs between the true and predictor-induced decompositions within these fibers. On a fixed coefficient curve, combining this risk with coefficient-path kinetic action yields a closed-form optimal time allocation. This construction extends to general linear prediction targets, and the risk profile can be estimated from an early baseline checkpoint. We evaluate DDPMs and flow matching across prediction targets, training configurations, risk-estimation checkpoints, datasets, and architectures. Our model-aware schedules consistently outperform strong baselines, including a 38.6% relative FID reduction for flow matching on CIFAR-10 at 16 function evaluations. Each model-agnostic kinetic baseline determines its own kinetic reference coordinate. In these coordinates, fiberwise-risk profiles from independently trained models in different settings align closely after normalization to unit area. The resulting schedule deformations used in training also align, suggesting empirical universality across the evaluated models and settings. Pretrained-checkpoint diagnostics extend this normalized-risk agreement to larger conditional latent diffusion and 2-RF models. A frozen analytic allocation template retains most of the model-aware improvement without further risk estimation or model-specific fitting.

We present a method for diagnosing interpretation in neural networks by identifying an input subspace where a proposed interpretation is highly faithful. Our method is particularly useful for causal-abstraction-style interpretability, where a high-level causal hypothesis is evaluated by interchange interventions. Rather than treating interchange intervention accuracy as a single global summary, we refine this framework by partitioning the input space into well-interpreted and under-interpreted regions according to pairwise interchange-intervention behavior. This turns causal abstraction from a purely global evaluation into a more diagnostic tool: it not only measures whether an interpretation works, but also reveals where it works, where it fails, and what distinguishes the two cases. This diagnostic view also provides practical heuristics for improving interpretations. By analyzing the structure of the well-interpreted and under-interpreted regions, we can identify missing distinctions in a high-level hypothesis, discover previously unmodeled intermediate variables, and combine complementary partial interpretations into a stronger one. We instantiate this idea as a simple four-step recipe and show that it yields informative error analyses across multiple causal abstraction settings. In a toy logic task, recursively applying the recipe recovers a high-level hypothesis from scratch. More broadly, our results suggest that partitioning the input space is a useful step toward more precise, constructive, and scalable mechanistic interpretability.

Reinforcement learning (RL) has become a key paradigm for enhancing the reasoning of large language models, yet the high dimensionality of parameter updates makes its training dynamics hard to analyze. We study reinforcement learning with verifiable rewards (RLVR) and use vector steering to identify a low-dimensional effective manifold in activation space associated with RL-induced gains. We uncover two geometric properties. (1) Effective Manifold Capacity: the capacity needed to reproduce RL gains can be very small but is not infinitely compressible; at extremely low capacity, intervention dimensionality and input-dependent expressiveness become key constraints, and this requirement varies with injection depth. (2) Control Manifold Separation: effective control directions lie mainly in the low-variance complement of the activation principal subspace. Within a task and base model, the learned geometry stays largely consistent across training configurations, and across tasks geometric alignment correlates with capability transfer. Experiments on 5 LLMs and 6 verifiable-reward tasks support these findings. We then propose Alpha-Stabler, a plug-and-play framework with a Predictor that monitors principal-subspace intrusion for early collapse warnings, and a Controller that removes the principal-subspace component of activation gradients during backpropagation while preserving the orthogonal complement. Alpha-Stabler stabilizes training for 2,000 steps and consistently improves RL gains, offering practical insights for robust post-training. Code: https://github.com/caiyuchen-ustc/On_Policy_Vector_Training

While transformer models are widely believed to operate in high-dimensional hidden spaces, we show that attention outputs are confined to a surprisingly low-dimensional subspace, where about 60\% of the directions account for 99\% of the variance--a phenomenon that is induced by the attention output projection matrix and consistently observed across diverse model families and datasets. Critically, we find this low-rank structure as a fundamental cause of the prevalent dead feature problem in sparse dictionary learning, where it creates a mismatch between randomly initialized features and the intrinsic geometry of the activation space. Building on this insight, we propose a subspace-constrained training method for sparse autoencoders (SAEs), initializing feature directions into the active subspace of activations. Our approach reduces dead features from 87\% to below 1\% in Attention Output SAEs with 1M features, and can further extend to other sparse dictionary learning methods. Our findings provide both new insights into the geometry of attention and practical tools for improving sparse dictionary learning in large language models.

Recent advances in large language models (LLMs) have intensified the need to understand and reliably curb their harmful behaviours. We introduce a multidimensional framework for probing and steering harmful content in model internals. For each of 55 distinct harmfulness subconcepts (e.g., racial hate, employment scams, weapons), we learn a linear probe, yielding 55 interpretable directions in activation space. Collectively, these directions span a harmfulness subspace that we show is strikingly low-rank. We then test ablation of the entire subspace from model internals, as well as steering and ablation in the subspace's dominant direction. We find that dominant direction steering allows for near elimination of harmfulness with a low decrease in utility. Our findings advance the emerging view that concept subspaces provide a scalable lens on LLM behaviour and offer practical tools for the community to audit and harden future generations of language models.

Auxiliary signal pathways in VLMs are routinely fitted with learnable gates so the optimiser can decide how much of the signal to admit. We find that the optimiser almost always decides on zero: across five injection designs, every gated pathway becomes behaviourally closed, with accuracy invariant to ablating the pathway at inference even when the gate parameter would nominally pass 30-45% of the signal. We attribute this suppression phenomenon to two regimes, a dead-gradient regime formalised through the caption-invariance of image-derived signals, and a negative-utility regime in which the auxiliary signal actively hurts the loss. Rather than fight suppression, we exploit it: we regularise LoRA fine-tuning with geometric auxiliary losses from hyperbolic visual relational graphs (IoA-driven entailment cones and angular repulsion on the Lorentz manifold), coupled only through the forward pass at training time and dropped at inference. Disaggregating GQA by question type exposes a clean dissociation. Three configurations without geometric losses at inference lose 2.85-3.39pp on relational questions while gaining ~1pp on attribute questions; a fourth that trains with the losses but infers through a soft prompt loses 5.14pp on rel for only +0.23pp on attr, so training-time regularisation alone does not protect relational accuracy without a geometric inference pathway. Configurations that keep the geometric pathway at inference preserve vanilla-level relational accuracy and match the attribute gain. Out of distribution on VSR, the RMS-prefix recipe preserves the spatial signal; stripping the geometric losses (G2) collapses VSR by 4.6pp, isolating them as the OOD source. A secondary result: embedding-norm alignment is necessary for generation-safe prefix injection, and learnable gates should be replaced with fixed, non-optional injection at matched scales.

Predicting enzyme kinetic parameters quantifies how efficiently an enzyme catalyzes a specific substrate under defined biochemical conditions. Canonical parameters such as the turnover number (k_cat), Michaelis constant (K_m), and inhibition constant (K_i) depend jointly on the enzyme sequence, the substrate chemistry, and the conformational adaptation of the active site during binding. Many learning pipelines simplify this process to a static compatibility problem between the enzyme and substrate, fusing their representations through shallow operations and regressing a single value. Such formulations overlook the staged nature of catalysis, which involves both substrate recognition and conformational adaptation. In this regard, we reformulate kinetic prediction as a staged multimodal conditional modeling problem and introduce the Enzyme-Reaction Bridging Adapter (ERBA), which injects cross-modal information via fine-tuning into Protein Language Models (PLMs) while preserving their biochemical priors. ERBA performs conditioning in two stages: Molecular Recognition Cross-Attention (MRCA) first injects substrate information into the enzyme representation to capture specificity; Geometry-aware Mixture-of-Experts (G-MoE) then integrates active-site structure and routes samples to pocket-specialized experts to reflect induced fit. To maintain semantic fidelity, Enzyme-Substrate Distribution Alignment (ESDA) enforces distributional consistency within the PLM manifold in a reproducing kernel Hilbert space. Experiments across three kinetic endpoints and multiple PLM backbones, ERBA delivers consistent gains and stronger out-of-distribution performance compared with sequence-only and shallow-fusion baselines, offering a biologically grounded route to scalable kinetic prediction and a foundation for adding cofactors, mutations, and time-resolved structural cues.

Large-scale text-to-image diffusion models excel in generating high-quality images from textual inputs, yet concerns arise as research indicates their tendency to memorize and replicate training data, raising We also addressed the issue of memorization in diffusion models, where models tend to replicate exact training samples raising copyright infringement and privacy issues. Efforts within the text-to-image community to address memorization explore causes such as data duplication, replicated captions, or trigger tokens, proposing per-prompt inference-time or training-time mitigation strategies. In this paper, we focus on the feed-forward layers and begin by contrasting neuron activations of a set of memorized and non-memorized prompts. Experiments reveal a surprising finding: many different sets of memorized prompts significantly activate a common subspace in the model, demonstrating, for the first time, that memorization in the diffusion models lies in a special subspace. Subsequently, we introduce a novel post-hoc method for editing pre-trained models, whereby memorization is mitigated through the straightforward pruning of weights in specialized subspaces, avoiding the need to disrupt the training or inference process as seen in prior research. Finally, we demonstrate the robustness of the pruned model against training data extraction attacks, thereby unveiling new avenues for a practical and one-for-all solution to memorization.

Genetic pathways usually encode molecular mechanisms that can inform targeted interventions. It is often challenging for existing machine learning approaches to jointly model genetic pathways (higher-order features) and variants (atomic features), and present to clinicians interpretable models. In order to build more accurate and better interpretable machine learning models for genetic medicine, we introduce Pathway Augmented Nonnegative Tensor factorization for HighER-order feature learning (PANTHER). PANTHER selects informative genetic pathways that directly encode molecular mechanisms. We apply genetically motivated constrained tensor factorization to group pathways in a way that reflects molecular mechanism interactions. We then train a softmax classifier for disease types using the identified pathway groups. We evaluated PANTHER against multiple state-of-the-art constrained tensor/matrix factorization models, as well as group guided and Bayesian hierarchical models. PANTHER outperforms all state-of-the-art comparison models significantly (p<0.05). Our experiments on large scale Next Generation Sequencing (NGS) and whole-genome genotyping datasets also demonstrated wide applicability of PANTHER. We performed feature analysis in predicting disease types, which suggested insights and benefits of the identified pathway groups.

Deep subspace clustering (DSC) networks based on self-expressive model learn representation matrix, often implemented in terms of fully connected network, in the embedded space. After the learning is finished, representation matrix is used by spectral clustering module to assign labels to clusters. However, such approach ignores complementary information that exist in other layers of the encoder (including the input data themselves). Herein, we apply selected linear subspace clustering algorithm to learn representation matrices from representations learned by all layers of encoder network including the input data. Afterward, we learn a multilayer graph that in a multi-view like manner integrates information from graph Laplacians of all used layers. That improves further performance of selected DSC network. Furthermore, we also provide formulation of our approach to cluster out-of-sample/test data points. We validate proposed approach on four well-known datasets with two DSC networks as baseline models. In almost all the cases, proposed approach achieved statistically significant improvement in three performance metrics. MATLAB code of proposed algorithm is posted on https://github.com/lovro-sinda/MLG-DSC.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle (<5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

Large language models (LLMs) store vast amounts of information, making them powerful yet raising privacy and safety concerns when selective knowledge removal is required. Existing unlearning strategies, ranging from gradient-based fine-tuning and model editing to sparse autoencoder (SAE) steering, either lack interpretability or fail to provide a robust defense against adversarial prompts. We propose SAE-Guided Subspace Projection Unlearning (SSPU), a novel framework that leverages SAE features to drive targeted updates in the model's parameter space, enabling precise, interpretable, and robust unlearning. SSPU's three-stage pipeline performs data-driven layer and feature selection, subspace construction via QR decomposition, and constrained optimization that controls activations into an "irrelevant" subspace while preserving retained knowledge. Overall, we use SAE features to construct a subspace that supervises unlearning, refining the loss and adding a regularization term to guide interpretable parameter updates. In experiments on the WMDP-Cyber forget set and three utility benchmarks (MMLU, TruthfulQA, GSM8K), SSPU reduces harmful knowledge accuracy by 3.22% compared to the strongest baseline. It also improves adversarial robustness, lowering malicious accuracy under jailbreak prompts compared to baselines. Our findings expose the limitations of prior unlearning methods and demonstrate how interpretable subspace-guided optimization can achieve robust, controllable model behavior.

Predicting spatial gene expression from hematoxylin and eosin (H\&E)-stained images offers a cost-effective alternative to spatial transcriptomics (ST). However, existing methods treat H\&E images as generic visual inputs and ignore their intrinsic biological hierarchy, where spatially organized cell types collectively form functional tissue microenvironments that govern local gene expression programs. To bridge this gap, we formulate H\&E-to-ST prediction as a cross-modal semantic translation task and propose Path2ST, a hierarchically grounded autoregressive framework featuring three key components: (i) a Hierarchical Cell-Tissue Conditioning mechanism that fuses explicit and implicit cellular features with tissue-level semantic representations to construct hierarchical conditioning signals; (ii) a Scale-Adaptive Autoregressive Generation process over a hierarchical semantic vocabulary, enabling coarse-to-fine, biologically consistent expression synthesis; and (iii) SpectraLoss, a full-spectrum objective that jointly enforces ordinal fidelity, models transcriptional bursts, and aligns semantic structures with cell types. Extensive experiments on three datasets demonstrate state-of-the-art performance, validating that Path2ST generates highly accurate and spatially coherent transcriptomic profiles. The related code is released at https://github.com/RuochenLiu23/Path2ST.

Arditi et al. (2024) has shown that refusal in safety fine-tuned chat models is mediated by a single linear direction in the residual stream, recoverable by a difference-in-means (DiM) of harmful and harmless activations. We compare DiM-based interventions (activation addition and directional ablation) with two interventions derived from Iterative Nullspace Projection (INLP) -- nullspace projection and counterfactual flipping -- on five open-weight chat models, asking whether INLP can match DiM at steering refusal and whether its richer parameterisation yields more tweakable interventions. INLP counterfactual flipping is competitive with DiM directional ablation on refusal suppression, while nullspace projection is consistently weaker. Restricting INLP to the leading directions of the extracted subspace preserves most of the suppression effect at near-baseline perplexity, giving a tunable capability. Geometrically, the two INLP interventions land in qualitatively different regions of activation space: nullspace projection collapses transformed activations between the harmful and harmless clusters, while counterfactual flipping moves them into the opposite cluster, suggesting that the model encodes the absence of a concept differently from its opposite -- an intriguing distinction that warrants further investigation in future work.

Predicting cellular responses to genetic perturbations helps prioritize experiments in single-cell genomics, where exhaustive measurement is infeasible. While computational models increasingly predict these responses, three evaluation deficiencies obscure what their scores demonstrate. First, absolute metrics cannot separate target-specific predictions from a shared background response. Second, common metrics remain high under gene shuffling, so gene-level accuracy is never verified. Third, a score at one training size says nothing about coverage, which depends on representation-space proximity and response-constraining power. We propose AmbiModBench, a specificity-aware, gene-resolved and coverage-aware benchmark. It pairs every score with a training-mean reference fitted on the same split, screens each readout by gene-coordinate permutation, and links embedding distance to response variation. Across K562, RPE1 and Norman, strong absolute scores largely reflect shared background rather than target-specific learning. Widely used readouts track response magnitude distributions rather than the affected genes. Detectable gain follows representation-space coverage rather than training-set size. Nonetheless, on RPE1 the protocol yields a reproducible target-specific gain across five additional splits and three gene selections, which absolute scores alone cannot distinguish from shared background.

Existing BraTS-GLI datasets provide a widely used benchmark for adult glioma MRI segmentation, but their task definition focuses on tumor subregions and does not systematically represent coexisting white matter hyperintensities (WMH). In joint segmentation settings, such unlabeled abnormalities introduce task-specific label noise by treating pathological regions as normal tissue. To address this limitation, we introduce BraTS-GLI Anatomy-Lesion, a controlled-access, labels-only derived resource built from the BraTS 2023-GLI training cohort. The resource provides 1,251 unified eight-class anatomy-lesion label sets aligned with the original four-modal MRI cases, including image-repair labels for 116 cases requiring repaired imaging inputs. The cohort is organized into a 394-case purified subset and an 857-case extended subset, with case-level metadata covering label source, image-repair requirements, quality-control status, access conditions, checksums, and release boundaries. Compared with the original BraTS-GLI annotations, the resource substantially expands foreground supervision by incorporating healthy brain tissues and previously unlabeled coexisting abnormalities within a unified label space. A validation study using MedNeXt and T1/FLAIR inputs suggests that WMH-aware supervision preserves healthy-tissue segmentation performance across both in-domain GLI and external WMH datasets, while improving sensitivity to coexisting lesions relative to noisy-control training. The resource is intended for scientific research and supports joint anatomy-lesion supervision, label-noise analysis, and reproducible evaluation. Data are available at https://www.synapse.org/Synapse:syn75210889/wiki/, and code is available at https://github.com/xyx200/brats-gli-anatomy-lesion-code. The data resource DOI is https://doi.org/10.7303/SYN75210889.

Merging models fine-tuned from a common, extensively pre-trained large model but specialized for different tasks has been demonstrated as a cheap and scalable strategy to construct a multi-task model that performs well across diverse tasks. Recent research, exemplified by task arithmetic, highlights that this multi-task model can be derived through arithmetic operations on task vectors. Nevertheless, current merging techniques frequently resolve potential conflicts among parameters from task-specific models by evaluating individual attributes, such as the parameters' magnitude or sign, overlooking their collective impact on the overall functionality of the model. In this work, we propose the CONtinuous relaxation of disCRETE (Concrete) subspace learning method to identify a common low-dimensional subspace and utilize its shared information to track the interference problem without sacrificing much performance. Specifically, we model the problem as a bi-level optimization problem and introduce a meta-learning framework to find the Concrete subspace mask through gradient-based techniques. At the upper level, we focus on learning a shared Concrete mask to identify the subspace, while at the inner level, model merging is performed to maximize the performance of the merged model. We conduct extensive experiments on both vision domain and language domain, and the results demonstrate the effectiveness of our method. The code is available at https://github.com/tanganke/subspace_fusion

Large language models (LLMs) handle many tasks with one set of parameters, but under KV-cached inference it is unclear what task-general structure, if any, is used at decode time rather than during prefill. We propose DecodeShare, a protocol that identifies a low-dimensional subspace consistently shared across tasks in decode-time hidden states, and then tests its causal role by removing that subspace only during decoding. In our experiments, disturbing the discovered shared subspace degrades decision performance far more than disturbing either a prefill-derived or random subspace under the same intervention budget. We further show this decode-shared subspace has practical consequences for activation steering: common steering directions can overlap the task-general decode channel. Projecting out this shared subspace directly separates the functional roles of the two components, while evaluating steering vectors at decode-time yields more reliable signal for downstream deployment than prefill-based proxies. Despite its compactness, the shared subspace can serve as a high-leverage causal channel at decode time. Code is available at: https://github.com/Zishan-Shao/decodeshare.git.

Clinical diagnostic workups typically follow a modality escalation pathway: after initial clinical evaluation, clinicians begin with routine structural imaging (e.g., MRI), selectively add sequences such as FLAIR or T2 to refine the differential, and reserve molecular imaging (e.g., amyloid-PET) for cases that remain uncertain after standard evaluation. Consequently, patients are observed with heterogeneous and often incomplete modality subsets. However, most current AI models assume fixed data modalities as the model inputs. In this paper, we present BrainAnytime, a unified pretraining framework pretrained on 34,899 3D brain scans from five datasets that support brain image analysis under arbitrary modality availability spanning multi-sequence MRI and amyloid-PET. A single model accepts whatever imaging is available, from a lone T1 scan to a full multimodal workup. Pretraining learns structural-molecular correspondences between MRI and PET via cross-modal distillation (RCMD) and prioritizes disease-vulnerable anatomy via atlas-guided curriculum masking (PACM), all within a shared 3D masked autoencoder (Multi-MAE3D). Across four downstream tasks and five clinically motivated modality settings, BrainAnytime largely outperforms modality-specific models, missing-modality baselines, and large-scale brain MRI pretrained foundation models on most modality settings. Notably, it surpasses the strongest missing-modality baselines with relative improvements of 6.2% and 7.0% in average accuracy on CN vs. AD and CN vs. MCI classification, respectively. Code is available at https://github.com/SDH-Lab/BrainAnytime.

Directional ablation removes an aligned language model's ability to refuse by projecting a single "refusal direction" out of the weights that write the residual stream. It needs no gradient-based training and no optimization, only a few hundred contrastive prompts, which makes it the canonical white-box attack on open-weight alignment. However, it has been established only on dense models up to roughly 70B parameters. We study whether it survives the shift to frontier mixture-of-experts (MoE) models whose residual streams are no longer a single tensor and whose weights ship quantized. We apply it to GLM-5.3-Flash (320B parameters, 288 routed experts, a four-wide hyper-connection residual, block-FP8). The attack survives the architecture, but what it reaches is no longer where a reader of the original recipe would look for it. Editing the attention, dense and routed-expert writers on their own removes 0.039, 0.016 and 0.148 of refusal respectively; editing all three together removes 0.776. As a result, 74% of the effect exists only under the joint intervention. The part the conventional recipe reaches by module-name matching accounts for 0.066 of that 0.776, which is why it fails silently on an MoE. The effect does not follow from removing just any direction: ablating a random direction orthogonal to it leaves refusal unchanged. A category-concentrated residue survives every edit we tried: subspaces fitted on violence, sexual content and hate leave measurable refusal at every rank from 1 to 12. We report the method, the 41-89 percentage-point reductions it achieves across seven harmful benchmarks with no detected change in capability, and the boundary where it stops.

Large Language Models (LLMs) are powerful text generators, yet they can produce toxic or harmful content even when given seemingly harmless prompts. This presents a serious safety challenge and can cause real-world harm. Toxicity is often subtle and context-dependent, making it difficult to detect at the token level or through coarse sentence-level signals. Moreover, efforts to mitigate toxicity often face a trade-off between safety and the coherence, or fluency of the generated text. In this work, we present a targeted subspace intervention strategy for identifying and suppressing hidden toxic patterns from underlying model representations, while preserving overall ability to generate safe fluent content. On the RealToxicityPrompts, our method achieves strong mitigation performance compared to existing baselines, with minimal impact on inference complexity. Across multiple LLMs, our approach reduces toxicity of state-of-the-art detoxification systems by 8-20%, while maintaining comparable fluency. Through extensive quantitative and qualitative analyses, we show that our approach achieves effective toxicity reduction without impairing generative performance, consistently outperforming existing baselines.

LLMs are multilingual by training, yet their lingua franca is often English, reflecting English language dominance in pretraining. Other languages remain in parametric memory but are systematically suppressed. We argue that language defaultness is governed by a sparse, low-rank control circuit, language neurons, that can be mechanistically isolated and safely steered. We introduce Neural FOXP2, that makes a chosen language (Hindi or Spanish) primary in a model by steering language-specific neurons. Neural FOXP2 proceeds in three stages: (i) Localize: We train per-layer SAEs so each activation decomposes into a small set of active feature components. For every feature, we quantify English vs. Hindi/Spanish selectivity overall logit-mass lift toward the target-language token set. Tracing the top-ranked features back to their strongest contributing units yields a compact language-neuron set. (ii) Steering directions: We localize controllable language-shift geometry via a spectral low-rank analysis. For each layer, we build English to target activation-difference matrices and perform layerwise SVD to extract the dominant singular directions governing language change. The eigengap and effective-rank spectra identify a compact steering subspace and an empirically chosen intervention window (where these directions are strongest and most stable). (iii) Steer: We apply a signed, sparse activation shift targeted to the language neurons. Concretely, within low to mid layers we add a positive steering along the target-language dominant directions and a compensating negative shift toward the null space for the English neurons, yielding controllable target-language defaultness.

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. Our algorithms show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These improvements allow us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 features. Finally, we apply our algorithms to match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to clarify the links between these methods and classical CCA, laying the groundwork for future insights.

Deep subspace clustering (DSC) algorithms face several challenges that hinder their widespread adoption across variois application domains. First, clustering quality is typically assessed using only the encoder's output layer, disregarding valuable information present in the intermediate layers. Second, most DSC approaches treat representation learning and subspace clustering as independent tasks, limiting their effectiveness. Third, they assume the availability of a held-out dataset for hyperparameter tuning, which is often impractical in real-world scenarios. Fourth, learning termination is commonly based on clustering error monitoring, requiring external labels. Finally, their performance often depends on post-processing techniques that rely on labeled data. To address this limitations, we introduce a novel single-view DSC approach that: (i) minimizes a layer-wise self expression loss using a joint representation matrix; (ii) optimizes a subspace-structured norm to enhance clustering quality; (iii) employs a multi-stage sequential learning framework, consisting of pre-training and fine-tuning, enabling the use of multiple regularization terms without hyperparameter tuning; (iv) incorporates a relative error-based self-stopping mechanism to terminate training without labels; and (v) retains a fixed number of leading coefficients in the learned representation matrix based on prior knowledge. We evaluate the proposed method on six datasets representing faces, digits, and objects. The results show that our method outperforms most linear SC algorithms with careffulyl tuned hyperparameters while maintaining competitive performance with the best performing linear appoaches.

A method is presented for accelerating inference in transformer language models by exploiting the low effective rank of the token activation manifold at each layer. The method decomposes each activation vector into a subspace component and a residual, computes the linear-layer output on the subspace component via a cached low-rank weight image at reduced memory bandwidth, and applies a per-token gate that determines whether the residual correction is computed or skipped. The gate ensures that the output distribution is preserved to within a controllable tolerance. Validation on three model families (GPT-2 124M, GPT-J 6B, OPT 6.7B) on AMD MI300X demonstrates effective speedups of 3.0x to 10.5x on linear-layer weight reads with perplexity ratios below 1.00 and top-1 token agreement above 98%. The method requires no retraining, no architectural modification, and no approximation of the attention mechanism. At the operating point (k = 256, ε = 0.05) on GPT-J 14 6B, the accelerated model produces character-for-character identical output to the baseline.

Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected across related but heterogeneous tasks, studies, domains, or populations. Applying such estimators separately to each task can lead to unstable estimates when sample sizes are limited relative to dimension, while completely pooling the data can obscure meaningful task-specific structure. We introduce Hierarchical Spectral Shrinkage (HSS), a scalable empirical-Bayes framework for partially pooling task-specific spectral estimators. The method regularizes the leading spectral directions of each task toward a data-adaptivelylearned common basis, while allowing the amount of shrinkage to vary across tasks and spectral components. The proposed estimator arises as the posterior mean in a surrogate Bayesian regression formulation of the empirical singular vectors. For factor models, HSS yields partially pooled estimators of the group-specific loading spaces and covariance matrices and can be combined with different spectral estimators by replacing their empirical singular vectors with hierarchically regularized counterparts. More broadly, the same construction provides a mechanism for extending spectral estimators to collections of related but heterogeneous datasets. We demonstrate substantial improvements in estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches in synthetic experiments and multi-study gene-expression data.

We propose to improve transformers of a specific modality with irrelevant data from other modalities, e.g., improve an ImageNet model with audio or point cloud datasets. We would like to highlight that the data samples of the target modality are irrelevant to the other modalities, which distinguishes our method from other works utilizing paired (e.g., CLIP) or interleaved data of different modalities. We propose a methodology named Multimodal Pathway - given a target modality and a transformer designed for it, we use an auxiliary transformer trained with data of another modality and construct pathways to connect components of the two models so that data of the target modality can be processed by both models. In this way, we utilize the universal sequence-to-sequence modeling abilities of transformers obtained from two modalities. As a concrete implementation, we use a modality-specific tokenizer and task-specific head as usual but utilize the transformer blocks of the auxiliary model via a proposed method named Cross-Modal Re-parameterization, which exploits the auxiliary weights without any inference costs. On the image, point cloud, video, and audio recognition tasks, we observe significant and consistent performance improvements with irrelevant data from other modalities. The code and models are available at https://github.com/AILab-CVC/M2PT.

The activation function plays a crucial role in model optimisation, yet the optimal choice remains unclear. For example, the Sigmoid activation is the de-facto activation in balanced classification tasks, however, in imbalanced classification, it proves inappropriate due to bias towards frequent classes. In this work, we delve deeper in this phenomenon by performing a comprehensive statistical analysis in the classification and intermediate layers of both balanced and imbalanced networks and we empirically show that aligning the activation function with the data distribution, enhances the performance in both balanced and imbalanced tasks. To this end, we propose the Adaptive Parametric Activation (APA) function, a novel and versatile activation function that unifies most common activation functions under a single formula. APA can be applied in both intermediate layers and attention layers, significantly outperforming the state-of-the-art on several imbalanced benchmarks such as ImageNet-LT, iNaturalist2018, Places-LT, CIFAR100-LT and LVIS and balanced benchmarks such as ImageNet1K, COCO and V3DET. The code is available at https://github.com/kostas1515/AGLU.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.

Deep Learning of neural networks has gained prominence in multiple life-critical applications like medical diagnoses and autonomous vehicle accident investigations. However, concerns about model transparency and biases persist. Explainable methods are viewed as the solution to address these challenges. In this study, we introduce the Occlusion Sensitivity Analysis with Deep Feature Augmentation Subspace (OSA-DAS), a novel perturbation-based interpretability approach for computer vision. While traditional perturbation methods make only use of occlusions to explain the model predictions, OSA-DAS extends standard occlusion sensitivity analysis by enabling the integration with diverse image augmentations. Distinctly, our method utilizes the output vector of a DNN to build low-dimensional subspaces within the deep feature vector space, offering a more precise explanation of the model prediction. The structural similarity between these subspaces encompasses the influence of diverse augmentations and occlusions. We test extensively on the ImageNet-1k, and our class- and model-agnostic approach outperforms commonly used interpreters, setting it apart in the realm of explainable AI.

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

When a language model asserts that "the capital of Australia is Sydney," does it know this is wrong? We characterize the geometry of correctness representations across 9 models from 5 architecture families. The structure is simple: the discriminative signal occupies 3-8 dimensions, performance degrades with additional dimensions, and no nonlinear classifier improves over linear separation. Centroid distance in the low-dimensional subspace matches trained probe performance (0.90 AUC), enabling few-shot detection: on GPT-2, 25 labeled examples achieve 89% of full-data accuracy. We validate causally through activation steering: the learned direction produces 10.9 percentage point changes in error rates while random directions show no effect. Internal probes achieve 0.80-0.97 AUC; output-based methods (P(True), semantic entropy) achieve only 0.44-0.64 AUC. The correctness signal exists internally but is not expressed in outputs. That centroid distance matches probe performance indicates class separation is a mean shift, making detection geometric rather than learned.

Accurate classification of pediatric central nervous system tumors remains challenging due to histological complexity and limited training data. While pathology foundation models have advanced whole-slide image (WSI) analysis, they often fail to leverage the rich, complementary information found in clinical text and tissue microarchitecture. To this end, we propose PathMoE, an interpretable multimodal framework that integrates H\&E slides, pathology reports, and nuclei-level cell graphs via an interaction-aware mixture-of-experts architecture built on state-of-the-art foundation models for each modality. By training specialized experts to capture modality uniqueness, redundancy, and synergy, PathMoE employs an input-dependent gating mechanism that dynamically weights these interactions, providing sample-level interpretability. We evaluate our framework on two dataset-specific classification tasks on an internal pediatric brain tumor dataset (PBT) and external TCGA datasets. PathMoE improves macro-F1 from 0.762 to 0.799 (+0.037) on PBT when integrating WSI, text, and graph modalities; on TCGA, augmenting WSI with graph knowledge improves macro-F1 from 0.668 to 0.709 (+0.041). These results demonstrate significant performance gains over state-of-the-art image-only baselines while revealing the specific modality interactions driving individual predictions. This interpretability is particularly critical for rare tumor subtypes, where transparent model reasoning is essential for clinical trust and diagnostic validation.

Existing routers rely on semantic query features or handcrafted features, which often fail to capture model-specific failures or intrinsic task difficulty. We instead route using internal LLM activations, specifically the residual stream. Our key idea, Encoder-Target Decoupling, separates the model that produces the predictive signal (the Encoder) from the model whose correctness is being estimated (the Target), allowing open-weight encoders to predict the performance of closed-source target models. We evaluate layerwise geometric probes, finding that Fisher Separability (J) effectively identifies informative layers, supported by Effective Dimensionality (d_{eff}) diagnostics. We then utilize a SharedTrunkNet, a joint multi-output MLP that predicts simultaneous correctness probabilities across candidate models using concatenated prefill features. In our experiments, SharedTrunkNet consistently outperforms semantic baselines. At its best, SharedTrunkNet closes 45.58% of the gap between the strongest standalone model and the oracle while achieving 74.31% cost savings relative to the most expensive model. These results demonstrate that prefill activations provide a robust routing signal, establishing activation-based routing as a high-performance alternative to purely semantic selection.

Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a state-dependent, sparse expansion of a shared basis bank. Formally, DSC models the weight update as a residual trajectory within a Star- Shaped Domain, employing a Magnitude-Gated Simplex Interpolation to ensure continuity at the identity. Unlike standard Mixture-of-LoRAs, which incurs O(M rd) parameter complexity by retrieving independent rank-r matrices, DSC constructs a compositional rank-K approximation from decoupled unit-norm basis vectors. This reduces parameter complexity to O(M d) and memory traffic to O(Kd), while Frame-Theoretic regularization and spectral constraints provide rigorous worst-case bounds on the dynamic update. The code is available at https://github. com/VladimerKhasia/DSC

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

Activation sparsity denotes the existence of substantial weakly-contributed elements within activation outputs that can be eliminated, benefiting many important applications concerned with large language models (LLMs). Although promoting greater activation sparsity within LLMs deserves deep studies, existing works lack comprehensive and quantitative research on the correlation between activation sparsity and potentially influential factors. In this paper, we present a comprehensive study on the quantitative scaling properties and influential factors of the activation sparsity within decoder-only Transformer-based LLMs. Specifically, we propose PPL-p% sparsity, a precise and performance-aware activation sparsity metric that is applicable to any activation function. Through extensive experiments, we find several important phenomena. Firstly, different activation functions exhibit comparable performance but opposite training-time sparsity trends. The activation ratio (i.e., 1-sparsity ratio) evolves as a convergent increasing power-law and decreasing logspace power-law with the amount of training data for SiLU-activated and ReLU-activated LLMs, respectively. These demonstrate that ReLU is more efficient as the activation function than SiLU and can leverage more training data to improve activation sparsity. Secondly, the activation ratio linearly increases with the width-depth ratio below a certain bottleneck point, indicating the potential advantage of a deeper architecture at a fixed parameter scale. Finally, at similar width-depth ratios, we surprisingly find that the limit value of activation sparsity varies weakly with the parameter scale, i.e., the activation patterns within LLMs are insensitive to the parameter scale. These empirical laws towards LLMs with greater activation sparsity have important implications for making LLMs more efficient and interpretable.

Computational pathology models infer biologically and clinically meaningful outcomes from histology, but their predictions are shaped by complex, intertwined tissue signals whose roles are important to understand. Common pixel- and feature-space perturbations can produce implausible tissue, making model responses difficult to interpret. We introduce CPathOGen, a conditional latent-diffusion framework for generating paired H\&E counterfactuals with explicit controls over cellular spatial organization, nuclear morphology, and stain appearance. Cellular maps condition spatial structure through a spatial encoder, while a morphology/appearance vector modulates denoising through blockwise feature-wise linear modulation (FiLM). On held-out H\&E tiles, CPathOGen generates visually plausible tissue with improved distributional agreement after spatially guided selection, as reflected by lower Fréchet Inception Distance (FID) and Kernel Inception Distance (KID); generated cells track requested abundance and position, and measured morphology and color vary monotonically with their controls. We use these verified interventions to probe pathology encoders with endpoint heads, task-specific classifiers, and survival models. Responses are quantified using total variation distance and prediction-flip rate. We further introduce the Biology-Nuisance Sensitivity Ratio, a metric that contrasts model sensitivity to biologically motivated morphology and spatial factors with sensitivity to non-biological, stain-related nuisance variation. CPathOGen provides a practical, fidelity-audited framework for evaluating robustness and controlled feature sensitivity in computational pathology model. https://github.com/a12dongithub/PathOGen{GitHub} and https://huggingface.co/a12donhf/CPathOGen{Hugging~Face}.

We present Statistical Calibrated Activation Pruning (SCAP), a post-training activation pruning framework that (1) generalizes sparsification by input activations of Fully-Connected layers for generic and flexible application across Transformers, and (2) features a simple Mode-Centering technique to pre-calibrate activation distributions for maximizing post-training sparsity. Our results demonstrate robust Pareto efficiency compared to prior methods, translating to a 1.5x additional LLM decoding speedup against CATS at iso model quality. SCAP effectiveness is empirically verified across a wide range of models, including recent Transformer Decoders, MoE, Mamba2, Encoding Transformer, and pre-quantized models, highlighting its practicality and scalability. The code is available at: https://github.com/IntelLabs/SCAP.

We show that deep neural networks trained across diverse tasks exhibit remarkably similar low-dimensional parametric subspaces. We provide the first large-scale empirical evidence that demonstrates that neural networks systematically converge to shared spectral subspaces regardless of initialization, task, or domain. Through mode-wise spectral analysis of over 1100 models - including 500 Mistral-7B LoRAs, 500 Vision Transformers, and 50 LLaMA-8B models - we identify universal subspaces capturing majority variance in just a few principal directions. By applying spectral decomposition techniques to the weight matrices of various architectures trained on a wide range of tasks and datasets, we identify sparse, joint subspaces that are consistently exploited, within shared architectures across diverse tasks and datasets. Our findings offer new insights into the intrinsic organization of information within deep networks and raise important questions about the possibility of discovering these universal subspaces without the need for extensive data and computational resources. Furthermore, this inherent structure has significant implications for model reusability, multi-task learning, model merging, and the development of training and inference-efficient algorithms, potentially reducing the carbon footprint of large-scale neural models.

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

The wide-scale use of sparse autoencoders (SAEs) as interpretability tools is limited by inconsistent links between SAE features and model behavior. Features with clear activation descriptions may have weak or unexpected causal effects; steering can vary across prompts or oppose the intended direction; and activation-based feature selection can miss features that produce the desired output change. Prior work has studied feature geometry inside the model, where features are computed. We instead study the geometry of changes in model logits caused by feature interventions. We introduce Feature-Effect Geometry Analysis (FEGA), an unsupervised framework that removes the same active SAE feature across contexts and analyzes the resulting cloud of logit changes. Across SAE variants, consistent one-dimensional effects are rare: few features behave like reusable directions. To interpret this variation, we distinguish value-like features, tied to static information such as factual attributes, from pointer-like features, associated with context-dependent operations. Value-like features more often exhibit structured, low-dimensional effects, although these effects typically span several directions. Pointer-like features, by contrast, predominantly exhibit diffuse effects. Our results show that a feature can be interpretable and causally relevant without providing a stable direction for steering.

Sparse Autoencoders (SAEs) decompose residual-stream activations into interpretable features. Recent latent-space defenses increasingly rely on these decompositions, assuming that identified "unsafe" SAE features serve as actionable handles for monitoring and intervention. In this paradigm, clamping a specific harmful feature is expected to reliably prevent model misbehavior. However, we show that this success may hide a recoverable failure mode: the clamp may block one visible route to a behavior without eliminating the behavior itself. We formulate this vulnerability as post-intervention recovery, a constrained residual-space optimization problem. Starting from the post-intervention residual state, we optimize residual perturbations to recover the pre-intervention behavior while preserving the post-intervention values of the targeted SAE features. Even under a strong threat model where the intervention remains active throughout optimization and generation, recovery remains possible. To rule out that recovery simply undoes the intervention, we use encoder-orthogonal updates for single-layer interventions and the corresponding feature-map Jacobian in the cross-layer setting. Across TPP, unlearning, IOI, and refusal steering experiments, this stress test reveals recoverable behavior despite successful feature-level intervention. Especially in the safety-critical refusal-steering setting, we achieve a 95.8% recovery rate on valid samples while keeping defended-feature relative drift to 0.131, substantially below suffix-based baselines. A recovery-path attribution analysis further localizes this recovery to the SAE reconstruction residual, the component left unexplained by the SAE. These results expose a gap between feature-level control and behavioral completeness: SAE features can support causal intervention, but controlling them does not guarantee control over the underlying behavior.

The drug development pipeline for a new compound can last 10-20 years and cost over 10 billion. Drug repurposing offers a more time- and cost-effective alternative. Computational approaches based on biomedical knowledge graph representations have recently yielded new drug repurposing hypotheses. In this study, we present a novel, disease-specific hypergraph representation learning technique to derive contextual embeddings of biological pathways of various lengths but that all start at any given drug and all end at the disease of interest. Further, we extend this method to multi-disease hypergraphs. To determine the repurposing potential of each of the 1,522 drugs, we derive drug-specific distributions of cosine similarity values and ultimately consider the median for ranking. Cosine similarity values are computed between (1) all biological pathways starting at the considered drug and ending at the disease of interest and (2) all biological pathways starting at drugs currently prescribed against that disease and ending at the disease of interest. We illustrate our approach with Alzheimer's disease (AD) and two of its risk factors: hypertension (HTN) and type 2 diabetes (T2D). We compare each drug's rank across four hypergraph settings (single- or multi-disease): AD only, AD + HTN, AD + T2D, and AD + HTN + T2D. Notably, our framework led to the identification of two promising drugs whose repurposing potential was significantly higher in hypergraphs combining two diseases: dapagliflozin (antidiabetic; moved up, from top 32% to top 7%, across all considered drugs) and debrisoquine (antihypertensive; moved up, from top 76% to top 23%). Our approach serves as a hypothesis generation tool, to be paired with a validation pipeline relying on laboratory experiments and semi-automated parsing of the biomedical literature.

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large image dimension, circumventing the curse of dimensionality. In this work, we provide theoretical insights into this phenomenon by leveraging key empirical observations: (i) the low intrinsic dimensionality of image data, (ii) a union of manifold structure of image data, and (iii) the low-rank property of the denoising autoencoder in trained diffusion models. These observations motivate us to assume the underlying data distribution of image data as a mixture of low-rank Gaussians and to parameterize the denoising autoencoder as a low-rank model according to the score function of the assumed distribution. With these setups, we rigorously show that optimizing the training loss of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples. Based on this equivalence, we further show that the minimal number of samples required to learn the underlying distribution scales linearly with the intrinsic dimensions under the above data and model assumptions. This insight sheds light on why diffusion models can break the curse of dimensionality and exhibit the phase transition in learning distributions. Moreover, we empirically establish a correspondence between the subspaces and the semantic representations of image data, facilitating image editing. We validate these results with corroborated experimental results on both simulated distributions and image datasets.

Inasmuch as the removal of refusal behavior from instruction-tuned language models by directional abliteration requires the extraction of refusal-mediating directions from the residual stream activation space, and inasmuch as the construction of the contrast baseline against which harmful prompt activations are compared has been treated in the existing literature as an implementation detail rather than a methodological concern, the present work investigates whether a topically matched contrast baseline yields superior refusal directions. The investigation is carried out on the Qwen~3.5 2B model using per-category matched prompt pairs, per-class Self-Organizing Map extraction, and Singular Value Decomposition orthogonalization. It was found that topic-matched contrast produces no functional refusal directions at any tested weight level on any tested layer, while unmatched contrast on the same model, same extraction code, and same evaluation protocol achieves complete refusal elimination on six layers. The geometric analysis of the failure establishes that topic-matched subtraction cancels the dominant activation component shared between harmful and harmless prompts of the same subject, reducing the extracted direction magnitude below the threshold at which weight-matrix projection perturbs the residual stream. The implications for the design of contrast baselines in abliteration research are discussed.

Sensitivity to staining variation remains a major barrier to deploying computational pathology (CPath) models as hematoxylin and eosin (H&E) staining varies across laboratories, requiring systematic assessment of how this variability affects model prediction. In this work, we developed a three-step protocol for evaluating robustness to H&E staining variation in CPath models. Step 1: Select reference staining conditions, Step 2: Characterize test set staining properties, Step 3: Apply CPath model(s) under simulated reference staining conditions. Here, we first created a new reference staining library based on the PLISM dataset. As an exemplary use case, we applied the protocol to assess the robustness properties of 306 microsatellite instability (MSI) classification models on the unseen SurGen colorectal cancer dataset (n=738), including 300 attention-based multiple instance learning models trained on the TCGA-COAD/READ datasets across three feature extractors (UNI2-h, H-Optimus-1, Virchow2), alongside six public MSI classification models. Classification performance was measured as AUC, and robustness as the min-max AUC range across four simulated staining conditions (low/high H&E intensity, low/high H&E color similarity). Across models and staining conditions, classification performance ranged from AUC 0.769-0.911 (Δ = 0.142). Robustness ranged from 0.007-0.079 (Δ = 0.072), and showed a weak inverse correlation with classification performance (Pearson r=-0.22, 95% CI [-0.34, -0.11]). Thus, we show that the proposed evaluation protocol enables robustness-informed CPath model selection and provides insight into performance shifts across H&E staining conditions, supporting the identification of operational ranges for reliable model deployment. Code is available at https://github.com/CTPLab/staining-robustness-evaluation .

Capable language models hold what a character believes apart from what is true: told "Anna believes the cup is blue; in reality it is red," they answer blue about Anna and red about the world. Where in the computation does that separation live? We show it rests on two separable mechanisms at two positions. A generic value slot binds the attributed value. A router at the query position selects which frame, the character's belief or reality, a query reads out. Two routes fill the slot: an asserted belief, whose value the text supplies, binds in directly; a derived belief, whose value must be inferred from what the character could see, arrives by a visibility-gated lookback. A subspace trained on either route steers the other, and only the derived route depends on described visibility. The slot itself carries no belief-reality tag: intervening on it moves a reality readout as strongly as a belief one. The separation lives instead in a dissociated pair of routing subspaces, which flip a query between frames without injecting the donor's value. These results hold across three architectures, on stimuli de-confounded against theory-of-mind-benchmark shortcuts; the behavior itself emerges between 3B and 7B across five model families. This paper develops the single belief-reality axis in depth; a companion paper shows the same slot-and-router format is shared across the other non-actual contexts a sentence can open (counterfactual, fictional, temporal).

Learning hierarchical features in Sparse Autoencoders (SAEs) is essential for capturing the structured nature of real-world data and mitigating issues like feature absorption or splitting. Existing works attempt to identify hierarchical relationships within independent feature sets by relying on activation coverage, the assumption that child feature should only activate when its parent feature activates. However, we demonstrate that this condition alone is insufficient; that is, it often produces false positives where parent and child concepts are semantically unrelated. To address this, we introduce a novel reconstruction condition that enforces a deeper functional link between hierarchical levels. By combining both activation and reconstruction constraints, we propose the Tree SAE, a model designed to learn hierarchical structures directly from within the feature set. Our results demonstrate that Tree SAEs significantly surpass the existing SAEs at learning hierarchical pairs while maintaining competitive performance to the state-of-the-art on several key benchmarks. Finally, we demonstrate the practical utility of our Tree SAE in mapping the geometry of child feature subspaces and uncovering the complex hierarchical concept structures encoded within large language models.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

The diversity of post-training data is critical for effective downstream performance in large language models (LLMs). Many existing approaches to constructing post-training data quantify diversity using text-based metrics that capture linguistic variation, but such metrics provide only weak signals for the task-relevant features that determine downstream performance. In this work, we introduce Feature Activation Coverage (FAC) which measures data diversity in an interpretable feature space. Building upon this metric, we further propose a diversity-driven data synthesis framework, named FAC Synthesis, that first uses a sparse autoencoder to identify missing features from a seed dataset, and then generates synthetic samples that explicitly reflect these features. Experiments show that our approach consistently improves both data diversity and downstream performance on various tasks, including instruction following, toxicity detection, reward modeling, and behavior steering. Interestingly, we identify a shared, interpretable feature space across model families (i.e., LLaMA, Mistral, and Qwen), enabling cross-model knowledge transfer. Our work provides a solid and practical methodology for exploring data-centric optimization of LLMs.

Disentangled representation learning aims to map independent factors of variation to independent representation components. On one hand, purely unsupervised approaches have proven successful on fully disentangled synthetic data, but fail to recover semantic factors from real data without strong inductive biases. On the other hand, supervised approaches are unstable and hard to scale to large attribute sets because they rely on adversarial objectives or auxiliary classifiers. We introduce XFactors, a weakly-supervised VAE framework that disentangles and provides explicit control over a chosen set of factors. Building on the Disentangled Information Bottleneck perspective, we decompose the representation into a residual subspace S and factor-specific subspaces T_1,ldots,T_K and a residual subspace S. Each target factor is encoded in its assigned T_i through contrastive supervision: an InfoNCE loss pulls together latents sharing the same factor value and pushes apart mismatched pairs. In parallel, KL regularization imposes a Gaussian structure on both S and the aggregated factor subspaces, organizing the geometry without additional supervision for non-targeted factors and avoiding adversarial training and classifiers. Across multiple datasets, with constant hyperparameters, XFactors achieves state-of-the-art disentanglement scores and yields consistent qualitative factor alignment in the corresponding subspaces, enabling controlled factor swapping via latent replacement. We further demonstrate that our method scales correctly with increasing latent capacity and evaluate it on the real-world dataset CelebA. Our code is available at https://github.com/ICML26-anon/XFactors{github.com/ICML26-anon/XFactors}.

For many segmentation tasks, especially for the biomedical image, the topological prior is vital information which is useful to exploit. The containment/nesting is a typical inter-class geometric relationship. In the MICCAI Brain tumor segmentation challenge, with its three hierarchically nested classes 'whole tumor', 'tumor core', 'active tumor', the nested classes relationship is introduced into the 3D-residual-Unet architecture. The network comprises a context aggregation pathway and a localization pathway, which encodes increasingly abstract representation of the input as going deeper into the network, and then recombines these representations with shallower features to precisely localize the interest domain via a localization path. The nested-class-prior is combined by proposing the multi-class activation function and its corresponding loss function. The model is trained on the training dataset of Brats2018, and 20% of the dataset is regarded as the validation dataset to determine parameters. When the parameters are fixed, we retrain the model on the whole training dataset. The performance achieved on the validation leaderboard is 86%, 77% and 72% Dice scores for the whole tumor, enhancing tumor and tumor core classes without relying on ensembles or complicated post-processing steps. Based on the same start-of-the-art network architecture, the accuracy of nested-class (enhancing tumor) is reasonably improved from 69% to 72% compared with the traditional Softmax-based method which blind to topological prior.

As large language models (LLMs) scale, the question is not only how large they become, but how much of their capacity is effectively utilized. Existing scaling laws relate model size to loss, yet overlook how components exploit their latent space. We study feed-forward networks (FFNs) and recast width selection as a spectral utilization problem. Using a lightweight diagnostic suite -- Hard Rank (participation ratio), Soft Rank (Shannon rank), Spectral Concentration, and the composite Spectral Utilization Index (SUI) -- we quantify how many latent directions are meaningfully activated across LLaMA, GPT-2, and nGPT families. Our key finding is an asymmetric spectral scaling law: soft rank follows an almost perfect power law with FFN width, while hard rank grows only sublinearly and with high variance. This asymmetry suggests that widening FFNs mostly adds low-energy tail directions, while dominant-mode subspaces saturate early. Moreover, at larger widths, variance further collapses into a narrow subspace, leaving much of the latent space under-utilized. These results recast FFN width selection as a principled trade-off between tail capacity and dominant-mode capacity, offering concrete guidance for inference-efficient LLM design.

Multimodal clinical models are usually judged on accuracy with every modality present, but deployment removes modalities; an echocardiogram is often unavailable where an ECG is routine. Two questions then matter beyond the size of the accuracy loss: which modality was responsible, and whether the model fails loudly or silently once that modality is dropped. The distinction is per-example and modality-level, and is separate from post-hoc feature attribution (e.g. SHAP). Models are replaced often; the evaluation that answers these questions is reused. We present a model-agnostic modality-failure framework: given N modality embeddings, any mask-aware probe, and labels, it returns a per-example failure taxonomy, a per-modality complementarity matrix that attributes error to modalities, and a loud-vs-silent dropout profile separating monitorable failures from those that pass unflagged far from the decision boundary, using only deployment-observable signals. We release it as a small, unit-tested harness and validate it against planted ground truth. Across seeds it recovers that planted modality dominance and complementary subset, reports per-modality loud-vs-silent rates, and scales to a three-modality complementarity matrix; because the planted structure is known by construction, this validates recovery of per-example attribution rather than clinical performance. We then instantiate the framework on frozen EchoJEPA and HuBERT-ECG embeddings for LVEF and the EF <= 40% HFrEF gate over a paired MIMIC-IV cohort, where on the held-out test split (n = 245) dropping echo nearly doubles error. The narrow echo-to-ECG overlap that bounds cohort size is itself a deployment finding for cardiac foundation models. All of our work can be found at https://github.com/criticaldata/PRIMED-AI.

Class-Incremental Learning (CIL) requires a learning system to continually learn new classes without forgetting. Despite the strong performance of Pre-Trained Models (PTMs) in CIL, a critical issue persists: learning new classes often results in the overwriting of old ones. Excessive modification of the network causes forgetting, while minimal adjustments lead to an inadequate fit for new classes. As a result, it is desired to figure out a way of efficient model updating without harming former knowledge. In this paper, we propose ExpAndable Subspace Ensemble (EASE) for PTM-based CIL. To enable model updating without conflict, we train a distinct lightweight adapter module for each new task, aiming to create task-specific subspaces. These adapters span a high-dimensional feature space, enabling joint decision-making across multiple subspaces. As data evolves, the expanding subspaces render the old class classifiers incompatible with new-stage spaces. Correspondingly, we design a semantic-guided prototype complement strategy that synthesizes old classes' new features without using any old class instance. Extensive experiments on seven benchmark datasets verify EASE's state-of-the-art performance. Code is available at: https://github.com/sun-hailong/CVPR24-Ease

Sparse Autoencoders (SAEs) have been proposed as an unsupervised approach to learn a decomposition of a model's latent space. This enables useful applications such as steering - influencing the output of a model towards a desired concept - without requiring labeled data. Current methods identify SAE features to steer by analyzing the input tokens that activate them. However, recent work has highlighted that activations alone do not fully describe the effect of a feature on the model's output. In this work, we draw a distinction between two types of features: input features, which mainly capture patterns in the model's input, and output features, which have a human-understandable effect on the model's output. We propose input and output scores to characterize and locate these types of features, and show that high values for both scores rarely co-occur in the same features. These findings have practical implications: after filtering out features with low output scores, we obtain 2-3x improvements when steering with SAEs, making them competitive with supervised methods.

We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated to an unknown dynamical system. We build on the Symmetric Subspace Decomposition (SSD) algorithm, a centralized method that under mild conditions on data sampling provably finds the maximal Koopman-invariant subspace and all Koopman eigenfunctions in an arbitrary finite-dimensional functional space. A network of processors, each aware of a common dictionary of functions and equipped with a local set of data snapshots, repeatedly interact over a directed communication graph. Each processor receives its neighbors' estimates of the invariant dictionary and refines its estimate by applying SSD with its local data on the intersection of the subspaces spanned by its own dictionary and the neighbors' dictionaries. We identify conditions on the network topology to ensure the algorithm identifies the maximal Koopman-invariant subspace in the span of the original dictionary, characterize its time, computational, and communication complexity, and establish its robustness against communication failures.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

To perform few-shot learning, language models extract signals from a few input-label pairs, aggregate them into a learned prediction rule, and apply this rule to new inputs. How is this implemented in the forward pass of modern transformer models? To explore this question, we study a structured family of few-shot learning tasks for which the true prediction rule is to add an integer k to the input. We introduce a novel method that localizes the model's few-shot learning ability to only a few attention heads. This method and the findings generalize to four additional task families spanning arithmetic and semantic tasks. We then perform an in-depth analysis of individual heads via dimensionality reduction and decomposition of the heads' output spaces. For example, in Llama-3-8B-Instruct, we reduce the mechanism underlying these tasks to just three attention heads with six-dimensional subspaces, in which four dimensions track the units digit using trigonometric functions with periods 2, 5, and 10, while two dimensions track magnitude using low-frequency components. To deepen our understanding of this mechanism, we also derive a mathematical identity relating the ''aggregator'' and ''extractor'' subspaces of attention heads, allowing us to track the flow of information from individual examples to a final aggregated concept. Our results demonstrate how tracking low-dimensional subspaces of localized heads throughout a forward pass can provide insight into fine-grained computational structures in language models. Our code is available at https://github.com/xyVickyHu/addition-subspaces.

Single-cell transcriptomes are sparse observations of coordinated biological programmes, yet most self-supervised models learn by reconstructing individual genes. Here we present BioM-JEPA, a joint-embedding predictive architecture that instead predicts aggregate representations of graph-connected gene blocks defined by protein-association and corpus-derived coexpression evidence. A student network infers each target-block representation from the remaining genes in a cell, while a slowly updated teacher supplies the corresponding target from the full observed gene set. Under the reported extraction procedure, block-level prediction produced embeddings with higher effective rank and weaker association with detected-gene depth in the tested diagnostics than token-prediction, random-block and reconstruction controls. Across CellBench tasks, frozen BioM-JEPA embeddings retained expression, pathway and neighbourhood information and achieved the lowest aggregate perturbation-response error among the evaluated models. Representation diagnostics were also consistent with canonical pancreatic programmes and compositional relationships between genetic perturbations. Linear attention avoids constructing a quadratic gene-by-gene attention matrix; in a matched one-epoch hPancreas experiment at batch size 8, BioM-JEPA provided 5.75-fold higher fine-tuning throughput and 3.76-fold higher held-out embedding throughput than scFoundation. Together, these results support graph-connected gene blocks as useful prediction units for JEPA-style representation learning in single-cell biology.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

The truthfulness of existing explanation methods in authentically elucidating the underlying model's decision-making process has been questioned. Existing methods have deviated from faithfully representing the model, thus susceptible to adversarial attacks. To address this, we propose a novel eXplainable AI (XAI) method called SRD (Sharing Ratio Decomposition), which sincerely reflects the model's inference process, resulting in significantly enhanced robustness in our explanations. Different from the conventional emphasis on the neuronal level, we adopt a vector perspective to consider the intricate nonlinear interactions between filters. We also introduce an interesting observation termed Activation-Pattern-Only Prediction (APOP), letting us emphasize the importance of inactive neurons and redefine relevance encapsulating all relevant information including both active and inactive neurons. Our method, SRD, allows for the recursive decomposition of a Pointwise Feature Vector (PFV), providing a high-resolution Effective Receptive Field (ERF) at any layer.

Continuous Glucose Monitoring (CGM) can detect early metabolic subphenotypes (insulin resistance, IR; β-cell dysfunction), but population-scale deployment faces two coupled problems. First, the same physiological state appears through multiple views (CGM time series, venous OGTT, Glucodensity summaries), so single-view representations fail to transfer when deployment shifts the modality or setting. Second, baselines perform inconsistently across these shifts. Both problems point to one remedy: representations that abstract away from any single view to capture higher-level temporal and distributional structure. We propose CGM-JEPA, a self-supervised pretraining framework which predicts masked latent representations rather than raw values, yielding abstraction that transfers across modalities. X-CGM-JEPA adds a masked Glucodensity cross-view objective for complementary distributional information. We pretrain on sim389k unlabeled CGM readings from 228 subjects and evaluate on two clinical cohorts (N=27 and N=17 public-release subsets) across three regimes (cohort generalization, venous-to-CGM transfer, home CGM) under 20-iteration times 2-fold cross-validation. X-CGM-JEPA ranks first or second on AUROC for both endpoints across all three regimes while no baseline does, exceeding the strongest baseline by up to +6.5 pp in cohort generalization and +3.6 pp in venous-to-CGM transfer (paired Wilcoxon, p<0.001). Under modality shift, it matches mean AUROC while redistributing toward weaker subgroups (ethnicity AUROC gap shrinks 25-54%); on sparse in-domain venous data, the distributional view lifts label-aware clustering (ARI +39%, NMI +40%). Code and weights: https://github.com/cruiseresearchgroup/CGM-JEPA

Training Data Attribution (TDA) seeks to trace a model's predictions back to its training data. The gold standard for TDA relies on causal interventions, observing how a model changes when data is added or removed, but repeated retraining is computationally challenging for Large Language Models (LLMs). Consequently, most approaches approximate this effect in the parameter space using gradients. However, tracking gradients across billions of parameters is not only prohibitively expensive but relies on local approximations. In this work, we propose a shift: rather than estimating parameter changes, we model the functional effect of training data in the activation space. We introduce STRIDE (Steering-based Training Data Influence Decomposition), a framework that formulates TDA as a sparse recovery problem in the spirit of compressive sensing. STRIDE learns lightweight "steering operators" that mimic the behavioral shift caused by training on data subsets. By measuring how these operators perturb test predictions, we recover individual training example influences via sparse linear decomposition. STRIDE achieves state-of-the-art for LLM pre-training attribution while being an order of magnitude (13times) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative analysis.

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less. Code: https://github.com/google/svcca/

To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the token subspace is provably not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

Causal precedence between biochemical interactions is crucial in the biomedical domain, because it transforms collections of individual interactions, e.g., bindings and phosphorylations, into the causal mechanisms needed to inform meaningful search and inference. Here, we analyze causal precedence in the biomedical domain as distinct from open-domain, temporal precedence. First, we describe a novel, hand-annotated text corpus of causal precedence in the biomedical domain. Second, we use this corpus to investigate a battery of models of precedence, covering rule-based, feature-based, and latent representation models. The highest-performing individual model achieved a micro F1 of 43 points, approaching the best performers on the simpler temporal-only precedence tasks. Feature-based and latent representation models each outperform the rule-based models, but their performance is complementary to one another. We apply a sieve-based architecture to capitalize on this lack of overlap, achieving a micro F1 score of 46 points.

We present Three-Phase Transformer (3PT), a residual-stream structural prior for decoder-only Transformers on a standard SwiGLU + RMSNorm + RoPE + GQA backbone. The hidden vector is partitioned into N equally-sized cyclic channels, each maintained by phase-respecting ops: a per-channel RMSNorm, a 2D Givens rotation between attention and FFN that rotates each channel by theta + i*(2*pi/N), and a head-count constraint aligning GQA heads with the partition. The architecture is a self-stabilizing equilibrium between scrambling and re-imposition, not a bolted-on module. The partition carves out a one-dimensional DC subspace orthogonal to the channels, into which we inject a fixed Gabriel's horn profile r(p) = 1/(p+1) as an absolute-position side-channel composing orthogonally with RoPE's relative-position rotation. The canonical N=3 borrows its metaphor from balanced three-phase AC, where three sinusoids 120 degrees apart sum to zero with no anti-correlated pair. At 123M parameters on WikiText-103, 3PT achieves -7.20% perplexity (-2.62% bits-per-byte) over a matched RoPE-Only baseline at +1,536 parameters (0.00124% of total), with 1.93x step-count convergence speedup (1.64x wall-clock). N behaves as a parameter-sharing knob rather than a unique optimum: at 5.5M an N-sweep over {1,2,3,4,6,8,12} is near-monotone with N=1 winning; at 123M a three-seed sweep finds N=3 and N=1 statistically indistinguishable. The load-bearing mechanism is the channel-partitioned residual stream, per-block rotation, per-phase normalization, and horn DC injection. We characterize (a) self-stabilization of the geometry without explicit enforcement, a novel instance of the conservation-law framework for neural networks; (b) a U-shaped depth profile of rotation-angle drift at 12 layers; (c) orthogonal composition with RoPE, attention, and FFN.

Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and conditional uniqueness of MSS are discussed with conditions generally satisfied in applications. Utilizing weak prior information of MSS, the minimality inspection of segments is further simplified to the prior detection of partitions. The MSS problem is then modeled as a computable optimization problem via self-expressiveness of samples. A closed form of representation matrices is first given for the self-expressiveness, and the connection of diagonal blocks is then addressed. The MSS model uses a rank restriction on the sum of segment ranks. Theoretically, it can retrieve the minimal sample subspaces that could be heavily intersected. The optimization problem is solved via a basic manifold conjugate gradient algorithm, alternative optimization and hybrid optimization, taking into account of solving both the primal MSS problem and its pseudo-dual problem. The MSS model is further modified for handling noisy data, and solved by an ADMM algorithm. The reported experiments show the strong ability of the MSS method on retrieving minimal sample subspaces that are heavily intersected.

Skills are a natural unit for describing what a language model can do and how its behavior can be changed. However, existing characterizations rely on human-written taxonomies, textual descriptions, or manual profiling pipelines--all external hypotheses about what matters that need not align with the model's internal representations. We argue that when the goal is to intervene on model behavior, skill characterization should be *model-native*: grounded in the model's own representations rather than imposed through external ontologies. We instantiate this view by recovering a compact orthogonal basis from sequence-level activations. The resulting basis is semantically interpretable but need not correspond to any predefined human ontology; instead, it captures axes of behavioral variation that the model itself organizes around. We validate this characterization on reasoning post-training, using the recovered basis for both SFT data selection and inference-time steering. We develop lightweight proxy interventions to identify which directions are most useful for a given model. Across Llama3-8B and Qwen2.5-3B, selecting data along those directions improves Pass@1 by up to 20% on MATH and 41% on AMC, outperforming data selection based on human-characterized skills. Because the basis lives in activation space, the same directions also serve as steering vectors at inference time, improving Pass@8 by up to 4.8% on MATH--an intervention that human-characterized skills cannot support. We further validate the characterization on safety alignment, where selecting adversarial training data for model-native skill coverage rather than textual diversity yields more sample-efficient learning. These results suggest that recovering skills from the model's own representations, rather than imposing them externally, provides a more effective foundation for intervening on model behavior. Codes are open-sourced.

Driven by the rapid growth of model parameters, parameter-efficient fine-tuning (PEFT) has become essential for adapting large models to diverse downstream tasks under constrained computational resources. Within this paradigm, orthogonal fine-tuning and its variants preserve semantic representations of pre-trained models, but struggle to achieve both expressiveness and efficiency in terms of parameter counts, memory, and computation. To overcome this limitation, we propose efficient Orthogonal Fine-Tuning with Principal Subspace adaptation (PSOFT), which confines orthogonal transformations to the principal subspace of pre-trained weights. Specifically, PSOFT constructs this subspace via matrix decomposition to enable compatible transformations with higher effective rank, establishes a theoretical condition that strictly maintains the geometry of this subspace for essential semantic preservation, and introduces efficient tunable vectors that gradually relax orthogonality during training to enhance adaptability. Extensive experiments on 35 NLP and CV tasks across four representative models demonstrate that PSOFT offers a practical and scalable solution to simultaneously achieve semantic preservation, expressiveness, and multi-dimensional efficiency in PEFT. The code is publicly available at https://github.com/fei407/PSOFT.

Scientific archives now contain hundreds of petabytes of data across genomics, ecology, climate, and molecular biology that could reveal undiscovered patterns if systematically analyzed at scale. Large-scale, weakly-supervised datasets in language and vision have driven the development of foundation models whose internal representations encode structure (patterns, co-occurrences and statistical regularities) beyond their training objectives. Most existing methods extract structure only for pre-specified targets; they excel at confirmation but do not support open-ended discovery of unknown patterns. We ask whether sparse autoencoders (SAEs) can enable open-ended feature discovery from foundation model representations. We evaluate this question in controlled rediscovery studies, where the learned SAE features are tested for alignment with semantic concepts on a standard segmentation benchmark and compared against strong label-free alternatives on concept-alignment metrics. Applied to ecological imagery, the same procedure surfaces fine-grained anatomical structure without access to segmentation or part labels, providing a scientific case study with ground-truth validation. While our experiments focus on vision with an ecology case study, the method is domain-agnostic and applicable to models in other sciences (e.g., proteins, genomics, weather). Our results indicate that sparse decomposition provides a practical instrument for exploring what scientific foundation models have learned, an important prerequisite for moving from confirmation to genuine discovery.

Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations by learning a sparse and overcomplete decomposition of the network's internal activations. However, SAEs are traditionally trained considering only activation values and not the effect those activations have on downstream computations. This limits the information available to learn features, and biases the autoencoder towards neglecting features which are represented with small activation values but strongly influence model outputs. To address this, we introduce Gradient SAEs (g-SAEs), which modify the k-sparse autoencoder architecture by augmenting the TopK activation function to rely on the gradients of the input activation when selecting the k elements. For a given sparsity level, g-SAEs produce reconstructions that are more faithful to original network performance when propagated through the network. Additionally, we find evidence that g-SAEs learn latents that are on average more effective at steering models in arbitrary contexts. By considering the downstream effects of activations, our approach leverages the dual nature of neural network features as both representations, retrospectively, and actions, prospectively. While previous methods have approached the problem of feature discovery primarily focused on the former aspect, g-SAEs represent a step towards accounting for the latter as well.

This paper introduces BioAgent Bench, a benchmark dataset and an evaluation suite designed for measuring the performance and robustness of AI agents in common bioinformatics tasks. The benchmark contains curated end-to-end tasks (e.g., RNA-seq, variant calling, metagenomics) with prompts that specify concrete output artifacts to support automated assessment, including stress testing under controlled perturbations. We evaluate frontier closed-source and open-weight models across multiple agent harnesses, and use an LLM-based grader to score pipeline progress and outcome validity. We find that frontier agents can complete multi-step bioinformatics pipelines without elaborate custom scaffolding, often producing the requested final artifacts reliably. However, robustness tests reveal failure modes under controlled perturbations (corrupted inputs, decoy files, and prompt bloat), indicating that correct high-level pipeline construction does not guarantee reliable step-level reasoning. Finally, because bioinformatics workflows may involve sensitive patient data, proprietary references, or unpublished IP, closed-source models can be unsuitable under strict privacy constraints; in such settings, open-weight models may be preferable despite lower completion rates. We release the dataset and evaluation suite publicly.

The growing use of generative models in daily life calls for efficient mechanisms to control their generation, to e.g., produce safe content or provide users with tools to explore style changes. Ideally, such mechanisms should require low volume of unpaired data (i.e., without explicit preference), and should be cheap, both at train and inference time, while preserving output quality. Recent research has shown that such mechanisms can be obtained by intervening exclusively on model activations, with the goal of correcting distributional differences between activations seen when using prompts from a source vs. a target set (e.g., toxic and non-toxic sentences). While cheap, these fast methods are inherently crude: their maps are tuned locally, not accounting for their impact on downstream layers, resulting in interventions that cause unintended shifts when used out-of-sample. We propose in this work linear end-to-end activation steering (LinEAS), an approach trained with a global loss that accounts simultaneously for all layer-wise distributional shifts. In addition to being more robust, the loss used to train LinEAS can be regularized with sparsifying norms, which can automatically carry out neuron selection. LinEAS only requires a handful of unpaired samples to be effective, and beats similar baselines on toxicity mitigation in language models, becoming competitive with oracle-dependent methods that have access to strong supervision. LinEAS is modality-agnostic and we empirically find that it outperforms existing activation steering methods at mitigating and including new concepts at the output of single-step text-to-image generation models.

Massive activations, residual-stream coordinates with magnitudes far larger than typical activations, are associated with attention sinks in transformers, but how their scale is regulated during training remains incompletely understood. Combining training-trajectory analyses and controlled interventions, we trace their emergence, growth, and consolidation. Sink-carrying channels vary across random seeds but stabilize early within each run. Over longer training, surrounding channels erode and the sink concentrates onto a few redundant carriers. Across ablations, gradient attenuation follows the sink token's collective root-mean-square magnitude rather than any single channel, making collective scale central to understanding their effects. Our central result is that weight decay causally controls the turnover of global activation scale. In controlled continuations, removing decay near the peak allows this scale to keep rising, whereas retaining it produces decline even at constant learning rate. We develop a balance model for the rise and peak of massive-activation magnitude, in which AdamW-preconditioned growth opposes weight decay. Sweeping the decay coefficient λ shifts peak timing approximately log-linearly and yields peak magnitudes scaling approximately as λ^{-1/2}, consistent with this balance. Optimizer measurements further show that preconditioning sustains the large-channel cohort against decay even when raw maintaining forces are too small to do so. Together, these findings connect the observed life cycle to scale-regulating training dynamics and establish weight decay as a training-time lever on activation magnitude.

While Multimodal Large Language Models (MLLMs) have demonstrated remarkable proficiency in tasks such as abnormality detection and report generation for anatomical modalities, their capability in functional imaging remains largely unexplored. In this work, we identify and quantify a fundamental functional perception gap: the inability of current vision encoders to decode functional tracer biodistribution independent of morphological priors. Identifying Positron Emission Tomography (PET) as the quintessential modality to investigate this disconnect, we introduce PET-Bench, the first large-scale functional imaging benchmark comprising 52,308 hierarchical QA pairs from 9,732 multi-site, multi-tracer PET studies. Extensive evaluation of 19 state-of-the-art MLLMs reveals a critical safety hazard termed the Chain-of-Thought (CoT) hallucination trap. We observe that standard CoT prompting, widely considered to enhance reasoning, paradoxically decouples linguistic generation from visual evidence in PET, producing clinically fluent but factually ungrounded diagnoses. To resolve this, we propose Atomic Visual Alignment (AVA), a simple fine-tuning strategy that enforces the mastery of low-level functional perception prior to high-level diagnostic reasoning. Our results demonstrate that AVA effectively bridges the perception gap, transforming CoT from a source of hallucination into a robust inference tool and improving diagnostic accuracy by up to 14.83%. Code and data are available at https://github.com/yezanting/PET-Bench.

Mechanistic interpretability seeks to understand the internal mechanisms of machine learning models, where localization -- identifying the important model components -- is a key step. Activation patching, also known as causal tracing or interchange intervention, is a standard technique for this task (Vig et al., 2020), but the literature contains many variants with little consensus on the choice of hyperparameters or methodology. In this work, we systematically examine the impact of methodological details in activation patching, including evaluation metrics and corruption methods. In several settings of localization and circuit discovery in language models, we find that varying these hyperparameters could lead to disparate interpretability results. Backed by empirical observations, we give conceptual arguments for why certain metrics or methods may be preferred. Finally, we provide recommendations for the best practices of activation patching going forwards.

Pre-trained encoders for offline feature extraction followed by multiple instance learning (MIL) aggregators have become the dominant paradigm in computational pathology (CPath), benefiting cancer diagnosis and prognosis. However, performance limitations arise from the absence of encoder fine-tuning for downstream tasks and disjoint optimization with MIL. While slide-level supervised end-to-end (E2E) learning is an intuitive solution to this issue, it faces challenges such as high computational demands and suboptimal results. These limitations motivate us to revisit E2E learning. We argue that prior work neglects inherent E2E optimization challenges, leading to performance disparities compared to traditional two-stage methods. In this paper, we pioneer the elucidation of optimization challenge caused by sparse-attention MIL and propose a novel MIL called ABMILX. It mitigates this problem through global correlation-based attention refinement and multi-head mechanisms. With the efficient multi-scale random patch sampling strategy, an E2E trained ResNet with ABMILX surpasses SOTA foundation models under the two-stage paradigm across multiple challenging benchmarks, while remaining computationally efficient (<10 RTX3090 hours). We show the potential of E2E learning in CPath and calls for greater research focus in this area. The code is https://github.com/DearCaat/E2E-WSI-ABMILX.

Biosecurity evaluations of language models typically ask whether models produce hazardous output. This paper asks a complementary question: when a model refuses, is that refusal structurally sound, or does it disappear under modest changes to prompt framing, formatting, or output length? Across five architectures, no model cleanly discriminated benign from hazard. Gemma 2 2B-IT never genuinely refused across 75 prompts, hedging on every hazard-adjacent query. Gemma 4 E2B-IT refused 65/75 prompts with chat-template formatting and 0/75 without it. Both Gemma models collapsed to 0% under an 80-token cap. Qwen 2.5 1.5B and Phi-3-mini over-refused, flagging 83-87% of benign biology as hazardous. Llama 3.2 1B showed the only meaningful tier gradient (61-point spread). To probe what drives such over-refusal, we tested a panel of Schedule I but biologically non-toxic compounds (notably psilocybin cultivation, with FDA Breakthrough Therapy status). Some models refused these at rates exceeding genuinely hazardous biology, suggesting refusal tracks legality and cultural salience over CBRN hazard. To measure the internal side, we introduce a divergence score D comparing a model's surface response label to its internal sparse autoencoder (SAE) feature activations. Full D was computed on Gemma 2 2B-IT (Gemma Scope 1) and Gemma 4 E2B-IT (author-trained bio SAE). Two fine-tuned Gemma 2 domain SAEs were released. On Gemma 4, comply and refuse responses separated by a 0.647-point gap with zero overlap (n=75), though this is preliminary, with a narrow catalog, within-sample calibration, and Gemma-family-only SAE coverage. Built over one hackathon weekend on consumer hardware (GTX 1650 Ti Max-Q, plus Colab T4 for SAE training), this preliminary evidence suggests activation-level auditing may surface failure modes invisible to behavioral evaluation, with substantial variation across architectures.

Vision Language Models (VLMs) are improving quickly, but standard benchmarks can hide systematic failures that reduce real world trust. We introduce MATS (Multimodal Audit for Truthful Spatialization), a compact behavioral audit that measures whether models reject visually contradicted statements, and two metrics Spatial Consistency Score (SCS) and Incorrect Agreement Rate (IAR). Instruction tuned generative VLMs (LLaVA 1.5, QwenVLchat) exhibit very low SCS and high IAR, while contrastive encoders (CLIP, SigLIP) are far more robust. Activation patching causally localizes failure loci (mid to late cross attention for generative models, pooled projection components for contrastive models) and suggests concrete repair paths.

Identifying metabolic sites where cytochrome P450 enzymes metabolize small-molecule drugs is essential for drug discovery. Although existing computational approaches have been proposed for site-of-metabolism prediction, they typically ignore cytochrome P450 isoform identity or model isoforms independently, thereby failing to fully capture inherent cross-isoform metabolic patterns. In addition, prior evaluations often rely on top-k metrics, where false positive atoms may be included among the top predictions, underscoring the need for complementary metrics that more directly assess binary atom-level discrimination under severe class imbalance. We propose ATTNSOM, an atom-level site-of-metabolism prediction framework that integrates intrinsic molecular reactivity with cross-isoform relationships. The model combines a shared graph encoder, molecule-conditioned atom representations, and a cross-attention mechanism to capture correlated metabolic patterns across cytochrome P450 isoforms. The model is evaluated on two benchmark datasets annotated with site-of-metabolism labels at atom resolution. Across these benchmarks, the model achieves consistently strong top-k performance across multiple cytochrome P450 isoforms. Relative to ablated variants, the model yields higher Matthews correlation coefficient, indicating improved discrimination of true metabolic sites. These results support the importance of explicitly modeling cross-isoform relationships for site-of-metabolism prediction. The code and datasets are available at https://github.com/dmis-lab/ATTNSOM.

Sparsely-activated Mixture-of-Experts (SMoE) models offer efficient pre-training and low latency but their large parameter counts create significant memory overhead, motivating research into expert compression. Contrary to recent findings favouring expert merging on discriminative benchmarks, we demonstrate that expert pruning is a superior strategy for generative tasks. We prove that merging introduces an irreducible error by causing a "functional subspace collapse", due to the loss of the router's independent, input-dependent control over experts. Leveraging this insight, we propose Router-weighted Expert Activation Pruning (REAP), a novel pruning criterion that considers both router gate-values and expert activation norms. Across a diverse set of SMoE models ranging from 20B to 1T parameters, REAP consistently outperforms merging and other pruning methods on generative benchmarks, especially at 50% compression. Notably, our method achieves near-lossless compression on code generation and tool-calling tasks with Qwen3-Coder-480B and Kimi-K2, even after pruning 50% of experts.

We introduce a comprehensive framework for modeling single cell transcriptomic responses to perturbations, aimed at standardizing benchmarking in this rapidly evolving field. Our approach includes a modular and user-friendly model development and evaluation platform, a collection of diverse perturbational datasets, and a set of metrics designed to fairly compare models and dissect their performance. Through extensive evaluation of both published and baseline models across diverse datasets, we highlight the limitations of widely used models, such as mode collapse. We also demonstrate the importance of rank metrics which complement traditional model fit measures, such as RMSE, for validating model effectiveness. Notably, our results show that while no single model architecture clearly outperforms others, simpler architectures are generally competitive and scale well with larger datasets. Overall, this benchmarking exercise sets new standards for model evaluation, supports robust model development, and furthers the use of these models to simulate genetic and chemical screens for therapeutic discovery.