Feature Space

Large language models (LLMs) have recently demonstrated improved machine translation performance over strong supervised baselines. This raises questions as to what mechanisms underlie how LLMs perform machine translation between languages. Motivated by recent interpretability findings--namely, that LLMs use massively multilingual latent feature representations to perform language modeling--we propose the interlingua hypothesis. The hypothesis holds that language models translate by reading a source sentence into a latent feature space, and generate a target sentence by reading from the latent feature space. We show three lines of evidence in support of this hypothesis: (1) variance in BLEU across language pairs is largely predictable from language-specific competences with no language pair-specific interaction terms; (2) many model components are causally influential in both monolingual tasks and translation tasks; and (3) fine-tuning on monolingual data recovers a large proportion of translation improvements relative to fine-tuning on aligned documents. Together, these provide convergent evidence in support of the interlingua hypothesis, and suggest new ways of understanding and improving how LLMs can be leveraged to perform translation tasks.

Most advances in keypoint descriptions address monomodal settings, where image variations arise from viewpoint, illumination, or contrast changes. Multimodal scenarios involve images produced by fundamentally different sensing processes, such as multispectral imaging, RGB-depth, satellite imagery, or medical imaging, causing the same structures to appear differently. A common solution to cross-modal description is to train descriptors for each modality pair, which requires retraining whenever the modalities change, or to train large models, which incur a significant increase in runtime. Instead, we propose CrossFeat, a framework that enables an existing monomodal descriptor to operate across modalities. Our method learns a crossing function in descriptor space that maps features from one modality to a representation compatible with another. To preserve the structural information captured by the original descriptor, CrossFeat introduces a geometry-appearance disentanglement such that only appearance is altered while the geometric properties are preserved. Experiments across multiple domains and datasets demonstrate improved performance in multimodal matching.

Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries. The mathematical essence of this phenomenon is that a symmetric input, after being processed by an equivariant map, experiences an increase in symmetry. While prior research has documented symmetry increase in specific cases, a rigorous understanding of its underlying causes and general reduction strategies remains lacking. In this paper, we provide a detailed and in-depth characterization of symmetry increase together with a principled framework for its reduction: (i) For any given feature space and input symmetry group, we prove that the increased symmetry admits an infimum determined by the structure of the feature space; (ii) Building on this foundation, we develop a computable algorithm to derive this infimum, and propose practical guidelines for feature design to prevent harmful symmetry increases. (iii) Under standard regularity assumptions, we demonstrate that for most equivariant maps, our guidelines effectively reduce symmetry increase. To complement our theoretical findings, we provide visualizations and experiments on both synthetic datasets and the real-world QM9 dataset. The results validate our theoretical predictions.

Domain adaptation has advanced cross-scene hyperspectral image classification, significantly improving discriminative capability in complex scenarios. However, privacy rules or storage limits often block access to data from the source domain. Conventional domain adaptation methods become impractical, severely restricting their utility in realistic remote sensing scenarios. To tackle this challenge, we propose a topology-aware source-free learning framework. We first introduce the entropy momentum pseudo-labeling (EMP) to refine k-means assignments by leveraging entropy-aware confidence and temporal prediction momentum. Under the guidance of the refined pseudo-labels, we further utilize the contextual neighborhood topology (CNT) to exploit the intrinsic geometric structure of the target feature space. Combining the global structural information extracted by collaborative representation with the local similarity information modeled by nearest neighbor search, the CNT accomplishes the comprehensive encoding of manifold-level geometric properties in the target domain feature space. The overall objective integrates cross-entropy on refined pseudo-labels, log inner product-based topology consistency, and an information-maximization term for balanced classification, ensuring stable adaptation in the source-free setting. Extensive experiments on three typical cross-scenarios demonstrate that the proposed method exceeds state-of-the-art performance, and ablation studies further validate the contribution of each module. The results highlight the critical role of topology-aware modeling in achieving robust and accurate classification without source data.

Text-to-image diffusion transformers learn about objects and scenes by learning to generate them, making them strong candidates for training-free zero-shot open-vocabulary semantic segmentation. State-of-the-art attribution methods score each pixel independently, comparing its features against a fixed text-derived class representation, whether as an output-space similarity or as a cross-attention weight. This discards structured signals the model itself exposes: the temporal structure of the generative trajectory, the visual appearance statistics of each concept, and the image's own pairwise feature geometry. We present MAVISEG, a training-free refinement layer that recovers these signals. Because its operators consume only a pixel-by-concept score field and a pixel feature space, MAVISEG is capture-agnostic rather than tied to one attribution method. Across six benchmarks it achieves the strongest overall results among training-free methods, including the best mIoU on every benchmark. Interestingly, gains are largest where the initial capture is weakest, and individual operators contribute depending on the noise in the field they refine. Our results indicate that diffusion transformers carry more concept-level information than current attribution methods recover, and that much of it is lost on the way to the mask rather than absent from the model.

World-action modeling has emerged as a promising paradigm for robotic control, as it empowers models to go beyond reacting to observations and anticipate how a scene will evolve. However, existing WAMs often incur substantial computational overhead. Pixel-space methods often allocate substantial capacity to visual details that may not be directly relevant to control, while some latent-space methods require multi-stage training to construct the reasoning space. The resulting training cost can make such methods difficult to train under modest computational budgets. In this work, we propose LiLa-WAM, a lightweight world-action model that reasons about the future in a compact latent space and can be trained end-to-end on a single 24GB GPU. Its core design is a compact latent reasoning space jointly shaped by future-state prediction and action generation, which keeps the model lightweight while remaining well aligned with control. For task specification, we further propose the Visual Transition Token(VTT), a language-free task representation that encodes each task as a direction in visual feature space. Experiments on RoboTwin~2.0, LIBERO, and real-robot tasks demonstrate LiLa-WAM's effectiveness, achieving 90.48% success across 50 RoboTwin tasks with single-GPU training.

Predicting spatial gene expression from histopathology images enables large-scale transcriptomic profiling without the cost of direct measurement. Existing methods decode the target gene set as a flat, unstructured vector, ignoring the inter-gene dependencies arising from shared biological pathways and regulatory programs. Without explicit structural guidance, models must infer these dependencies entirely from limited paired data, constraining prediction quality. We propose MSGR (Multi-Scale Gene Refiner), which bridges this gap by incorporating the Gene Ontology (GO), a curated functional hierarchy of genes, as an explicit structural prior. MSGR organizes target genes into a four-level GO tree. Its GO-guided decoder then progressively refines predictions from coarse functional domains to fine individual genes via residual corrections under scale-weighted supervision. Operating solely on the gene side, the GO-guided decoder serves as a seamless plug-in replacement that consistently improves existing architectures without requiring any image-side modifications. Extensive experiments on nine datasets from the HEST-1k benchmark provide empirical evidence for two central claims: GO-structured decoding consistently outperforms flat decoding, even against a state-of-the-art generative baseline, and the gain is attributable to biological ontology structure rather than hierarchical decomposition per se, as confirmed by a +0.027 margin over a structurally equivalent random hierarchy.

Low-light image enhancement (LLIE) aims to improve image quality and clarity in diverse and demanding low-illumination environments. However, existing deep learning-based LLIE methods struggle to accurately capture real-world illumination and restore texture details, largely because their algorithmic strengths remain underutilized. To address these issues, we present a supervised frequency domain deep learning network for LLIE, named multi-scale attention combined with the Fourier transform (MSFT) which adopts a U-shaped, one-stage architecture that infuses guidance from low-light images into the network by channeling it through multi-scale attention. We further fuse the amplitude information from priori channels with that of the low-light image in MSFT's self-created module, and carry out multi-scale guidance along with the network. Subsequently, to better enhance the faint feature, such as fine content and textures, and to better fuse global context confidence in the decoding stage, we separately introduce a multi-shape synergistic attention and a lightweight network that effectively integrate information in high-dimensional space to embed into the superlative feature space channel containing rich texture information. Extensive experiments conducted on LOL, SID, SMID, and SDSD datasets demonstrate that MSFT significantly outperforms state-of-the-art competitors. For example, compared with Retinexformer, our method achieves a peak signal-to-noise ratio of up to 41.76 decibels on the SDSD-outdoor dataset with an increase of 11.92 decibels and a structural similarity index of 0.988 with a 13.80% improvement.

Counterfactual explanations provide local, interpretable insight by identifying changes to an input that would alter its assigned outcome. Although well established in supervised learning, their extension to clustering is less direct, since cluster assignments are unlabeled and governed by the geometry of the partition. This paper introduces VoICE, a Voronoi-Induced Counterfactual Explainability framework for feature-weighted $k$-means clustering. Rather than treating cluster change as a crossing of a single pairwise centroid boundary, VoICE formulates counterfactual generation as projection onto the full weighted Voronoi region of a target cluster, incorporating feature weights directly into both the clustering geometry and the counterfactual objective to yield least-cost and parsimonious explanations under actionability constraints. Target regions are further intersected with data-derived bounds and homothetically contracted towards their centroids, limiting extrapolation and boundary sensitivity. VoICE consistently produces valid target-cluster membership, across several benchmark datasets, where the leading pairwise baseline does not.

Spatial transcriptomics enables profiling of spatial gene expression but is limited by high cost and low throughput, motivating prediction from H&E histopathology images. Existing context-aware methods mainly supervise absolute expression, while relative expression relationships between spots are rarely used explicitly. We propose COAST, a context-aware differential learning framework for spatial gene expression prediction. COAST conditions the local and global context features with type-specific modulation and aggregates the target and context spot tokens using a Transformer encoder to capture both fine-grained local patterns and slide-level structure. It is trained with a joint objective that combines absolute expression regression with signed differential regression between the target and context spots. Experiments on multiple spatial transcriptomics datasets show consistent improvements in correlation- and distribution-based metrics, demonstrating the effectiveness of context-aware differential learning for histology-based spatial gene expression prediction.

AI-generated image (AIGI) detection is undergoing a critical transition from laboratory benchmarks to open-world adversarial defense. The prevalent paradigm focuses on finding static feature spaces, assuming that some invariant artifacts learned from historical data can achieve universal zero-shot generalization. While achieving saturation on several AIGI benchmarks, this static hypothesis suffers a severe performance drop against rapidly evolving generators (e.g., SD3, Nano Banana Pro). To address these limitations, we propose that the field should expand beyond "static generalization" to a new paradigm of "dynamic adaptation". We introduce Fleet, a framework that pioneers a dynamic paradigm of continuous few-shot evolution, enabling rapid alignment with emerging generative threats. Fleet improves few-shot adaptation by replacing unconstrained feature updates with constrained routing correction, where avoidance routing redirects novel AI samples away from Non-AI-dominated routes within decoupled subspaces. To validate this, we present Treasure, a benchmark spanning 64 models and 360k images, featuring diverse architectures and 20 closed-source commercial engines. Experiments reveal that while static SOTA methods fail catastrophically on modern generators, Fleet restores performance from 20.4% to 73.1% with only 10-shot adaptation on "Doubao Seedream 4.0". Code and data are available at https://github.com/ICTMCG/Fleet .

World modeling requires forecasting uncertain futures while preserving information useful for downstream perception. Existing visual world models often struggle to satisfy both goals: VAE-based stochastic models operate in low-dimensional reconstruction latents, which can limit perception performance, while deterministic predictors using strong pretrained features collapse multimodal futures into a single blurry mean. In this work, we propose FlowWM, a stochastic world model that performs flow matching directly within pretrained feature space (e.g., DINOv3). This is challenging because pretrained features are substantially high-dimensional, making standard diffusion recipes suboptimal. To address this, we investigate the design choices needed for feature-space flow matching and introduce a differentiable one-step projection mechanism that enables efficient training with temporal consistency and task-driven objectives. We evaluate FlowWM on two benchmarks: a synthetic benchmark for systematic evaluation of accuracy and diversity, and a real-world benchmark FuturePerception. FlowWM improves perception performance, mode coverage, and horizon robustness, validating our proposed design for stochastic world modeling in high-dimensional feature spaces.

The incorporation of additional modalities into action recognition models increases their performance across a wide range of settings. However, how this additional information can contribute to making the models more robust remains underexplored, particularly for the case of multi-modal out-of-distribution (OOD) detection. While methods exist that regularize the multi-modal training process with OOD detection in mind, they still apply off-the-shelf OOD detectors designed for the uni-modal case during inference, discarding important information. Based on an interesting relationship we find between the multi-modal and uni-modal predictions, we propose to use this signal to build a post-hoc detector explicitly designed for the multi-modal scenario. We combine this new source of information with a feature-space score, which detects off-manifold samples in the multi-modal space, and normalize them by the multi-modal logits. In doing so, the proposed hybrid detector is compatible with existing training-time approaches and consistently improves performance. Experiments on a wide range of established datasets from the MultiOOD benchmark show that, on average, our approach outperforms the state of the art. Our results show the importance of explicitly considering the different modalities at inference time for multi-modal OOD detection.

Model merging (MM) has gained significant attention as a cost-effective approach to integrate multiple task-specific models into a unified model. However, recent work reveals that MM is highly susceptible to backdoor attacks. Existing defenses based on task arithmetic often fail to eliminate backdoors without substantially degrading clean-task performance, owing to their reliance on direct parameter-space editing. To address this gap, we propose Linear Feature Path Minimization (LFPM), a backdoor mitigation framework for model merging, which introduces an anti-backdoor task vector into the backdoored merged model. Unlike prior approaches, LFPM formulates the backdoor robustness of the merged model from a unified feature-space perspective under the Cross-Task Linearity (CTL) framework, which leverages the approximate linearity of features across tasks. This perspective guides the optimization of the anti-backdoor task to suppress backdoors while preserving clean-task performance. Furthermore, we introduce an effective optimization mechanism based on gradient accumulation and loss path-integral, ensuring robust backdoor suppression along the interpolation path. Extensive experiments demonstrate that LFPM consistently exhibits strong robustness against backdoor attacks in both full fine-tuning and Parameter-Efficient Fine-Tuning (PEFT) settings.

Annotation errors are widespread in computer vision datasets and can significantly degrade the performance of systems trained on them, particularly in complex tasks such as object detection. Several approaches exist to identify annotation errors, including training-free feature-space methods which provide a fast and interpretable way to analyze annotations. However, the behavior on object detection annotations, which include semantic and spatial information, remains largely unexplored. In this work we analyze the applicability of feature-space-based approaches for detecting annotation errors in object detection datasets. By adapting an existing feature-space method, we show that such approaches reliably expose semantic mislabel, while positional errors remain difficult to detect. We evaluate this behavior across multiple pretrained embedding models, synthetic noise types (symmetric, asymmetric, and positional), and real-world annotation errors using VOC2012 and KITTI. All code and real-world corruptions are publicly available at the following repository: https://github.com/ ChristianSieberichs/BoundingBox_corruption_detection

Deep neural networks (DNNs) excel in computer vision tasks given large annotated datasets. In real-world applications, however, labels are often corrupted by ambiguity, human error, or dynamic environments. Over-parameterized DNNs easily memorize these noisy labels during training, degrading model accuracy and generalization. Existing data-cleaning and sample-selection strategies often rely on manually specified thresholds, prior knowledge of the noise ratio, or a single metric (either learning dynamics or geometric structure), making them unstable in complex data regimes. This paper proposes a self-adaptive data-cleaning framework that integrates local, global, and learning dynamics cues for robust noisy-label detection. Samples are mapped into a unified low-dimensional feature space through a modular feature concatenation paradigm. We provide two instantiations: a 2D metric integrating class-adaptive KNN-based local disagreement with k-means-based global centroid distance, and a 3D multi-metric that additionally incorporates a z-normalized score. Unlike conventional 1D Gaussian Mixture Models applied to a single scalar metric, our framework performs multi-metric clustering on the feature space to adaptively partition samples into clean-dominant and noise-dominant components without requiring manual thresholds or noise priors. Experiments on CIFAR-10, MNIST, and ImageNet-100 with 5% to 40% symmetric label noise show high recall across settings, including near-perfect recall (>=98%) on ImageNet-100 at 40% noise. Subsequent training yields accuracy gains across evaluated settings, especially under severe corruption on ImageNet-100. These findings suggest that multi-metric integration provides a threshold-free, practical, and low-tuning strategy for noisy label detection.

Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution. While recent foundation models achieve strong in-domain performance through large-scale pretraining, their effectiveness often relies on broad data coverage and implicit pattern memorization, which can limit generalization when data are scarce or source and target domains are disjoint. In this work, we propose FSA, a feature-to-strategy framework for controlled zero-shot univariate forecasting. Instead of directly modeling raw sequences in the observation space, FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in our controlled zero-shot setting.

Two-sample testing is a fundamental tool for detecting distributional differences across scientific domains, but classical tests (including kernel-based tests) can be ineffective on high-dimensional structured data such as images. Recent deep two-sample tests improve sensitivity in these settings by learning informative representations, yet they provide limited insight into which data features drive rejection of the null hypothesis $H_0$. To address this issue, we propose a counterfactual explanation framework for deep two-sample testing that generates sample-level edits moving observations from a source group toward a target group while explicitly reducing the discrepancy measured by the test. Our method combines a diffusion autoencoder with a pretrained deep two-sample test model and optimizes a maximum mean discrepancy (MMD) objective in the test model's representation space to produce plausible counterfactuals. We quantify distribution-level effects through changes in the test statistic and the resulting two-sample p-values. We evaluate the method on synthetic 2D shape datasets and two MRI cohorts. Across both settings, the counterfactual transformations consistently increase p-values relative to the original samples, indicating that the edited source set becomes statistically closer to the target distribution under the test. We measure minimality using LPIPS to ensure the counterfactuals remain close to the original samples. The resulting edits provide interpretable evidence of the features associated with the detected group differences. On MRI, the localized changes are consistent with known anatomical differences between cohorts.

This work proposes a context-aware middleware for medical workflow organization and efficiency improvement. In hospitals, laboratories and teleradiology companies, each physician or technician is specialized in a specific kind of diagnosis or analysis. Therefore, certain types of medical images are often forwarded to a certain physician or a certain group. This forwarding is time consuming. That is, repeatedly deciding who would be the best physician, whether he is available at a certain moment given a certain context is exhaustive and may be very inefficient. Thus, the proposed middleware has the ability to process and collect data from images analyzed by each medical staff. Based on the collected data and current clinical context, the middleware is able to infer who would be the best fit staff to receive a certain incoming medical image.

Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering clean samples during training. However, simple sample filtering within feature spaces degraded by noise struggles to distinguish between challenging samples and noisy samples, creating a bottleneck for model performance. We highlight for the first time the fundamental importance of actively reshaping feature space geometry for learning from noisy data. We propose a novel Geometry-aware Manifold Regularization Paradigm whose core idea is to explicitly construct energy barriers between data manifolds by actively synthesizing virtual outlier samples. By imposing geometric constraints that promote intra-class compactness and inter-class separation, this approach enhances the discriminability between hard and noisy samples, leading to the learning of more robust representations. Our regularization mechanism exhibits high universality, with effectiveness independent of any prior assumptions about noise patterns. It can be integrated as a standalone mechanism into existing sample selection frameworks, providing stronger robustness against diverse noisy environments. Experiments demonstrate that our paradigm achieves performance surpassing current state-of-the-art (SOTA) methods on multiple benchmarks, including CIFAR-10, with particularly pronounced advantages under more challenging asymmetric noise conditions. Furthermore, this paradigm significantly enhances the model's capability in Out-of-Distribution (OOD) detection, ensuring superior reliability and safety for deployment in open-world scenarios.

Query-based Vision Transformer segmentation models typically reconstruct dense spatial feature maps to predict masks, inheriting design patterns from convolutional architectures. We show that this explicit image-space reconstruction is not required. We introduce TokenMask, a token-space mask head that computes mask logits directly from query-token affinities and performs interpolation in logit space rather than feature space. This reformulation preserves the original linear scoring mechanism while simplifying the computational structure. Across diverse ViT backbones, datasets and segmentation tasks, TokenMask consistently improves efficiency over prior approaches by reducing computational and memory requirements while maintaining competitive accuracy, leading to tangible speedups on NVIDIA Jetson AGX Orin using TensorRT FP16 inference. Overall, TokenMask yields a simpler and more deployment-friendly design for embedded vision systems.

This letter presents LiteLoc, a novel and efficient localizer built on 3D Gaussian Splatting (3DGS). The previous state-of-the-art (SoTA) sparse-to-dense localizer, STDLoc, has shown remarkable localization capability but suffers from severe storage redundancy and computational latency. By revisiting its design decisions, we derive two simple yet highly effective improvements that cumulatively make LiteLoc much more efficient in both memory and computation, while also being easier to train. One key observation is that the color field, inherited directly from Feature 3DGS, is functionally useless for localization. Yet, its reconstruction of high-frequency photometric details necessitates excessive Gaussian primitives, resulting in a tightly coupled color-feature representation with significant memory overhead and sub-optimal feature field optimization. To resolve this, we propose a color-free decoupled feature field that constructs a compact Gaussian scene representation by retaining only task-essential feature attributes, thereby eliminating approximately 94% of redundant storage with no loss of localization-relevant information. We further find that the primary computational bottleneck lies in the dense Perspective-n-Point (PnP) solver, where most matches contribute saturated geometric constraints with diminishing accuracy gains. Accordingly, we propose a condensing strategy that distills dense matches into a subset of 5% representative matches, enabling a nearly 19-fold speedup in robust estimation with negligible performance drop. Extensive experiments show that LiteLoc surpasses STDLoc in multiple scenes with considerable efficiency benefits, opening up exciting prospects for latency-sensitive visual localization.

The lottery ticket hypothesis posits that dense networks contain sparse subnetworks, ``winning tickets,'' that, when rewound to their initial weights and retrained in isolation, match the performance of the full model. We ask a more mechanistic question: what internal object does a winning ticket preserve? We work in a combinatorial, clause-structured toy setting that admits an interpretable feature-space representation with well-defined combinatorial distances between features. We show that winning tickets in weight space correspond to precursor locations in feature space that are already near, at initialization, to the final feature-channel codes. Dense SGD resolves these locations through structured selection: proximal locations either converge to final codes or are rejected, with rejection concentrated at more crowded neurons, implicating competition under superposition. A winning ticket is thus a family of compatible code locations that jointly balance proximity to final codes with low inter-feature interference. Sparse retraining often re-expresses the same clause/template family on a different row, so the preserved object is family-level rather than microscopic row identity. We validate this account with lightweight probes based on feature-space distance and motion; in our setting, these probes frequently outperform established weight-based ticket discovery methods in both accuracy and exact code recovery. Although these findings are grounded in a toy setting, they suggest that the lottery ticket structure is governed by hidden feature-space geometry rather than weight-space subnetwork identity.

Concealed Object Segmentation (COS) encompasses a family of dense-prediction tasks, including camouflaged object detection, polyp segmentation, transparent object detection, and industrial defect inspection, where targets are visually entangled with their surroundings through different physical mechanisms. Existing methods either operate directly on RGB images or employ \emph{heterogeneous} decompositions (\eg, Fourier, wavelet) that redistribute spatial evidence across scale/frequency coefficients, making pixel-aligned cues less direct. We introduce a fundamentally different perspective: \textbf{homogeneous image decomposition} via Retinex theory, which factorizes an image into illumination and reflectance components within the \emph{same} spatial domain. Our key insight is that visual entanglement enforces appearance matching in the composite space, but this does \emph{not} necessitate simultaneous matching in both component spaces, a phenomenon we formalize as the \textbf{Discriminability Gap Theorem}. Crucially, we show that across diverse COS sub-tasks, the underlying physical processes systematically anti-correlate illumination and reflectance differences, yielding theoretical guarantees that Retinex decomposition preserves or strictly improves total foreground--background discriminability across the full physical regime, with anti-correlation maximizing the gain. Building on this, we propose \textbf{RIDE} comprising: (i) a Task-Driven Retinex Decomposition module that learns segmentation-optimal factorizations end-to-end; (ii) a Discriminability Gap Attention mechanism that adaptively exploits where decomposition helps; and (iii) a Camouflage-Breaking Contrastive loss operating in reflectance feature space.

Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

Intermediate feature representations represent the backbone for the expressivity and adaptability of deep neural networks. However, their geometric structure remains poorly understood. In this submission, we provide indirect insights into this matter by applying a broad selection of manipulations in input space, ranging from geometric and photometric transformations to local masking and semantic manipulations using generative image editing models, and assess the feasibility of learning a mapping in the feature space, mapping from the original to the manipulated feature map. To this end, we devise different types of mappings, from linear to non-linear and local to global mappings and assess both the reconstruction quality of the mapping as well as the semantic content of the mapped representations. We demonstrate the feasibility of learning such mappings for all considered transformations. While global (transformer) models that operate on the full feature map often achieve best results, we show that the same can be achieved with a shared linear model operating on a single feature vector typically with very little degradation in reconstruction quality, even for highly non-trivial semantic manipulations. We analyze the corresponding mappings across different feature layers and characterize them according to dominance of weight vs. bias and the effective rank of the linear transformations. These results provide hints for the hypothesis that the feature space is to a first degree of approximation organized in linear structures. From a broader perspective, the study demonstrates that generative image editing models might open the door to a deeper understanding of the feature space through input manipulation.

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified learning theory for these settings has been lacking. To start addressing this gap, we introduce a novel convolutional learning framework for possibly infinite-dimensional signals supported on a manifold. Namely, we use the connection Laplacian associated with a Hilbert bundle as a convolutional operator, and we derive filters and neural networks, dubbed as \textit{HilbNets}. We make HilbNets and, more generally, the convolution operation, implementable via a two-stage sampling procedure. First, we show that sampling the manifold induces a Hilbert Cellular Sheaf, a generalized graph structure with Hilbert feature spaces and edge-wise coupling rules, and we prove that its sheaf Laplacian converges in probability to the underlying connection Laplacian as the sampling density increases. Notably, this result is a generalization to the infinite-dimensional bundle setting of the Belkin & Niyogi \cite{BELKIN20081289} convergence result for the graph Laplacian to the manifold Laplacian, a theoretical cornerstone of geometric learning methods. Second, we discretize the signals and prove that the discretized (implementable) HilbNets converge to the underlying continuous architectures and are transferable across different samplings of the same bundle, providing consistency for learning. Finally, we validate our framework on synthetic and real-world tasks. Overall, our results broaden the scope of geometric learning as a whole by lifting classical Laplacian-based frameworks to settings where the signal at each point lives in its own Hilbert space.

This paper proposes latent visualization by optimization (LVO), a mechanistic interpretability technique that extends feature visualization by optimization - originally developed for convolutional neural networks - to latent diffusion models. LVO employs sparse autoencoders (SAEs) to disentangle polysemantic layer representations into monosemantic features. Key contributions include latent-space optimization, time-step activity analysis, schedule-matched noise injection, prior initialization through feature steering, and suitable regularization strategies. We demonstrate the method on Stable Diffusion 1.5 fine-tuned on the Style50 dataset, showing that SAE features produce clear visualizations of recognizable concepts - including diagonal compositions, human figures, roses, cables, and waterfall foam - that correlate with dataset examples, while the baseline without disentanglement produces less coherent results. We further show that regularization techniques from pixel-space feature visualization transfer to the latent domain, though they require different configurations for the raw-layer and SAE variants. Compared to dataset examples and steering, LVO provides complementary insights by directly revealing what activates a feature rather than its downstream effects.

We show that Fréchet Distance (FD), long considered impractical as a training objective, can in fact be effectively optimized in the representation space. Our idea is simple: decouple the population size for FD estimation (e.g., 50k) from the batch size for gradient computation (e.g., 1024). We term this approach FD-loss. Optimizing FD-loss reveals several surprising findings. First, post-training a base generator with FD-loss in different representation spaces consistently improves visual quality. Under the Inception feature space, a one-step generator achieves0.72 FID on ImageNet 256x256. Second, the same FD-loss repurposes multi-step generators into strong one-step generators without teacher distillation, adversarial training or per-sample targets. Third, FID can misrank visual quality: modern representations can yield better samples despite worse Inception FID. This motivates FDr$^k$, a multi-representation metric. We hope this work will encourage further exploration of distributional distances in diverse representation spaces as both training objectives and evaluation metrics for generative models.

We study the problem of understanding where two populations differ within a feature space, which we formalize in the concept of a differential subgroup: a subset of individuals from both populations who, despite sharing similar characteristics, exhibit exceptional differences in a target outcome. Differential subgroups reveal the regions of the feature space where population-level gaps are most pronounced and can help practitioners identify the covariate combinations that are structurally responsible for these differences, e.g.~in clinical analysis, model diagnostics, or treatment-effect studies. We introduce a general optimization objective for discovering differential subgroups and establish conditions under which the resulting subgroups admit a causal interpretation of population differences. We propose DiffSub, a gradient-based approach that discovers interpretable differential subgroups in tabular data. Across synthetic benchmarks, medical case studies, model-error analyses, and treatment-effect settings, DiffSub identifies informative subgroups that reveal where population differences arise and why.

We show that the geometric relations between semantic features in large language models' hidden states closely mirror human psychological associations. We construct feature vectors corresponding to 360 words and project them on 32 semantic axes (e.g. beautiful-ugly, soft-hard), and find that these projections correlate highly with human ratings of those words on the respective semantic scales. Second, we find that the cosine similarities between the semantic axes themselves are highly predictive of the correlations between these scales in the survey. Third, we show that substantial variance across the 32 semantic axes lies on a low-dimensional subspace, reproducing patterns typical of human semantic associations. Finally, we demonstrate that steering a word on one semantic axis causes spillover effects on the model's rating of that word on other semantic scales proportionate to the cosine similarity between those semantic axes. These findings suggest that features should be understood not only in isolation but through their geometric relations and the meaningful subspaces they form.

One of the most exciting applications of vision models involve pixel-level reasoning. Despite the abundance of vision foundation models, we still lack representations that effectively embed spatio-temporal properties of visual scenes at the pixel level. Existing frameworks either train on image-based pretext tasks, which do not account for dynamic elements, or on video sequences for action-level reasoning, which does not scale to dense pixel-level prediction. We present a framework that learns pixel-accurate feature descriptors from videos, LILA. The core element of our training framework is linear in-context learning. LILA leverages spatio-temporal cue maps -- depth and motion -- estimated with off-the-shelf networks. Despite the noisy nature of those cues, LILA trains effectively on uncurated video datasets, embedding semantic and geometric properties in a temporally consistent manner. We demonstrate compelling empirical benefits of the learned representation across a diverse suite of vision tasks: video object segmentation, surface normal estimation and semantic segmentation.

We propose PathBoost, a gradient tree boosting method for graph-level classification and regression that learns discriminative path-based features directly from the input graph structure. Building on a previous work, which was tailored to a specific chemistry application, PathBoost introduces three key extensions: (i) adaptation to binary classification through gradient boosting with a logistic loss, (ii) incorporation of multiple node and edge attributes into the path feature space via a prefix-based decomposition, and (iii) automatic anchor node selection based on categorical attribute diversity, eliminating the need for the user to specify the starting point of the considered path features. We compared PathBoost to graph neural networks and graph kernel approaches on several benchmark datasets, obtaining better results in half of them, and comparable results in the rest. PathBoost shows better performances on graphs with larger average node counts. Overall, the results demonstrate that path-based boosting methods can be competitive with more complex black-box approaches.

Standard supervised learning optimizes for predictive accuracy but remains agnostic to the internal geometry of learned features, often yielding representations that are entangled and brittle. We propose Class-Conditional Activation Regularization (CCAR) to explicitly engineer the feature space, imposing a block-diagonal structure via a soft inductive bias. By shaping the latent representation to confine class energy to orthogonal subspaces, we create an intrinsic geometric scaffold that naturally filters noise and adversarial perturbations. We provide theoretical analysis linking this structural constraint to the maximization of the Fisher Discriminant Ratio, establishing a formal connection between geometric disentanglement and algorithmic stability. Empirically, this approach demonstrates that robustness is an emergent property of a well-engineered feature space, significantly outperforming baselines on label noise and input corruption benchmarks.