Representation Learning

The rapid development of large language models (LLMs) has raised concerns about misuse such as plagiarism, misinformation, and automated influence operations, motivating the need for robust detectors. Recent work has shown that neural representations of writing style are effective for detection and, crucially, robust to adversarial attacks that defeat most existing detectors. However, current style-based detectors rely on authorship labels for training, and are limited to few-shot inference for detection, requiring in-distribution samples that may not always be available. We learn discriminative style features without authorship labels by training a style encoder to reconstruct human-authored text from its machine-generated paraphrase; freezing a semantic encoder during training biases the style encoder to capture only the non-semantic features needed for reconstruction. We evaluate the learned representations via two detection strategies: a few-shot detector and a zero-shot DeepSVDD-based detector. Across benchmarks, our method matches or outperforms all baselines in the few-shot setting and, in the zero-shot regime, is competitive with fully supervised classifiers on in-distribution test data while generalizing better to unseen LLMs. Beyond detection, the learned representations generalize to unseen tasks, achieving competitive performance on authorship verification and fine-grained style discrimination despite never being trained on either objective.

Embodied world models have emerged as a pivotal paradigm for visual robotic decision-making and interactive environment simulation. However, conventional embodied frameworks rely on low-dimensional structured action vectors (e.g., joint angles and end-effector poses), which suffer from limited expressive capacity, poor generalization across diverse embodiments, and unnatural dynamic modeling for complex physical interactions. To address these limitations, this paper proposesiMac (Image as Action Control), a novel unified control paradigm that treats raw visual images as native action representations for embodied world models. Departing from traditional explicit kinematic action encoding, iMac formulates continuous visual manipulation as image-based action tokens, which inherently encapsulate spatial motion intentions, interactive geometric constraints and subtle physical dynamics. We construct a dual-branch embodied architecture consisting of an image-action encoder and a dynamic world predictor: the encoder compresses target-driven visual images into compact action embeddings, while the predictor learns environment transition rules conditioned on image actions to achieve high-fidelity future state prediction and closed-loop embodied control. Extensive experiments are conducted on public embodied manipulation benchmarks and real-world robotic scenarios. The results demonstrate that iMac outperforms vector-based action control baselines in prediction accuracy, task success rate and cross-scene generalization ability. Moreover, our image-action design eliminates the reliance on manually defined action spaces, realizing flexible and universal control for heterogeneous embodied agents. This work provides an innovative visual-action perspective for embodied world models, offering a simple yet effective paradigm for scalable robotic perception and manipulation.

Force and tactile sensing are indispensable in contact-rich manipulation. However, force-aware robot learning faces critical challenges due to the incompatible assembly of tactile and force sensors in handheld or wearable devices. To address these limitations, we first introduce AetheRock for gripper-force, vision, and tactile data collection, which is an arm-worn device featuring a modular and easily manufactured visuo-tactile sensor, GelSlim-MiniFab, at the fingertip, a resistive pressure sensor at the human finger contact region, a customized PCB module, and a wearable kit for comfortable and robust collection. Building on this, we propose ForceVT, a representation learning framework that uses force and vision to guide fidelity-agnostic tactile learning, enabling robust inference in any tactile situation. Real-world experiments show that AetheRock achieves qualified data efficiency and that ForceVT effectively alleviates inefficiencies when visuo-tactile sensors exhibit manufacturing and utilization inconsistencies. Overall, our work mitigates the limitations of gripper-force vision-tactile robot learning through innovative hardware design and algorithms.

Muon has recently emerged as a state-of-the-art optimizer for pretraining Large Language Models (LLMs) and vision classifiers. Despite its efficiency advantage over Adam and SGD, the feature-learning advantage of Muon remains unclear. This paper investigates Muon's feature-learning advantage through the lens of robustness and transferability. First, by evaluating pretrained models on corrupted images and texts, we show that features learned by Muon are consistently more robust than those learned by Adam and SGD across different architectures, including transformers and Convolutional Neural Networks (CNNs). Using trained layer-wise probes, we further show that this robustness advantage is reflected in larger logit margins across layers. Second, by training linear classifiers or fine-tuning full models from pretrained parameters on downstream tasks, we demonstrate that Muon-learned features transfer more effectively than those learned by Adam and SGD. This transferability advantage is further supported by the diversity of hidden states across layers, as measured by effective rank. Finally, in a representative classification problem with multi-component features, we prove that Muon attains larger margins and higher effective rank than Adam and SGD, providing theoretical support for our empirical findings.

Selecting which companies to approach is a central challenge in business-to-business (B2B) sales, where decisions are often based on manual research and fragmented information sources. Modern B2B sales platforms centralize company records and use learned company embeddings to support tasks such as recommending and prioritizing potential clients. In this study, we investigate whether enriching these company embeddings with Semantic knowledge from DBpedia improves downstream interaction-prediction performance, within a pipeline that integrates structured company attributes and text embeddings deployed on a real B2B platform. We evaluate the learned embeddings on a downstream interaction prediction task using real user feedback data from the platform. Results show that DBpedia enrichment improves downstream performance, with gains observed on ranking and discrimination metrics.

Football event data constitute a rich spatiotemporal source for quantitative analysis of player actions in team sports. These datasets contain heterogeneous features, combining continuous location coordinates with categorical variables such as action type, action outcome, and body part. Such data have been applied in sports analytics for match outcome forecasting, player evaluation, and tactical pattern recognition. However, existing approaches predominantly encode categorical features using one-hot or ordinal embedding representations, overlooking the intrinsic semantics of action descriptors. The Transformer is a deep neural network architecture based on self-attention that captures dependencies between input features at arbitrary positions. We propose and implement a Transformer-based model to learn latent dependencies among categorical event features and produce dense representations of football events. By encoding categorical features as learned embedding vectors, sport-specific action semantics are captured during pretraining, enabling the representations to support downstream tasks such as action value estimation and play style recognition. Empirical evaluation shows that the embedding representations yield superior probability calibration over task-specific baselines on the downstream prediction tasks, as measured by Brier score.

Tabular encoders are usually evaluated inside task-specific end-to-end pipelines, so models from different training paradigms are difficult to compare directly even when they operate on similar tabular signals. We introduce TRL-Bench, a multi-granular tabular representation learning (TRL) benchmark that standardizes cross-paradigm representation-level evaluation: each encoder exports row-, column-, or table embeddings through its supported wrapper, and shared lightweight heads probe them across three suites: TRL-CTbench (column/table), TRL-Rbench (row), and TRL-DLTE (compositional Data-Lake Table Enrichment spanning all three granularities). To support this standardized setting, we release curated benchmark assets and task reformulations, including 50 OpenML tables with 123 verified targets, 16 row-pair linkage rewrites, and a 47,772-table DLTE lake derived from 1,379 parent tables. Across 20 models and 16 tasks, TRL-Bench shows that once downstream conditions are standardized, encoder quality is capability-specific rather than captured by a single leaderboard. In TRL-CTbench, generic text encoders often lead on tasks with strong surface-text signal, while tabular specialists win where their pretraining objective aligns with the task. In TRL-Rbench, within-table prediction and cross-table linkage favor different training regimes, with atomic linkage performance correlating strongly with the row-matching stage of DLTE pipelines. In TRL-DLTE, the strongest pipelines combine capability-matched specialists rather than reuse a single encoder, and top end-to-end quality depends on non-additive compositional fit rather than per-stage marginal rank alone. TRL-Bench provides a common protocol for measuring reusable signal in exported tabular representations under shared downstream conditions. Code and data: https://github.com/LOGO-CUHKSZ/TRL-Bench

Multispectral point cloud (MPC) is composed of 3D spatial-spectral information, which holds tremendous potential for accurate land-cover classification. However, the representation power of classification models is limited by inherent high-dimensional and heterogeneous spatial-spectral information, unbalanced sample distribution, and inter-class spectral similarity of airborne MPCs. We build two MPC datasets and propose an enhanced geometric-spectral feature learning framework based on attentions for airborne MPC classification. A key component in our model is a two-stream feature fusion method with attention mechanisms, which enhances the representation capability of spatial-spectral features from high-dimensional heterogeneous MPCs. The first stream aims to extract position-encoded global spectral features with fusion self-attention, and the second stream comprises a multikernel point convolution and feature aggregation attention to extract spectral-guided geometric features. We then develop a residual attention fusion block to integrate the most informative geometric-spectral features from the two parallel streams. Another important contribution of this work is a joint loss function to improve the learning ability on unbalanced and interclass similar samples. Experimental results on two airborne MPC datasets demonstrate the effectiveness of the proposed method compared with the state-of-the-art methods. Furthermore, the codes and datasets used in this paper will be made available freely at https://github.com/HITlixian/TGRS_GSFF.

Instruction-based controllable speech synthesis enables users to specify emotions through natural language. However, existing approaches often rely on coarse emotion labels and lack explicit modeling of fine-grained intensity. We propose EmoInstruct-TTS, a dual-path instruction-guided framework for emotional speech synthesis. We introduce Emotion2embed, a supervised semantic-acoustic emotion embedding covering 48 emotional states, including fine-grained categories and intensity levels. To infer embeddings from free-form instructions, we design an Instruction-Conditioned Emotion Flow Model (ICE-Flow) that generates acoustically grounded emotion representations. The inferred embeddings are integrated into an LLM-based synthesis pipeline to provide explicit emotional control while preserving semantic planning. Experiments show improved emotional controllability and speech naturalness over strong baselines.

Action-supervised fine-tuning of vision-language-action (VLA) policies can compress visual structure that is weakly constrained by the action objective. We formalize this as residual visual collapse along local action fibers and propose FiberTune, a training-time objective that preserves teacher-structured visual residuals without adding inference-time overhead. FiberTune uses an online action probe to filter action-predictive directions from intermediate visual-token representations. It preserves the residuals through centered directional alignment with a frozen visual teacher and effective-rank regularization. Under identical training conditions, FiberTune improves over task-loss-only fine-tuning in every one of six simulation settings spanning two benchmarks and two architectures ($π_{0.5}$ and OpenVLA-OFT), as well as on physical SO-101 pick-and-place; representative gains include +10.7 pp SR(5) on long-horizon CALVIN ABC$\rightarrow$D and physical SO-101 task success rising from 72.7% to 78.1%. Representation analyses support the preservation of visual information in the residuals.

Sparse coding provides a principled framework for signal representation by expressing an input as a linear combination of only a small number of basis functions. The Locally Competitive Algorithm (LCA) is particularly attractive in the context of neuromorphic computing because its dynamics, leaky integration, thresholding, and lateral inhibition map naturally to neuromorphic hardware. While prior work has studied non-convolutional LCA on Loihi 2, the convolutional setting is of particular interest because it introduces spatial structure, weight sharing, overlapping receptive fields, and scaling behavior that are more representative of practical sparse inference workloads. In this work, we present a Loihi 2 implementation of convolutional sparse coding via the LCA and evaluate it against a conventional GPU baseline on the same inference problems. The implementation follows a one-layer recurrent LCA formulation and extends it to convolutional feature maps with local inhibitory kernels derived from pairwise filter interactions. To the best of our knowledge, this is the first implementation and benchmark of convolutional LCA on Loihi 2. Our goal is not only to demonstrate feasibility, but also to clarify in which operating regimes convolutional sparse inference becomes attractive on neuromorphic hardware. The resulting study positions convolutional LCA as a useful benchmark for structured sparse inference on emerging neuromorphic systems.

Neural fields parameterize data as functions from coordinates to values, providing a unified framework for representation learning across modalities. Existing approaches are dominated by per-sample meta-learning, which scales poorly due to memory-intensive inner-loop optimization. The natural alternative -- feed-forward encoding -- typically introduces modality-specific assumptions, sacrificing the generality that makes learning with neural fields attractive. We argue that locality and hierarchy are useful priors for learning field representations that can be injected without compromising modality-agnosticism. We propose LH-NeF, a framework to learn general-purpose tokenized representations of continuous signals. A locality-preserving hierarchical encoder maps raw coordinate-value field observations to structured tokens, from which the field is reconstructed during training. By replacing meta-learning's inner loop with a single forward pass, LH-NeF uses 42$\times$ less memory and supports 133$\times$ larger batches than the strongest modality-agnostic baseline. Across images, 3D shapes, and climate fields, our learned representations match or exceed performance of modality-agnostic, modality-specific, and specialized generative neural field baselines on both reconstruction and downstream tasks.

Self-supervised methods that learn representations and predict dynamics fully in the latent space, such as JEPA, have been shown to confuse slowly varying noise with the dynamical signals they aim to capture. Specifically, when noise features remain approximately constant within each trajectory, contrastive predictive objectives preferentially encode these features instead of the true latent variables governing the system. The learned representation then becomes dominated by trajectory-specific noise, so downstream performance degrades with noise strength and does not improve even as the number and duration of training trajectories increase. We argue that this failure is a property of the objective itself, shared by a long line of contrastive predictive objectives that sample negatives across trajectories. To illustrate this generality, we study the failure mode and its remedy in two settings: a standard SimCLR-style JEPA on a synthetic moving-dot dataset, and DySIB, a recently introduced method designed for extracting physically interpretable representations of dynamics, on movies of a rigid-body pendulum. When negatives are instead sampled within a single trajectory, the slow noise can no longer distinguish frames within that trajectory, removing the predictive shortcut. Training one encoder simultaneously on many such trajectories then forces it to encode the variables relevant for the dynamics, with longer trajectories yielding better representations even for strong slow noise. Our results point toward principles for designing contrastive predictive objectives in dynamical representation learning, especially for physical systems with noisy experimental observations.

Representation learning is central to modern machine learning, but most research examines how representations are optimized after a framework has been selected. Less attention is given to when a new representational level becomes necessary. This article introduces the Bootstrap Theory of Representational Emergence (TBER), an initial conceptual theory and research program describing how new representations arise when existing ones become explanatorily insufficient. A representation may remain descriptively useful while failing to make certain observations, relations, transformations, or organizational properties intelligible. TBER treats this explanatory insufficiency as a positive signal for representational transition rather than as simple falsification or prediction error. The proposed recursive process follows five stages: stabilized observation, anomaly detection, recognition of explanatory insufficiency, representational emergence, and provisional stabilization. The framework concerns transitions between scientific or computational representations, not equivalent transitions within the physical systems being observed. Its scope includes representation learning, latent spaces, foundation models, world models, digital twins, adaptive biological systems, and scientific discovery. TBER does not propose a new algorithm, model architecture, benchmark, or optimization procedure. Its contribution is meta-representational: it provides a framework for interpreting when and why new representational levels become necessary. A possible implication for future artificial intelligence is the development of systems able to detect when their own internal representations have reached explanatory limits and to initiate representational refinement or transition.

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.

In the current era of deep learning and especially generative models, there is significant investment in training very large deep neural networks. Thus far, such models have been "black boxes" that are difficult to understand in the sense that they have opaque internal mechanisms, leading to difficulties in interpretability, reliability, and control. Naturally, this lack of understanding has led to both hype and fear. This book is an attempt to "open the black box" and understand the mechanisms of large deep networks, through the perspective of representation learning, which is a major factor - arguably the single most important one - in the empirical power of deep learning models. A brief outline of this book is as follows. Chapter 1 will summarize the threads that underlie the whole text. Chapters 2, 3, 4, 5, and 6 will explain the design principles of modern neural network architectures through optimization and information theory, reducing the process of architecture development (long having been described as a sort of "alchemy") to undergraduate-level linear algebra and calculus exercises once the underlying principles are introduced. Chapters 7 and 8 will discuss applications of these principles to solve problems in more paradigmatic ways, obtaining new methods and models which are efficient, interpretable, and controllable by design, and yet no less - sometimes even more - powerful than the black-box models they resemble. Chapter 9 will discuss potential future directions for deep learning, the role of representation learning, as well as some open problems.

Research metrics use attention as evidence of societal impact. Yet attention serves as evidence only once interpreted, and its meaning depends on its contextual structure, not on volume alone. Altmetrics represents signals in isolation, keeping a count of the attention an output received, or a sequence of when. We address this with attention flows, representations that situate an output's attention in the contexts through which it is distributed. To evaluate the flow, we build a benchmark of analogy queries, each testing whether the relationship between two outputs, applied to a third, yields a fourth. The count and sequence baselines fail to recover these relationships, whereas flows learned as dynamic contextualised representations recover them. The recovered structure also survives partial observation and rests on its contexts instead of volume. These findings support attention represented as contextually structured for research evaluation.

Diffusion MRI (dMRI) tractography is the only noninvasive approach for mapping white-matter pathways in the living human brain. It represents each brain as a tractogram: a large, unordered set of three-dimensional streamlines that includes information about both local streamline geometry and whole-brain anatomical organization. This structure makes tractograms a natural but challenging target for representation learning. Existing methods treat streamline classification and subject-level prediction as separate problems: streamline classifiers focus on geometric patterns, whereas subject-level prediction often depends on hand-crafted features. As a result, current methods do not learn reusable representations that connect streamline anatomy with whole-brain inter-subject variation. Here we introduce TractFM, a tractogram foundation model that learns reusable representations directly from whole-brain streamline sets. TractFM combines a local streamline encoder with a permutation-equivariant tractogram encoder, allowing all streamlines from a subject to be contextualized jointly in a single forward pass. Pretraining on dense anatomical tract parcellation, i.e., assigning anatomical labels to individual streamlines, yields two complementary representations: contextualized streamline-level embeddings for tract parcellation and compact subject-level descriptors for downstream prediction of subject phenotypes. Across three tractography algorithms and five dMRI datasets, TractFM transfers to both streamline-level and subject-level tasks. Its frozen representations achieve accurate tract parcellation and predict age and sex across independent datasets. These results show that whole-brain geometric context, learned once, can generalize across tractography pipelines, datasets, and prediction tasks.

Ranking in digital marketplaces is a dynamic exposure-allocation mechanism: displayed items shape discovery trajectories and success events logged by the platform to update future allocation policies. Modern ranking systems rely heavily on exposure-confounded signals (e.g. popularity estimates, CTR/CVR aggregates, and ID-based representation), because they are highly predictive under stationary demand. Yet this predictive power can become a learning shortcut: early access to exposure-dependent belief signals steers optimization toward over-reliance on them and away from exposure-independent merit signals (e.g., content-based competitiveness and semantic affinity). Consequently, the learned policy tends to entrench incumbents and degrade cold-start generalization and robustness under distribution shift. We propose Representation Curriculum (RC), a training-time intervention that temporally stages feature utilization. RC foregrounds content-based merit signals initially, then introduces exposure-dependent belief signals while anchoring the content pathway near the learned merit representation, curbing shortcut reliance on historical signals and mitigating gradient starvation on content signals. We formalize RC independently of task and hypothesis class and provide ranking-specific instantiations. In a Gaussian linear ridge setting, we derive closed-form solutions and sufficient conditions under which RC strictly reduces population risk on a cold-start target distribution, with a quantified Pareto tradeoff against source performance. Experiments on public learning-to-rank and recommendation benchmarks, and randomized online experiments in a large-scale e-commerce search system, show that RC measurably shifts reliance from historical belief signals toward content-based merit signals and yields consistent gains on cold populations with a controlled trade-off in head performance.

The rapid advancement of high-throughput sequencing has led to large, high-dimensional omics datasets. Deep unsupervised learning architectures, particularly Autoencoders (AEs), are increasingly used for dimensionality reduction and representation learning in this domain. However, AEs are highly sensitive to architectural choices and hyperparameters, and unsupervised optimization typically relies on reconstruction loss, which may be a poor proxy for downstream utility. Exhaustive hyperparameter optimization (HPO) is computationally expensive, leading researchers to frequently rely on suboptimal default configurations. To democratize access to large-scale unsupervised HPO research, we introduce $\textbf{BBOmix}$, the first open-source tabular benchmark for unsupervised representation learning on real-world biological data. Our benchmark includes 105,000 evaluations across four AE architectures and seven multi-omics modalities from the TCGA and SCHC datasets. We quantify the correlation between reconstruction loss and downstream task performance and provide an extensive evaluation of state-of-the-art single-fidelity, multi-fidelity, and transfer learning HPO methods, establishing a rigorous baseline for future research in unsupervised biological representation learning.

High-dimensional and incomplete (HDI) data are prevalent in many real-world big data scenarios. Latent factor models serve as a common representation learning approach, capable of uncovering informative latent factors from such data. Nevertheless, most existing latent factor models rely solely on gradient descent for optimization, which may lead to insufficient and biased representations, particularly when dealing with heterogeneous HDI data. Thus, this study proposes an Ensembled Latent Factor Model via Differential Evolution and Gradient Descent Optimization (ELFM-DEGDO) with two-fold designed: 1) two diverse latent factor models are independently modeled via differential evolution and gradient descent optimization, respectively, and 2) the two diverse latent factor models are combined via a customized self-adaptive weighting mechanism to effectively fuse their strengths. By leveraging the complementary advantages of both optimization paradigms, ELFM-DEGDO is able to produce more comprehensive and less biased representations for HDI data. Three HDI datasets are tested to show that ELFM-DEGDO consistently performs better than related several latent factor models.

Multi-vector visual document retrievers achieve strong fine-grained matching by representing each page with multiple vectors from deep Vision-Language Models (VLMs), but this design makes deployment expensive in both storage and computational overhead. Existing efficiency techniques usually optimize only part of this budget, leaving multimodal retrievers without a unified way to trade accuracy for both vector width and encoder depth. Therefore, we propose MM-Matryoshka, a 2D Matryoshka training framework for budget-elastic Visual Document Retrieval (VDR), enabling ColPali-style multi-vector retrieval elastic along both dimension and layer. At inference time, a single retriever can select a 2D selectable budget without training separate models for different budgets. Through comprehensive experiments across multiple representative backbones, we demonstrate that by retaining significantly higher quality than direct truncation baselines while substantially reducing storage and computational overhead, MM-Matryoshka can offer robust budget elasticity for efficient VDR.

Embodied agents that navigate cities rely on world models that predict how their surroundings will change as they move. But for navigation, what matters is not what the buildings look like; it is where the agent can go. Most world models nonetheless predict appearance, learning how a scene looks rather than the space an agent can move through. Those that do target geometry, such as bird's-eye-view occupancy grids, flatten the three-dimensional environment onto a ground plane, discarding the above-ground and multi-level structure that shapes real navigation. What is missing is a predictive target that captures the navigable geometry an agent actually traverses, without photometric entanglement and without collapsing the third dimension. Our key idea is to model the open volume between buildings, the negative space, encoded as a 3D isovist: a spherical visibility-depth map recording the distance to the nearest surface in every direction. We introduce an embodied world model that predicts the next isovist from a short history of past isovists and a movement action. The prediction is formulated as a depth residual so the decoder inherits sharp building edges, trained with self-rollout scheduled sampling to keep corrupted context on the geometry manifold, and equipped with a persistent latent bird's-eye-view spatial map for cross-path consistency. Our central finding is emergent and unexpected: a single city-blind model trained on Manhattan and Paris develops a cross-city spatial signature, with city identity linearly decodable from its temporal latents far above single-frame baselines, so the signature lives in the learned dynamics rather than in appearance. The representation is lightweight, interpretable, and reproducible, offering a geometric substrate for spatial reasoning in embodied AI, robotics, and urban analysis, released with an open dataset and pipeline.

Representation learning is often described as preserving the information in an input that is relevant for prediction. This work asks what relevance means for a fixed supervised decision problem. A representation is defined to be Bayes-sufficient for a joint distribution and loss if some prediction head can use it to implement a Bayes-optimal action rule. This makes the target information loss-dependent. In the almost-surely unique Bayes-action case, the relevant object is a Bayes quotient, which identifies inputs that require the same Bayes-optimal action. A representation is sufficient when it refines this quotient, and Bayes-minimal when it is informationally equivalent to it. The framework connects naturally to property elicitation: zero-one loss requires the Bayes class, squared loss the conditional mean, Brier loss the conditional probability in binary prediction, and log loss or strictly proper scoring rules the predictive distribution. Controlled finite experiments, learned neural bottleneck experiments, and a real-data iNaturalist taxonomic refinement experiment illustrate the distinction between sufficiency, minimality, and retained non-required information. For a fixed supervised problem, the distribution and the loss determine the Bayes action, the Bayes action determines the quotient, and the quotient determines the minimal information required for Bayes-optimal prediction.

Test-time adaptation (TTA) aims to align a model to shifting test domains using only unlabeled streaming data. Most existing methods implicitly infer a single global domain distribution, ignoring the multidimensional and sample-specific nature of real-world domain shifts, leading to fragile adaptation. We propose DOME, an effective domain encoder that explicitly models each sample's domain in a zero-shot manner. DOME leverages vision-language pretraining to extract dense, continuous representations, parameterizes domains as distributional variables, and introduces a momentum-updated sparse domain bank for disentangled supervision. By injecting these explicit domain cues into downstream models, even a basic entropy-minimization TTA strategy achieves state-of-the-art performance across ImageNet-C, ImageNet-R, and ImageNet-Sketch, outperforming complex TTA approaches. Our results demonstrate that robust adaptation stems not from intricate adaptation algorithms, but from explicit, structured domain representation.

Knowledge Distillation (KD) is a powerful tool for model compression, yet the precise mechanisms by which student models acquire feature representations remain underexplored. In this work, we analyze student feature learning using the Interaction Tensor framework. Our analysis reveals that effective KD acts as a regularizer that prunes low-frequency, sample-specific features, encouraging the student to rely on a compact set of highly reusable features. Crucially, we observe that the dataset-level confusion matrix contains structural information analogous to the teacher's "Dark Knowledge." Leveraging this insight, we propose Confusion Distillation (CD), a teacher-free self-distillation method that utilizes the model's own evolving )confusion patterns as dynamic soft targets. CD achieves competitive performance on ResNet-34 and ResNet-50 for CIFAR-100, outperforming existing self-distillation methods like CS-KD and PS-KD by 1.2% while offering a computationally efficient alternative to standard KD.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict $g_1 \star g_2$ for elements of a finite group $G$. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce coherence, a geometric property inspired by neural coding in the brain, where neurons like grid cells and head direction cells respond to contiguous regions of state space. A non-negative matrix is coherent if each row (sample) attends to geometrically clustered columns (features) and vice versa, and in addition every sample is well described by some feature and every feature is needed by some sample. We prove that coherent matrices induce a bounded interleaving between the Vietoris-Rips filtrations of samples and features, guaranteeing that both spaces share compatible topological structure. This geometric constraint facilitates interpretability. For example, if data lies on a circle, coherent features must tile that circle into contiguous arcs. We introduce Coh, a differentiable objective function based on Fréchet variance that enforces coherence during training. Unlike sparsity, which bounds how many samples a feature activates on, coherence bounds which samples, requiring geometric connectivity rather than only rarity. This yields not just interpretable features but an interpretable feature space. We validate Coh in an auto-encoder using synthetic and rotated MNIST datasets and in a token embedding of BERT using language data.

Sparse Autoencoders (SAEs) have found success parsing neural representations into interpretable concepts, providing a basis for understanding and control. However, what exactly SAEs extract, and, correspondingly, the scientific conclusions we can draw from them, are not obvious. Empirically, the proof is in the pudding: SAEs learn interpretable features. Theoretically, we lack a clear account of what properties a 'concept' must satisfy for an SAE to extract it. There has been extensive identifiability work studying the conditions under which sparse coding recovers ground-truth features; however, these approaches tends to focus on simple data-generating models (e.g. sparse independent features) which poorly approximate the internet-swallowing language-model representations on which SAEs are trained. Here, avoiding data-generating models, we ask simply what properties any dictionary learning optimum must satisfy. Concretely, we extend local optimality analyses (Gribonval & Schnass, 2010) to the nonnegative joint-optimisation problem that vanilla SAEs approximate, and derive constraints relating optimal SAE features to their distributions. We use these constraints to explain a range of observed SAE behaviours - hierarchical splitting & absorption, the structure of residuals, and dense antipodal features - each reflecting how L1+nonnegativity interact with data to structure optimal dictionaries. Finally, we construct a novel large-dictionary convex problem and explore the wide atom-per-datapoint limit. In sum, we hope to tease model assumptions from unexpected observations, letting us learn more from SAEs' successes and provide principles for designing their successors.

Earth Observation (EO) has fundamentally transformed the monitoring of environmental processes and human activities up to planetary scale. Recent advances in self-supervised learning have given rise to Earth Observation Foundation Models (EOFMs), which leverage petabyte-scale unlabeled EO data to learn transferable representations across a wide range of downstream geospatial tasks. Despite these advances, current EOFMs remain largely confined to raster modalities, overlooking the rich, structured information encoded in openly-accessible vector data sources such as OpenStreetMap and Overture. Vector data provides explicit and compact representations of geographic entities, including geometry, topology, and semantic relationships, offering critical contextual signals that are often ambiguous or inaccessible in imagery alone. Raster and vector data thus represent complementary views of geographic space: raster data captures continuous physical and spectral patterns, while vector data encodes discrete objects and their relational structure and often represents more of the human rather than the physical systems (e.g. social or demographic data). However, existing geospatial representation learning paradigms treat these modalities in isolation, relying on imperfect and often lossy transformations to bridge them. This perspective paper calls for a paradigm shift toward joint Spatial Representation Learning (SRL) in an unified embedding space that integrate raster perception with vector-based reasoning. Building on emerging efforts in multimodal geospatial learning, we highlight conceptual foundations, technical challenges, and promising directions for aligning heterogeneous spatial data sources. We contend that such integration is essential for developing next-generation geospatial AI systems capable of more accurate, interpretable, and semantically grounded understanding of the Earth.