Representation Learning

Urban representation learning encodes complex urban environments into general-purpose embeddings for diverse downstream tasks and emerging urban foundation models. However, current evaluations are limited, typically focusing on one or two cities and tasks and relying on random splits that introduce spatial leakage, leading to inflated performance and weak support for cross-location generalization and fair comparison. To address this, we propose CityRep, a unified benchmark that evaluates urban representations across data modalities, cities, and tasks using spatially structured splits. CityRep consists of three key components: (1) a spatial unit-agnostic evaluation framework that supports heterogeneous urban representations through a standardized alignment module; (2) a unified evaluation protocol using block-based spatial splits to mitigate spatial leakage and enable rigorous model comparison; and (3) an extensible multi-city, multi-task benchmark suite spanning 8 cities and 8 tasks across regression, classification, and distribution prediction. We evaluate 11 representative urban representation models. Results show that performance is highly sensitive to the split protocol, with random splits inflating scores and altering model rankings. We also observe substantial variability across cities and tasks, underscoring the need for generalization-aware evaluation. CityRep is released as a reproducible benchmark with datasets, evaluation pipelines, and diagnostic tools to facilitate fair comparison and support future research in urban representation learning towards urban foundation models.

Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple yet effective representation-level prior that inserts a fixed orthonormal projection to constrain encoder features to a low-dimensional subspace, requiring no auxiliary objectives, pretraining, or changes to the underlying RL algorithm. Under a linear realizability assumption, we prove that when the bottleneck dimension exceeds the intrinsic rank of the optimal value function in feature space, the bottleneck preserves expressivity and leaves the induced gradient dynamics unchanged up to an equivalent low-dimensional parameterization. Empirically, we find that across both single and multi-task benchmarks, baseline performance is either matched or improved once the bottleneck dimension exceeds a small task-dependent threshold; in many cases, value representations can be compressed to extremely low dimensions without loss, and the minimal sufficient dimension depends far more on environment complexity than encoder width. In addition, we analyze representation geometry and find that orthogonal bottlenecks stabilize feature norms and are associated with higher effective rank. Together, these results support a representation-space interpretation of the manifold hypothesis in reinforcement learning and position orthogonal bottlenecks as a lightweight, architecture-agnostic mechanism for shaping RL representations.

Accurately predicting crystal properties is critical for accelerating materials discovery, but it is often limited by scarce labeled data and costly theoretical calculations. To alleviate this, we propose UNATE (Unsupervised Atomic Embedding), a framework that leverages structural information extracted from unlabeled crystal structures. UNATE integrates an unsupervised denoising autoencoder with self-supervised contrastive learning to learn robust atomic representations, which are then used as input features for downstream property prediction. Experimental results show that replacing raw atomic numbers with UNATE-pretrained node embeddings yields a 2.7% improvement over the full-data baseline. Notably, the benefits become more pronounced in scenarios with limited labeled data, reaching improvements of up to 10% when only 25% of the labeled data is used.

Weak-to-strong (W2S) generalization is a promising framework for scalable oversight, yet existing evaluations often test students under matched train-test distributions. Therefore, we study W2S preference learning under zero-shot distribution shift and find that strong students trained on weak preference labels can appear successful in-distribution while failing to transfer across preference datasets. We provide evidence for a representational failure mode in which weak-supervised fine-tuning can pull the strong model toward source-domain features instead of maintaining broadly transferable preference representations. To mitigate this, we propose Representation Anchoring (Anchor), a simple yet effective regularizer that constrains excessive drift from the pretrained strong model's representation space during fine-tuning, while still allowing task-relevant adaptation. Across preference domains, datasets, and model families, Anchor consistently improves out-of-distribution transfer while maintaining competitive in-distribution performance. Together, our evaluation protocol, transfer-aware metrics, and method expose hidden brittleness in current W2S reward modeling and provide a practical path toward more robust preference transfer.

While feed-forward 3D Gaussian splatting reconstructs renderable Gaussian primitives from sparse context views without per-scene optimization, existing pipelines do not provide a compact scene representation for storage or transmission. A natural solution is to apply existing 3DGS compression methods to the generated Gaussian primitives. However, this approach operates on the final irregular 3D representation and is decoupled from the internal feature-to-Gaussian generation process, which limits compression efficiency. To address this, we introduce CodecSplat, an ultra-compact latent coding framework for feed-forward 3D Gaussian splatting. CodecSplat first encodes an intermediate 2D Gaussian-generation feature into an entropy-coded scene bitstream. At the decoder, the latent feature is reconstructed and used to predict depth and Gaussian parameters, which are then mapped to 3D Gaussian primitives. By integrating compression into the feed-forward Gaussian generation pipeline, CodecSplat avoids inefficient compression over irregular 3D Gaussian primitives and allows the codec to exploit the structured intermediate feature representation. We instantiate CodecSplat on a feed-forward Gaussian splatting backbone with depth-guided multi-view feature refinement and a hierarchical learned feature codec. On DL3DV and RealEstate10K datasets, CodecSplat achieves 23.56-26.36 dB and 24.76-27.05 dB PSNR with only 20.00-107.77 KiB and 3.37-12.51 KiB per scene, respectively. This is roughly one order of magnitude smaller than compressing feed-forward generated Gaussian primitives, while preserving controllable rate-distortion behavior. Code is available at https://github.com/pengpeng-yu/CodecSplat.

Long-tailed recognition suffers from a persistent head--tail trade-off: improving tail performance often degrades head accuracy and can increase training instability. Despite strong empirical results from re-weighting, decoupled training, and multi-expert methods, key design choices about representation sharing between head and tail classes and supervision weighting across class groups remain largely heuristic. In this work, we propose OSDTW, a principled task-decomposition framework that partitions the original single-label recognition problem into a head task and a tail task, implemented with a shared encoder and task-specific decoders. To handle the mutual exclusivity and statistical dependence between the two label groups, we introduce a factorized model and show that the resulting Kullback--Leibler divergence-based generalization error can be written as the sum of task-wise terms up to an additive constant, yielding a well-defined task-wise objective. We further develop a three-stage training pipeline: independent task training to estimate task-wise optima and the Fisher information matrix, weighted joint training to learn a shared encoder, and branch assembly to construct the final decoupled model. Under a block-diagonal Fisher approximation, we derive a computable second-order expansion of the expected generalization error, decomposing it into encoder variance, encoder bias, and decoder variance. This bias--variance decomposition provides a computable proxy to select the shared depth and task weights, enabling efficient hyper-parameter search. Experiments on standard long-tailed benchmarks demonstrate the effectiveness of the proposed approach over strong baselines.

Vision-Language-Action (VLA) models commonly adapt pretrained Vision-Language Models (VLMs) to robot control by mapping visual observations and language instructions to continuous actions. Existing approaches typically take an action-insufficiency view, assuming that pretrained VLM latents either lack directly usable action information or should be shielded from action-learning signals. Against this view, our Quotient Theory for VLA shows that pretrained VLM latents are not action-insufficient but action-sufficient: they already contain the information needed for control, yet remain overcomplete by distinguishing prompt-level variations that induce the same optimal action behavior. To operationalize this theory, we propose QuoVLA, a quotient-space framework for VLA that compresses pretrained VLM latents into action-sufficient representations. Specifically, QuoVLA instantiates this principle with a quantization module and a dual-branch design with relative temporal-complexity regularization, preserving action-relevant information while removing prompt-level redundancy. Extensive experiments across multiple benchmarks demonstrate that QuoVLA achieves strong performance, with particularly notable improvements in generalization under visual, linguistic, and environmental distribution shifts. Our code will be made publicly available.

Concept formation in transformer language models is depth-extended, not a single-layer event: concepts emerge gradually across a contiguous region of the residual stream. Mechanistic interpretability methods identify the single layer of peak class separation -- the "best layer" -- capturing a snapshot rather than the process itself. We introduce the Concept Allocation Zone (CAZ): the depth interval within which a concept becomes measurably separable, the region allocated to its geometric expression. We formalize the CAZ through three layer-wise metrics (Separation, Concept Coherence, Concept Velocity) and derive principled boundary detection without manual layer sweeps. A CAZ is not a concept: it is the depth region within which the model organizes its geometry to make a concept separable. A single concept typically participates in multiple CAZes; multiple concepts may share one. Empirical validation across 34 models from 8 architectural families and 7 concepts reveals that the separation curve S(l) is frequently multimodal. A scored detector uncovers "gentle CAZes" -- subtle allocation regions invisible to standard peak detection but causally active in 93-100% of cases under ablation (16 of 34 models; 26 in the companion validation paper). The framework generates seven testable predictions; four yield clear verdicts (two not supported, one partially supported, one supported), one had its precondition invalidated by the data, and two are underpowered -- with cross-architecture alignment confirmed as depth-matched rather than monolithic under leave-one-concept-out cross-validation. Reference implementation: rosetta_tools v1.3.1 (doi:10.5281/zenodo.20361433).

While Vision Foundation Models (VFMs) excel at predictive tasks on satellite imagery, their performance can arise from visual correlations rather than underlying structural invariants, making even perception-based out-of-distribution accuracy a poor proxy for scientific utility. As a result, models may look correct without reasoning correctly, a discrepancy we term the Perception-Physics Paradox. To address this gap, we introduce scientific alignment as an implicit objective for representation learning in scientific domains. We study a principled, testable aspect of scientific alignment through structural isomorphism, which requires latent representations to uniquely identify physical systems up to a linear reparameterization. This perspective induces a hierarchy of necessary conditions and yields a systematic probing protocol for physical and causal interpretability. To operationalize this framework, we release TC-Bench, a global, reproducible benchmark dataset with an automated construction pipeline for tropical cyclone research, and show that current VFMs rely on visual shortcuts that collapse in intense regimes, indicating that scientific alignment does not arise as a natural byproduct of scaling alone.

Reward modeling is not only a prediction problem: in KL-regularized policy optimization, the learned reward is exponentiated to define the deployed policy, so downstream value depends on errors in reward-tilted regions. We study this feedback in a Gaussian single-index model with $r^*(x) = σ^*(\langle θ^*, x\rangle)$ and $x \sim N(0, I_d)$. We analyze a two-stage neural reward model that first learns the hidden direction $θ^*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression. Exponential reward weighting changes the Hermite signal available to the first layer; for any feature-learning temperature $β_1$ above a dimension-free $O(1)$ threshold, a constant fraction of neurons recover the hidden direction, with weak-recovery complexity governed by the generative exponent. After feature recovery, we derive tilted-policy value-gap bounds for an idealized label-weighted fit with weights $e^{y/β_2}$ and a more practical surrogate-weighted fit with weights $e^{r_{a_0}(x)/β_2}$. Keeping the $β_2$-dependence explicit yields an admissible set of deployment temperatures, balancing the gain from lowering $β_2$ against the learning cost amplified by exponential weighting; in the surrogate-weighted case, proxy-dependent factors shrink this admissible set.

We establish four structural results for feature learning in wide two-layer neural networks under the Maximal Update Parametrization ($μ$P). First, we prove global existence and uniqueness of the mean-field limit of noisy gradient descent under $μ$P, identifying the maximal admissible weight $w^*$ on the moment sequence of the initialization as the reciprocal parameter-moment-growth boundary, and hence the largest weighted moment class propagated by the flow. The finite-particle approximation has uniform-in-time squared-Wasserstein rate $O(N^{-1})$. Second, we characterize identifiability of the mean-field limit: two admissible parameter measures induce the same network function in $L^2$ exactly when their active components agree modulo the finite-rank realization symmetry of the architecture. The orbit depth $D^*_{\mathrm{orb}}$ is separated from the moment-variety depth $D^*_{\mathrm{var}}$. Third, under the Barron-Hermite target condition the active support of the long-time limit measure admits a sparse-dictionary decomposition: it is supported on at most $S^*$ atoms modulo finite-rank realization symmetry, with $S^*$ bounded by an explicit coefficient-threshold number. Fourth, we derive the total feature-learning-error decomposition into statistical, optimization, propagation-of-chaos, and sparse-residual components, with a target-dependent Hermite/Barron tail replacing any initialization-only residual. The four results are tied together by an architectural identity: the triple $(w^*, D^*_{\mathrm{orb}}, S^*)$ -- the maximal admissible weight, the orbit identifiability depth, and the sparse-dictionary depth at which the target is realizable -- is the natural learning cell of the architecture-data pair $(σ, ρ)$. The proofs are self-contained except for standard results from $μ$P and mean-field Langevin theory.

Amodal instance segmentation aims to predict the complete object mask including occluded regions that lack pixel-level observations and must be inferred with the aid of shape priors. Existing methods acquire shape priors through fixed-capacity encoding spaces or expensive generative models, and inject them uniformly across all spatial positions without adapting to the varying prior demand between visible and occluded regions. In this paper, we propose a gated reliability-adaptive shape prior framework, which introduces a shape prior memory module that combines learnable prototypes via cross-attention to produce instance-adaptive shape priors through weighted prototype combination rather than generation. A spatial adaptive reliability gate then employs the signed distance field of the visible mask to modulate injection intensity at each position according to its occlusion depth, preserving reliable features in visible regions while directing shape compensation toward occluded areas. Experiments on two mainstream amodal instance segmentation benchmarks demonstrate that the proposed method outperforms existing approaches under multiple evaluation settings, improving the mean intersection-over-union over occluded regions by over 11 percentage points on one of the two benchmarks under the standard setting, while using approximately one-third of the total parameters. Linear probing analysis further reveals that the visible-mask cross-attention module implicitly encodes occlusion geometry into visual token representations, explaining the effectiveness of the proposed module decomposition.

The integration of fairness and privacy in centralized data-driven applications is critical, especially as these systems increasingly influence sectors with significant societal impact. Current methods rarely address privacy, fairness, and accuracy together, which can potentially compromise ethical standards and privacy regulations. However, balancing these three objectives is quite challenging since each of objective often imposes conflicting requirements on the design and training of models, making it difficult to optimize one without compromising the others. This paper introduces a novel multitask adversarial model that treats fairness and privacy as integral objectives rather than afterthoughts, and learns a latent representation that hides sensitive attributes while preserving essential task-related information. Our approach dynamically balances fairness with accuracy and privacy through an optimized cost function with minimal performance loss even under strict conditions. Extensive testing on diverse datasets shows the ability of our model to achieve high standards of fairness and privacy without significant sacrifice to accuracy. Benchmarking against state-of-the-art privacy and fairness standards shows that our method enhances the robustness of privacy, fairness, and accuracy optimization, proving its adaptability across various datasets.

Variational autoencoders (VAEs) often struggle to represent non-commutative structure in learned latent spaces. Symmetry-aware VAEs commonly address this issue by enforcing commutativity through algebraic regularization, which is appropriate for commutative transformation groups but can suppress meaningful non-commutative structure when it is intrinsic to the data. We argue that non-commutativity should instead be explicitly diagnosed and reflected in reconstruction behavior. We introduce a Lie Group VAE framework that combines geometric and algebraic perspectives on uncertainty while separating discrete generative factors from continuous geometric transformations. In a first phase, the model is trained without structural constraints while algebraic non-commutativity is measured through finite Baker-Campbell-Hausdorff deviations and decoder order sensitivity is measured through reconstruction order-swap tests. These diagnostics reveal a scale mismatch between latent non-commutativity and reconstruction behavior under unconstrained training. In a second phase, we introduce a deformation-stability constraint with a data-driven calibration constant that aligns decoder sensitivity with algebraic non-commutativity. We evaluate the framework on dSprites, 3DShapes, 3DCars, and CelebA against generic and symmetry-aware baselines, including beta-VAE, CLG-VAE, and CFASL. Across synthetic benchmarks, the method improves reconstruction quality and yields decoder-level behavior more consistent with latent non-commutative structure. Qualitative analyses show clearer order-dependent latent compositions and more stable reconstructions. On CelebA, the model yields more faithful reconstructions and factor-specific latent traversals than CFASL, while also exhibiting meaningful order-dependent interactions between learned latent directions.

In curriculum reinforcement learning (CRL), an agent incrementally accumulates knowledge over a sequence of tasks (i.e., a curriculum), and the learning process is aimed at using the accumulated knowledge to finally solve a challenging target task. While early CRL works focus on sequencing candidate tasks, recent research explores automatic curriculum generation. Among the rich CRL literature, the interpolation-based CRL paradigm is a main body, which automatically generates intermediate tasks by interpolating between the initial task distribution and the target task distribution in task space with meaningful distance metrics (i.e., can measure the task similarity). However, in challenging navigation tasks, the non-Euclidean context (task) space invalidates this assumption. To achieve automatic curriculum generation in complex task, we propose a novel automatic curriculum generation approach based on measurable task representation learning. To better measure the similarity, we propose to transform the task space to a latent space. Through a variational autoencoder structure that encodes the reward and the state transitions, we achieve a latent task representation with a task similarity measurement property, and two close task embeddings correspond to two similar tasks in terms of rewards and state transitions. Based on the learned task representation, we further develop an automatic curriculum generation scheme, which can effectively generate new tasks more and more similar to the target task. We evaluate our method in a variety of challenging navigation tasks, and the experiment results indicate that the proposed approach surpasses state-of-the-art CRL approaches based on interpolation and generative adversarial networks.

Relational databases (RDBs) remain the cornerstone of modern data systems and support diverse predictive tasks. Recent relational deep learning (RDL) methods enable end-to-end prediction by converting RDBs into graphs, where rows are represented as nodes and inter-table interactions are represented as edges, and then applying graph-based models for representation learning. Despite the strong capability of RDL, effective self-supervised pre-training for RDBs remains non-trivial. RDB tasks often require multi-faceted information across different perspectives and granularities. For example, user churn classification may rely more on interaction patterns, whereas consumption value prediction requires both user-item behaviors and intrinsic user attributes for fine-grained regression. Such heterogeneous needs challenge RDB representation learning, as pre-training objectives should cover comprehensive information for downstream adaptation. However, existing SSL methods typically derive supervision from a single facet, such as node-level intrinsic attributes or subgraph-level relational structures, providing limited adaptability. To this end, we propose RelPrism, a multi-faceted self-supervised learning framework for RDBs. RelPrism constructs intrinsic, relational, and hybrid attributes from distinct perspectives, and applies multi-granularity clustering to each perspective to form corresponding pseudo-task pools. Pre-training over these pools exposes representations to broader perspectives and granularity levels, yielding a stronger basis for downstream adaptation. Experiments on 14 tasks across 5 real-world datasets show that RelPrism improves ROC-AUC by 4.15% for classification and reduces MAE by 10.75% for regression over state-of-the-art baselines. Our code is available at https://anonymous.4open.science/r/RelPrism.

What does a world model learn from physical exploration, without any linguistic supervision? We argue the answer is organized by a single principle: the geometric structure of the physical world. Training a VAE-based world model on random embodied exploration, we find that its latent space develops spatial semantic structure that mirrors physical geometry -- direction accuracy 0.677+-0.029 versus 0.547 for a randomly initialized encoder, and position RSA 0.192+-0.047 versus 0.029 for random encoders (6.6x improvement), showing that training induces genuine structural organization beyond CNN inductive bias. Across 20 temporal checkpoints, prediction performance and semantic alignment co-improve (Spearman r=-0.61, p=0.004), consistent with the shared-driver account. We confirm this through a double knockout: standard KL regularization (beta=0.1) forces the encoder away from geometric structure, and both prediction performance and semantic alignment collapse simultaneously to near-chance by step 50,000 -- exactly as the shared-driver account predicts. Reducing beta to 0.001 restores geometric access and recovers both capabilities together. These findings establish physical world geometry as the organizing principle of world model representations, with direct implications for the design of semantically grounded embodied agents.

Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation dynamics to detect these moments in real time. Analyzing a passive GMM probe attached to the evolving encoder, we show the onset of structure corresponds to a supercritical pitchfork bifurcation driven by the loss Hessian. The system exhibits a theoretically predictable zero-crossing ($β_c$) that, compared to the network's current state ($β$), yields a dynamic ratio $β(t)/β_c(t)$: a universal, label-free phase coordinate for representation dynamics, computable entirely from hidden states. We empirically validate four distinct transition regimes predicted by this coordinate across diverse settings: SAEs on language models (Pythia), SSL (CIFAR), and grokking (modular arithmetic). Crucially, under finite dissipation, macroscopic symmetry-breaking can lag the initial zero-crossing by orders of magnitude, which providing a rigorous dynamical account of the delayed escape observed in grokking. Microscopically, the bifurcation creates a shared unstable subspace, forcing collective symmetry breaking. We term this the "feature lottery" in SAE training: a feature's terminal interpretability becomes predictable remarkably early. By only 5% of training, early atom purity robustly predicts final convergence purity, with top-decile early atoms achieving over 12x the baseline purity at convergence. Beyond explaining concept emergence, $β/β_c$ provides a practical early-warning indicator for training health, detecting the onset of usable structure, the crystallization of feature identity, and representational collapse epochs before downstream metrics react.

Existing language-image pre-training for remote sensing object detection is constrained by Monolithic Label Learning, which relies on exhaustively enumerating open-set categories via black-box data to acquire fine-grained representations, creating a dependency incompatible with the domain's inherent data scarcity. To transcend this bottleneck, we propose SLIP-RS, establishing a Structured-Attribute Decoupling Paradigm that maps the open-ended category space into a finite, physically meaningful attribute space, unlocking fine-grained discriminability via explicit structural logic. This paradigm is realized via two technical pillars: (1) Structured-Attribute Contrastive Learning, which enforces the learning of decoupled intrinsic visual logic via combinatorial attribute augmentation; and (2) Conformal Attribute Reliability Engine, which leverages conformal prediction theory to rigorously distill high-fidelity supervision from noisy sources, yielding RS-Attribute-15M, the largest dataset with over 15 million attribute annotations. Extensive experiments demonstrate that SLIP-RS establishes unprecedented performance in fine-grained detection and cross-domain generalization, validating structured attributes as a vital foundation for remote sensing. Code: https://github.com/facias914/SLIP-RS.

Electroencephalography (EEG) visual decoding remains challenging due to the modality gap between low-SNR neural signals and highly structured vision--language spaces, making direct cross-modal alignment unstable. To address this, we propose STAMBRIDGE, a versatile two-stage framework that sequentially tackles feature conditioning and cross-modal alignment. First, we introduce a Spectral-Temporal Amplitude-aware Modulation (STAM) to extract well-conditioned EEG representations. By replacing hard frequency masking with amplitude-derived soft channel weighting and multi-scale temporal convolutions, STAM explicitly preserves frequency-aware transients while reducing the risk of time-domain ringing artifacts. Building upon these robust neural features, we further introduce a model-agnostic Mid-Feature Semantic Bridge (MFSB) that constructs a regularized intermediate space through directed cross-modal interactions, enabling staged distillation and more stable semantic alignment. Experiments on the THINGS-EEG benchmark show competitive 200-way zero-shot retrieval performance, with 34.50% Top-1 and 65.95% Top-5 accuracy. In addition, embeddings learned by STAMBRIDGE produce semantically coherent image reconstructions with a diffusion model, demonstrating robust EEG-to-vision semantic alignment. The code is available at: https://github.com/thabeatmjh/STAMBRIDGE.

Video representation learning has seen tremendous progress in recent years. This has been driven by many factors, including the scale of training and the success of self-supervised models trained on next-frame prediction. While these factors have pushed the boundaries of what video models can do, they also introduce their own set of limitations. First, scaling video models can reach prohibitive costs, with recent models needing hundreds of years of video to be trained. Second, learning to predict the next frame (or embedding of the frame) naturally focuses on spatial information and as a result, video models still struggle with temporal understanding. In this paper we propose a novel approach that uses motion as a modality to alleviate both of these core issues. Given the motion in a video in the form of point tracks, we mask some of the tracks and use a masked autoencoder to reconstruct the missing tracks. This allows us to learn a representation in a self-supervised manner which we call TIME (Temporally-Informed Motion Embedding), and is focused on capturing temporal information. Also, as motion is inherently appearance-invariant, TIME needs far fewer examples to generalize well. As a result, without bells and whistles, on temporal tasks TIME performs on par with state-of-the-art models, using up to 4 orders of magnitude less training data. For general tasks, TIME can be used in combination with existing representations, and we observe that it leads to a significant improvement for V-JEPA 2, RVM and VideoMAE on standard benchmarks such as SSV2, EgoExo4D and Diving48. These results point to a new promising video paradigm for both more temporally-aware as well as more scalable models.

Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study entropy-regulated learning under separately specified task, risk, and intervention constraints. A noise-calibrated log-determinant functional yields an exact spectral force formula and a metric decomposition into observable and prediction-null velocities. For scalar feedback, we characterize the complete interval of coefficients preserving a task-descent fraction and meeting an entropy-rate request; restricting intervention to observable directions can make that interval empty. For several protected risks, we derive an exact minimax certificate of feasibility within a specified subspace and norm budget, an exact robust extension for uncertain constraint rows, and a cone-projection formula for the entropy reduction remaining after protection. These formulas use standard convex geometry but identify when apparently active entropy control has no admissible effect. Barrier comparisons, finite-step curvature and gradient-error margins, and fresh-data audits give distinct conditional guarantees for risk thresholds. Human authority enters through the specification and release policy; the mathematics does not identify compression with alignment or certify human well-being. A memorization counterexample separates fresh-input information from sample-level information, and a noisy sample-code assumption supports a conditional generalization bound. Reproducible mathematical checks and a small real-data experiment expose both feasible interventions and failures. The resulting theory characterizes admissible entropy regulation and its limitations, rather than asserting universal accuracy or safety improvements.

Coffee and tea share many properties, yet they evoke strikingly different situations, atmospheres, and affective associations. These situated dimensions of word meaning are real and systematic, but they remain implicit in most computational representations of lexical meaning. We propose Scene Abstraction, a framework for constructing structured representations of the interpretive scenes that words participate in across usage contexts. Each scene consists of a Contextual Scene (Events, Entities, Setting) and an expression-centered Expression Profile (Engaged events, Generalizable properties, Evoked emotions), operationalized through few-shot prompting of a large language model. Our contributions are three-fold: (1) a structured representation framework for situated lexical meaning; (2) COCA-Scenes, a dataset of 520 usage instances across 26 keywords for distinct scene identification; and (3) empirical evidence from two experiments suggesting that scenes are reliably identifiable across human observers (82.4% accuracy, +11.8 pp over text-only embeddings) and that our scene profiles more closely align with human interpretation of words in context than ATOMIC-based alternatives (86.4% preference across three semantic dimensions).

Winner-take-all (WTA) networks constitute a central circuit motif in cortical networks of the brain. In addition, WTA-like activations are abundant in modern deep learning models in the form of the softmax activation for example in attention layers of transformers. While their role in the extraction of latent factors has been studied for relatively simple generative models, their role in the context of highly non-linearly entangled latent factors has remained elusive. In this article, we show that a WTA bottleneck within a deep neural network can enforce under certain well-defined conditions the extraction of categorical latent factors of the data in a multi-task learning setup. In particular, we prove that the representation that emerges in the WTA bottleneck is highly symbolic, where a single neuron or a population of neurons encodes the presence of a single abstract feature such as a specific object, color, or position. We furthermore show empirically on two datasets, that this also holds for architectures and setups that do not fully comply with the assumptions of our theorem and demonstrate the advantages of the acquired symbolic representation for generalization. Our proposed model provides insights into the generalization capabilities of deep neural networks with WTA-like components and may serve as an interface between symbolic and subsymbolic AI systems.

Statistical decision algorithms are increasingly deployed in domains where ground-truth labels are hard to obtain, such as hiring, university admissions, and content moderation. In these settings, models are typically trained on historical human evaluations -- for example, using past hiring decisions as a proxy for true applicant quality. However, if past evaluations unjustly favor certain groups, models trained on these labels may inherit those biases. To address this problem, we propose basing predictions on rubric embeddings, a representation framework that replaces standard black-box embeddings with features derived from expert-defined criteria that align with the underlying construct of interest. By anchoring predictions to semantically meaningful dimensions, this approach guards against biased proxy signals. We provide both theoretical and empirical evidence that rubric embeddings mitigate label bias under plausible conditions. Empirically, we evaluate our method on a novel dataset of applications to a large master's program. We find that models trained on rubric embeddings reduce group disparities while improving measures of cohort quality. Our results suggest that basing predictions on interpretable, domain-grounded representations offers a practical approach to learning in the presence of biased labels.

Reaction condition recommendation sits immediately after retrosynthetic disconnection selection, and in practice, chemists require both accurate predictions and the precedents that justify them. We present HiRes (Hierarchical Reaction Representations), a retrieval-augmented condition recommendation system whose learned reaction space serves as both a classifier feature and an inspectable precedent memory. The model combines a graph encoder, transformation-aware cross-attention, multi-stream reaction fusion, and a k-NN retrieval layer. HiRes achieves state-of-the-art performance among primary-slot USPTO-Condition models, reaching Catalyst, Solvent, and Reagent top-1 accuracies (Acc@1) of 0.929, 0.534, and 0.530 respectively. It ties the best reported baseline on Catalyst while outperforming models such as REACON on Solvent and Reagent. Furthermore, paired bootstrap analysis demonstrates that integrating retrieval with learned condition heads provides statistically significant gains for solvent and reagent selection over purely parametric approaches. Ultimately, HiRes bridges the gap between predictive accuracy and chemical interpretability, offering a single representation that supplies both competitive recommendations and the concrete chemical precedents necessary for practical synthesis planning.

What can representational similarity matrices (RSMs) tell us about a neural code? As the popularity of these summary statistics grows, so too does the need for a more complete characterization of their properties. Here, we show that symmetries in network inputs can confound RSM-based analyses. Stimulus symmetries render many representations functionally equivalent, but these different configurations can lead to different RSMs. These different RSMs reflect qualitatively different representational geometries. We show that stochastic gradient descent or energetic regularization can generate sparse, drifting codes, leading in turn to drifting RSMs. Moreover, we demonstrate that these phenomena are present in networks trained to encode image data, where the symmetry is latent. Our results illustrate the challenges inherent in comparing nonlinear neural codes, when functionally-equivalent representations are not related by a simple rotation.

Causal representation learning (CRL) and traditional representation learning have largely developed along different trajectories. Traditional representation learning has been driven mainly by applications and empirical objectives, whereas CRL has focused more on theoretical questions, particularly identifiability. This difference in emphasis has created a gap between the two fields in terminology, problem formulation, and evaluation, limiting communication and sometimes leading to disconnected or redundant efforts. In this paper, we argue that these two fields should be brought into dialogue rather than treated as separate paradigms. To this end, we introduce a unified formulation in which the representation learning is characterized by two components: a task component, which specifies what information the learned representation is required to preserve, and a constraint component, which specifies what structure is imposed on the latent space. Under this formulation, the benefits run in both directions. CRL provides theoretical tools for understanding when structured latent constraints are useful or necessary, while traditional representation learning offers practical insights on task design and objective choice that can improve the development of CRL methods. To illustrate this interaction, we experimentally study how different task components affect the behavior of CRL methods under different structured constraints. Results on CausalVerse show that the effectiveness of causal constraints depends strongly on the tasks with which they are paired.

High-dimensional biological data often exhibit a severe mismatch between feature dimensionality and sample size, making reliable classification difficult in extremely small-data regimes. In these settings, kernel methods can lose discriminative power when latent compression fails to preserve class-separating structure. We study this problem in fine-grained plant phenomics and propose a hybrid workflow that compresses 1280-dimensional deep image embeddings into a 64-dimensional PCA space and then restructures them into an 11-dimensional supervised latent space using Linear Discriminant Analysis (LDA), followed by GPU-accelerated Quantum Kernel Alignment (QKA) on NVIDIA L40S hardware. Empirically, supervised latent restructuring substantially improves the geometric separability of the compressed representation, increasing the Silhouette coefficient from 0.003 in the raw embedding space and -0.006 in PCA-64 to 0.197 in the supervised LDA-11 space. However, downstream classical evaluation reveals a clear compression trade-off: Linear SVM and XGBoost improve in the restructured latent space, whereas RBF-SVM and Random Forest degrade under the same 11-dimensional bottleneck. Under a constrained optimization budget, QKA in this regime remains challenging, indicating that latent geometry alone is not sufficient for strong trainable quantum performance. These findings position representation geometry as a central design variable in small-data quantum learning and expose the practical difficulty of recovering nonlinear discriminative structure from aggressively compressed biological representations.

Learning universal representations from electroencephalogram (EEG) signals is a cutting-edge approach in the field of neuroinformatics and brain-computer interfaces (BCIs). Conventionally, EEG is treated as a multivariate temporal signal, where time- or frequency-domain features are extracted for representation learning. This paper investigates a simple yet effective EEG representation, i.e., microstates. Microstates represent the building blocks of brain activity patterns at a microscopic time scale. We build a universal microstate tokenizer from a large medical EEG dataset by clustering continuous EEG signals into sequences of discrete microstates. The microstate tokenizer is then adopted universally across a series of downstream tasks, including sleep staging, emotion recognition, and motor imagery classification. Experimental results show that EEG representation learning with microstates outperforms traditional time-domain and frequency-domain features under different models and across different tasks. Further analysis shows that microstates offer greater interpretability and scalability, thereby opening up applications in both cognitive neuroscience and clinical research.