Why Deep Jacobian Spectra Separate: Depth-Induced Scaling and Singular-Vector Alignment

Understanding why gradient-based training in deep networks exhibits strong implicit bias remains challenging, in part because tractable singular-value dynamics are typically available only for balanced deep linear models. We propose an alternative route based on two theoretically grounded and empirically testable signatures of deep Jacobians: depth-induced exponential scaling of ordered singular values and strong spectral separation. Adopting a fixed-gates view of piecewise-linear networks, where Jacobians reduce to products of masked linear maps within a single activation region, we prove the existence of Lyapunov exponents governing the top singular values at initialization, give closed-form expressions in a tractable masked model, and quantify finite-depth corrections. We further show that sufficiently strong separation forces singular-vector alignment in matrix products, yielding an approximately shared singular basis for intermediate Jacobians. Together, these results motivate an approximation regime in which singular-value dynamics become effectively decoupled, mirroring classical balanced deep-linear analyses without requiring balancing. Experiments in fixed-gates settings validate the predicted scaling, alignment, and resulting dynamics, supporting a mechanistic account of emergent low-rank Jacobian structure as a driver of implicit bias.

Evaluating Robustness of Reasoning Models on Parameterized Logical Problems

Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine satisfiability. We introduce a diagnostic benchmark for 2-SAT built from parameterized families of structured 2--CNF formulas, where satisfiability is characterized by the implication graph and can be tuned along interpretable axes. Our generators isolate distinct competencies and failure modes: (i) contradiction-cycle UNSAT cores with controllable size and imbalance, (ii) SAT instances with a prescribed fraction of free variables to control solution multiplicity, (iii) planted backbones that modulate propagation, (iv) late bridge clauses that couple otherwise monotone regions to probe sensitivity to ordering and revision, and (v) symmetry/duplication variants that test abstraction under renaming and redundant structure. We evaluate LLM-based reasoners on decision accuracy and assignment validity, and quantify robustness under semantics-preserving perturbations such as clause reordering, filler clauses, and variable renaming. Across models, we observe sharp performance transitions under targeted structural interventions even when surface statistics are held fixed, revealing brittleness regimes that are invisible to aggregate SAT accuracy.

Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling

The discovery of new crystalline materials calls for generative models that handle periodic boundary conditions, crystallographic symmetries, and physical constraints, while scaling to large and structurally diverse unit cells. We propose a reciprocal-space generative pipeline that represents crystals through a truncated Fourier transform of the species-resolved unit-cell density, rather than modeling atomic coordinates directly. This representation is periodicity-native, admits simple algebraic actions of space-group symmetries, and naturally supports variable atomic multiplicities during generation, addressing a common limitation of particle-based approaches. Using only nine Fourier basis functions per spatial dimension, our approach reconstructs unit cells containing up to 108 atoms per chemical species. We instantiate this pipeline with a transformer variational autoencoder over complex-valued Fourier coefficients, and a latent diffusion model that generates in the compressed latent space. We evaluate reconstruction and latent diffusion on the LeMaterial benchmark and compare unconditional generation against coordinate-based baselines in the small-cell regime ($\leq 16$ atoms per unit cell).

Credal Concept Bottleneck Models: Structural Separation of Epistemic and Aleatoric Uncertainty

Decomposing predictive uncertainty into epistemic (model ignorance) and aleatoric (data ambiguity) components is central to reliable decision making, yet most methods estimate both from the same predictive distribution. Recent empirical and theoretical results show these estimates are typically strongly correlated, so changes in predictive spread simultaneously affect both components and blur their semantics. We propose a credal-set formulation in which uncertainty is represented as a set of predictive distributions, so that epistemic and aleatoric uncertainty correspond to distinct geometric properties: the size of the set versus the noise within its elements. We instantiate this idea in a Variational Credal Concept Bottleneck Model with two disjoint uncertainty heads trained by disjoint objectives and non-overlapping gradient paths, yielding separation by construction rather than post hoc decomposition. Across multi-annotator benchmarks, our approach reduces the correlation between epistemic and aleatoric uncertainty by over an order of magnitude compared to standard methods, while improving the alignment of epistemic uncertainty with prediction error and aleatoric uncertainty with ground-truth ambiguity.

Skim-Aware Contrastive Learning for Efficient Document Representation

Although transformer-based models have shown strong performance in word- and sentence-level tasks, effectively representing long documents, especially in fields like law and medicine, remains difficult. Sparse attention mechanisms can handle longer inputs, but are resource-intensive and often fail to capture full-document context. Hierarchical transformer models offer better efficiency but do not clearly explain how they relate different sections of a document. In contrast, humans often skim texts, focusing on important sections to understand the overall message. Drawing from this human strategy, we introduce a new self-supervised contrastive learning framework that enhances long document representation. Our method randomly masks a section of the document and uses a natural language inference (NLI)-based contrastive objective to align it with relevant parts while distancing it from unrelated ones. This mimics how humans synthesize information, resulting in representations that are both richer and more computationally efficient. Experiments on legal and biomedical texts confirm significant gains in both accuracy and efficiency.

MODE: Multi-Objective Adaptive Coreset Selection

We present Mode(Multi-Objective adaptive Data Efficiency), a framework that dynamically combines coreset selection strategies based on their evolving contribution to model performance. Unlike static methods, \mode adapts selection criteria to training phases: emphasizing class balance early, diversity during representation learning, and uncertainty at convergence. We show that MODE achieves (1-1/e)-approximation with O(n \log n) complexity and demonstrates competitive accuracy while providing interpretable insights into data utility evolution. Experiments show \mode reduces memory requirements

Generalizing Analogical Inference from Boolean to Continuous Domains

Analogical reasoning is a powerful inductive mechanism, widely used in human cognition and increasingly applied in artificial intelligence. Formal frameworks for analogical inference have been developed for Boolean domains, where inference is provably sound for affine functions and approximately correct for functions close to affine. These results have informed the design of analogy-based classifiers. However, they do not extend to regression tasks or continuous domains. In this paper, we revisit analogical inference from a foundational perspective. We first present a counterexample showing that existing generalization bounds fail even in the Boolean setting. We then introduce a unified framework for analogical reasoning in real-valued domains based on parameterized analogies defined via generalized means. This model subsumes both Boolean classification and regression, and supports analogical inference over continuous functions. We characterize the class of analogy-preserving functions in this setting and derive both worst-case and average-case error bounds under smoothness assumptions. Our results offer a general theory of analogical inference across discrete and continuous domains.

Towards a Neurosymbolic Reasoning System Grounded in Schematic Representations

Despite significant progress in natural language understanding, Large Language Models (LLMs) remain error-prone when performing logical reasoning, often lacking the robust mental representations that enable human-like comprehension. We introduce a prototype neurosymbolic system, Embodied-LM, that grounds understanding and logical reasoning in schematic representations based on image schemas-recurring patterns derived from sensorimotor experience that structure human cognition. Our system operationalizes the spatial foundations of these cognitive structures using declarative spatial reasoning within Answer Set Programming. Through evaluation on logical deduction problems, we demonstrate that LLMs can be guided to interpret scenarios through embodied cognitive structures, that these structures can be formalized as executable programs, and that the resulting representations support effective logical reasoning with enhanced interpretability. While our current implementation focuses on spatial primitives, it establishes the computational foundation for incorporating more complex and dynamic representations.

Enhancing DR Classification with Swin Transformer and Shifted Window Attention

Diabetic retinopathy (DR) is a leading cause of blindness worldwide, underscoring the importance of early detection for effective treatment. However, automated DR classification remains challenging due to variations in image quality, class imbalance, and pixel-level similarities that hinder model training. To address these issues, we propose a robust preprocessing pipeline incorporating image cropping, Contrast-Limited Adaptive Histogram Equalization (CLAHE), and targeted data augmentation to improve model generalization and resilience. Our approach leverages the Swin Transformer, which utilizes hierarchical token processing and shifted window attention to efficiently capture fine-grained features while maintaining linear computational complexity. We validate our method on the Aptos and IDRiD datasets for multi-class DR classification, achieving accuracy rates of 89.65% and 97.40%, respectively. These results demonstrate the effectiveness of our model, particularly in detecting early-stage DR, highlighting its potential for improving automated retinal screening in clinical settings.

Grounding Agent Reasoning in Image Schemas: A Neurosymbolic Approach to Embodied Cognition

Despite advances in embodied AI, agent reasoning systems still struggle to capture the fundamental conceptual structures that humans naturally use to understand and interact with their environment. To address this, we propose a novel framework that bridges embodied cognition theory and agent systems by leveraging a formal characterization of image schemas, which are defined as recurring patterns of sensorimotor experience that structure human cognition. By customizing LLMs to translate natural language descriptions into formal representations based on these sensorimotor patterns, we will be able to create a neurosymbolic system that grounds the agent's understanding in fundamental conceptual structures. We argue that such an approach enhances both efficiency and interpretability while enabling more intuitive human-agent interactions through shared embodied understanding.