HypCBC: Domain-Invariant Hyperbolic Cross-Branch Consistency for Generalizable Medical Image Analysis

Robust generalization beyond training distributions remains a critical challenge for deep neural networks. This is especially pronounced in medical image analysis, where data is often scarce and covariate shifts arise from different hardware devices, imaging protocols, and heterogeneous patient populations. These factors collectively hinder reliable performance and slow down clinical adoption. Despite recent progress, existing learning paradigms primarily rely on the Euclidean manifold, whose flat geometry fails to capture the complex, hierarchical structures present in clinical data. In this work, we exploit the advantages of hyperbolic manifolds to model complex data characteristics. We present the first comprehensive validation of hyperbolic representation learning for medical image analysis and demonstrate statistically significant gains across eleven in-distribution datasets and three ViT models. We further propose an unsupervised, domain-invariant hyperbolic cross-branch consistency constraint. Extensive experiments confirm that our proposed method promotes domain-invariant features and outperforms state-of-the-art Euclidean methods by an average of $+2.1\%$ AUC on three domain generalization benchmarks: Fitzpatrick17k, Camelyon17-WILDS, and a cross-dataset setup for retinal imaging. These datasets span different imaging modalities, data sizes, and label granularities, confirming generalization capabilities across substantially different conditions. The code is available at https://github.com/francescodisalvo05/hyperbolic-cross-branch-consistency .

Agentic Proposing: Enhancing Large Language Model Reasoning via Compositional Skill Synthesis

Advancing complex reasoning in large language models relies on high-quality, verifiable datasets, yet human annotation remains cost-prohibitive and difficult to scale. Current synthesis paradigms often face a recurring trade-off: maintaining structural validity typically restricts problem complexity, while relaxing constraints to increase difficulty frequently leads to inconsistent or unsolvable instances. To address this, we propose Agentic Proposing, a framework that models problem synthesis as a goal-driven sequential decision process where a specialized agent dynamically selects and composes modular reasoning skills. Through an iterative workflow of internal reflection and tool-use, we develop the Agentic-Proposer-4B using Multi-Granularity Policy Optimization (MGPO) to generate high-precision, verifiable training trajectories across mathematics, coding, and science. Empirical results demonstrate that downstream solvers trained on agent-synthesized data significantly outperform leading baselines and exhibit robust cross-domain generalization. Notably, a 30B solver trained on only 11,000 synthesized trajectories achieves a state-of-the-art 91.6% accuracy on AIME25, rivaling frontier-scale proprietary models such as GPT-5 and proving that a small volume of high-quality synthetic signals can effectively substitute for massive human-curated datasets.

Robust Domain Generalization under Divergent Marginal and Conditional Distributions

Domain generalization (DG) aims to learn predictive models that can generalize to unseen domains. Most existing DG approaches focus on learning domain-invariant representations under the assumption of conditional distribution shift (i.e., primarily addressing changes in $P(X\mid Y)$ while assuming $P(Y)$ remains stable). However, real-world scenarios with multiple domains often involve compound distribution shifts where both the marginal label distribution $P(Y)$ and the conditional distribution $P(X\mid Y)$ vary simultaneously. To address this, we propose a unified framework for robust domain generalization under divergent marginal and conditional distributions. We derive a novel risk bound for unseen domains by explicitly decomposing the joint distribution into marginal and conditional components and characterizing risk gaps arising from both sources of divergence. To operationalize this bound, we design a meta-learning procedure that minimizes and validates the proposed risk bound across seen domains, ensuring strong generalization to unseen ones. Empirical evaluations demonstrate that our method achieves state-of-the-art performance not only on conventional DG benchmarks but also in challenging multi-domain long-tailed recognition settings where both marginal and conditional shifts are pronounced.

Position: The Inevitable End of One-Architecture-Fits-All-Domains in Time Series Forecasting

Recent work has questioned the effectiveness and robustness of neural network architectures for time series forecasting tasks. We summarize these concerns and analyze groundly their inherent limitations: i.e. the irreconcilable conflict between single (or few similar) domains SOTA and generalizability over general domains for time series forecasting neural network architecture designs. Moreover, neural networks architectures for general domain time series forecasting are becoming more and more complicated and their performance has almost saturated in recent years. As a result, network architectures developed aiming at fitting general time series domains are almost not inspiring for real world practices for certain single (or few similar) domains such as Finance, Weather, Traffic, etc: each specific domain develops their own methods that rarely utilize advances in neural network architectures of time series community in recent 2-3 years. As a result, we call for the time series community to shift focus away from research on time series neural network architectures for general domains: these researches have become saturated and away from domain-specific SOTAs over time. We should either (1) focus on deep learning methods for certain specific domain(s), or (2) turn to the development of meta-learning methods for general domains.

Adversarial construction as a potential solution to the experiment design problem in large task spaces

Despite decades of work, we still lack a robust, task-general theory of human behavior even in the simplest domains. In this paper we tackle the generality problem head-on, by aiming to develop a unified model for all tasks embedded in a task-space. In particular we consider the space of binary sequence prediction tasks where the observations are generated by the space parameterized by hidden Markov models (HMM). As the space of tasks is large, experimental exploration of the entire space is infeasible. To solve this problem we propose the adversarial construction approach, which helps identify tasks that are most likely to elicit a qualitatively novel behavior. Our results suggest that adversarial construction significantly outperforms random sampling of environments and therefore could be used as a proxy for optimal experimental design in high-dimensional task spaces.

Conflict-Resolving and Sharpness-Aware Minimization for Generalized Knowledge Editing with Multiple Updates

Large language models (LLMs) rely on internal knowledge to solve many downstream tasks, making it crucial to keep them up to date. Since full retraining is expensive, prior work has explored efficient alternatives such as model editing and parameter-efficient fine-tuning. However, these approaches often break down in practice due to poor generalization across inputs, limited stability, and knowledge conflict. To address these limitations, we propose the CoRSA (Conflict-Resolving and Sharpness-Aware Minimization) training framework, a parameter-efficient, holistic approach for knowledge editing with multiple updates. CoRSA tackles multiple challenges simultaneously: it improves generalization to different input forms and enhances stability across multiple updates by minimizing loss curvature, and resolves conflicts by maximizing the margin between new and prior knowledge. Across three widely used fact editing benchmarks, CoRSA achieves significant gains in generalization, outperforming baselines with average absolute improvements of 12.42% over LoRA and 10% over model editing methods. With multiple updates, it maintains high update efficacy while reducing catastrophic forgetting by 27.82% compared to LoRA. CoRSA also generalizes to the code domain, outperforming the strongest baseline by 5.48% Pass@5 in update efficacy.

A vector logic for intensional formal semantics

Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped by usage. This paper proves that these frameworks are structurally compatible for intensional semantics. We establish that Kripke-style intensional models embed injectively into vector spaces, with semantic functions lifting to (multi)linear maps that preserve composition. The construction accommodates multiple index sorts (worlds, times, locations) via a compound index space, representing intensions as linear operators. Modal operators are derived algebraically: accessibility relations become linear operators, and modal conditions reduce to threshold checks on accumulated values. For uncountable index domains, we develop a measure-theoretic generalization in which necessity becomes truth almost everywhere and possibility becomes truth on a set of positive measure, a non-classical logic natural for continuous parameters.

Generalizable and Interpretable RF Fingerprinting with Shapelet-Enhanced Large Language Models

Deep neural networks (DNNs) have achieved remarkable success in radio frequency (RF) fingerprinting for wireless device authentication. However, their practical deployment faces two major limitations: domain shift, where models trained in one environment struggle to generalize to others, and the black-box nature of DNNs, which limits interpretability. To address these issues, we propose a novel framework that integrates a group of variable-length two-dimensional (2D) shapelets with a pre-trained large language model (LLM) to achieve efficient, interpretable, and generalizable RF fingerprinting. The 2D shapelets explicitly capture diverse local temporal patterns across the in-phase and quadrature (I/Q) components, providing compact and interpretable representations. Complementarily, the pre-trained LLM captures more long-range dependencies and global contextual information, enabling strong generalization with minimal training overhead. Moreover, our framework also supports prototype generation for few-shot inference, enhancing cross-domain performance without additional retraining. To evaluate the effectiveness of our proposed method, we conduct extensive experiments on six datasets across various protocols and domains. The results show that our method achieves superior standard and few-shot performance across both source and unseen domains.

Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning

The Homotopy paradigm, a general principle for solving challenging problems, appears across diverse domains such as robust optimization, global optimization, polynomial root-finding, and sampling. Practical solvers for these problems typically follow a predictor-corrector (PC) structure, but rely on hand-crafted heuristics for step sizes and iteration termination, which are often suboptimal and task-specific. To address this, we unify these problems under a single framework, which enables the design of a general neural solver. Building on this unified view, we propose Neural Predictor-Corrector (NPC), which replaces hand-crafted heuristics with automatically learned policies. NPC formulates policy selection as a sequential decision-making problem and leverages reinforcement learning to automatically discover efficient strategies. To further enhance generalization, we introduce an amortized training mechanism, enabling one-time offline training for a class of problems and efficient online inference on new instances. Experiments on four representative homotopy problems demonstrate that our method generalizes effectively to unseen instances. It consistently outperforms classical and specialized baselines in efficiency while demonstrating superior stability across tasks, highlighting the value of unifying homotopy methods into a single neural framework.

Efficient Algorithms for Partial Constraint Satisfaction Problems over Control-flow Graphs

In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we define a set of variables, a set of constraints, and a finite domain $D$ that encompasses all possible values for each variable. The objective is to assign a value to each variable in such a way that all constraints are satisfied. In the graph variant of CSP, an underlying graph is considered and we have one variable corresponding to each vertex of the graph and one or several constraints corresponding to each edge. In PCSPs, we allow for certain constraints to be violated at a specified cost, aiming to find a solution that minimizes the total cost. Numerous classical compiler optimization tasks can be framed as PCSPs over control-flow graphs. Examples include Register Allocation, Lifetime-optimal Speculative Partial Redundancy Elimination (LOSPRE), and Optimal Placement of Bank Selection Instructions. On the other hand, it is well-known that control-flow graphs of structured programs are sparse and decomposable in a variety of ways. In this work, we rely on the Series-Parallel-Loop (SPL) decompositions as introduced by~\cite{RegisterAllocation}. Our main contribution is a general algorithm for PCSPs over SPL graphs with a time complexity of \(O(|G| \cdot |D|^6)\), where \(|G|\) represents the size of the control-flow graph. Note that for any fixed domain $D,$ this yields a linear-time solution. Our algorithm can be seen as a generalization and unification of previous SPL-based approaches for register allocation and LOSPRE. In addition, we provide experimental results over another classical PCSP task, i.e. Optimal Bank Selection, achieving runtimes four times better than the previous state of the art.