Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models have shown remarkable success in generating complex, high-dimensional data, their usage in general regression tasks often lacks uncertainty-related evaluation and remains limited to domain-specific applications. We propose a novel diffusion-based framework for probabilistic regression that learns predictive distributions in a nonparametric way. More specifically, we propose to model the full distribution of the diffusion noise, enabling adaptation to diverse tasks and enhanced uncertainty quantification. We investigate different noise parameterizations, analyze their trade-offs, and evaluate our framework across a broad range of regression tasks, covering low- and high-dimensional settings. For several experiments, our approach shows superior performance against existing baselines, while delivering calibrated uncertainty estimates, demonstrating its versatility as a tool for probabilistic prediction.

Graph Neural Networks (GNNs) are powerful tools for precessing relational data but often struggle to generalize to unseen graphs, giving rise to the development of Graph Foundational Models (GFMs). However, current GFMs are challenged by the extreme heterogeneity of graph data, where each graph can possess a unique feature space, label set, and topology. To address this, two main paradigms have emerged. The first leverages Large Language Models (LLMs), but is fundamentally text-dependent, thus struggles to handle the numerical features in vast graphs. The second pre-trains a structure-based model, but the adaptation to new tasks typically requires a costly, per-graph tuning stage, creating a critical efficiency bottleneck. In this work, we move beyond these limitations and introduce \textbf{G}raph \textbf{I}n-context \textbf{L}earning \textbf{T}ransformer (GILT), a framework built on an LLM-free and tuning-free architecture. GILT introduces a novel token-based framework for in-context learning (ICL) on graphs, reframing classification tasks spanning node, edge and graph levels in a unified framework. This mechanism is the key to handling heterogeneity, as it is designed to operate on generic numerical features. Further, its ability to understand class semantics dynamically from the context enables tuning-free adaptation. Comprehensive experiments show that GILT achieves stronger few-shot performance with significantly less time than LLM-based or tuning-based baselines, validating the effectiveness of our approach.

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the Distortion-Measure (DM) form and Quantile-Function (QF) form. The DM-form employs a three-timescale algorithm to track quantiles, compute their gradients, and update decision variables, utilizing the Generalized Likelihood Ratio and kernel-based density estimation. The QF-form provides a simpler two-timescale approach that avoids the need for complex quantile gradient estimation. A hybrid form integrates both approaches, applying the DM-form for robust performance around distortion function jumps and the QF-form for efficiency in smooth regions. Proofs of strong convergence and convergence rates for the proposed algorithms are provided. In particular, the DM-form achieves an optimal rate of $O(k^{-4/7})$, while the QF-form attains a faster rate of $O(k^{-2/3})$. Numerical experiments confirm their effectiveness and demonstrate substantial improvements over baselines in robust portfolio selection tasks. The method's scalability is further illustrated through integration into deep reinforcement learning. Specifically, a DRM-based Proximal Policy Optimization algorithm is developed and applied to multi-echelon dynamic inventory management, showcasing its practical applicability.

Federated learning has attracted increasing attention at recent large-scale optimization and machine learning research and applications, but is also vulnerable to Byzantine clients that can send any erroneous signals. Robust aggregators are commonly used to resist Byzantine clients. This usually requires to estimate the unknown number $f$ of Byzantine clients, and thus accordingly select the aggregators with proper degree of robustness (i.e., the maximum number $\hat{f}$ of Byzantine clients allowed by the aggregator). Such an estimation should have important effect on the performance, which has not been systematically studied to our knowledge. This work will fill in the gap by theoretically analyzing the worst-case error of aggregators as well as its induced federated learning algorithm for any cases of $\hat{f}$ and $f$. Specifically, we will show that underestimation ($\hat{f}

As systems trend toward superintelligence, a natural modeling premise is that agents can self-improve along every facet of their own design. We formalize this with a five-axis decomposition and a decision layer, separating incentives from learning behavior and analyzing axes in isolation. Our central result identifies and introduces a sharp utility--learning tension, the structural conflict in self-modifying systems whereby utility-driven changes that improve immediate or expected performance can also erode the statistical preconditions for reliable learning and generalization. Our findings show that distribution-free guarantees are preserved iff the policy-reachable model family is uniformly capacity-bounded; when capacity can grow without limit, utility-rational self-changes can render learnable tasks unlearnable. Under standard assumptions common in practice, these axes reduce to the same capacity criterion, yielding a single boundary for safe self-modification. Numerical experiments across several axes validate the theory by comparing destructive utility policies against our proposed two-gate policies that preserve learnability.

Text editing can involve several iterations of revision. Incorporating an efficient Grammar Error Correction (GEC) tool in the initial correction round can significantly impact further human editing effort and final text quality. This raises an interesting question to quantify GEC Tool usability: How much effort can the GEC Tool save users? We present the first large-scale dataset of post-editing (PE) time annotations and corrections for two English GEC test datasets (BEA19 and CoNLL14). We introduce Post-Editing Effort in Time (PEET) for GEC Tools as a human-focused evaluation scorer to rank any GEC Tool by estimating PE time-to-correct. Using our dataset, we quantify the amount of time saved by GEC Tools in text editing. Analyzing the edit type indicated that determining whether a sentence needs correction and edits like paraphrasing and punctuation changes had the greatest impact on PE time. Finally, comparison with human rankings shows that PEET correlates well with technical effort judgment, providing a new human-centric direction for evaluating GEC tool usability. We release our dataset and code at: https://github.com/ankitvad/PEET_Scorer.

Neural network training is typically viewed as gradient descent on a loss surface. We propose a fundamentally different perspective: learning is a structure-preserving transformation (a functor L) between the space of network parameters (Param) and the space of learned representations (Rep). This categorical framework reveals that different training runs producing similar test performance often belong to the same homotopy class (continuous deformation family) of optimization paths. We show experimentally that networks converging via homotopic trajectories generalize within 0.5% accuracy of each other, while non-homotopic paths differ by over 3%. The theory provides practical tools: persistent homology identifies stable minima predictive of generalization (R^2 = 0.82 correlation), pullback constructions formalize transfer learning, and 2-categorical structures explain when different optimization algorithms yield functionally equivalent models. These categorical invariants offer both theoretical insight into why deep learning works and concrete algorithmic principles for training more robust networks.

Many high-stakes AI applications target low-prevalence events, where apparent accuracy can conceal limited real-world value. Relevant AI models range from expert-defined rules and traditional machine learning to generative LLMs constrained for classification. We outline key considerations for critical appraisal of AI in rare-event recognition, including problem framing and test set design, prevalence-aware statistical evaluation, robustness assessment, and integration into human workflows. In addition, we propose an approach to structured case-level examination (SCLE), to complement statistical performance evaluation, and a comprehensive checklist to guide procurement or development of AI models for rare-event recognition. We instantiate the framework in pharmacovigilance, drawing on three studies: rule-based retrieval of pregnancy-related reports; duplicate detection combining machine learning with probabilistic record linkage; and automated redaction of person names using an LLM. We highlight pitfalls specific to the rare-event setting including optimism from unrealistic class balance and lack of difficult positive controls in test sets - and show how cost-sensitive targets align model performance with operational value. While grounded in pharmacovigilance practice, the principles generalize to domains where positives are scarce and error costs may be asymmetric.

Low-Rank Adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) technique that adapts large pre-trained models by adding low-rank matrices to their weight updates. However, in the context of fine-tuning multi-head self-attention (MHA), LoRA has been employed to adapt each attention head separately, thereby overlooking potential synergies across different heads. To mitigate this issue, we propose a novel Hyper-shared Low-Rank Adaptation (HoRA) method, which utilizes joint hypernetworks to generate low-rank matrices across attention heads. By coupling their adaptation through a shared generator, HoRA encourages cross-head information sharing, and thus directly addresses the aforementioned limitation of LoRA. By comparing LoRA and HoRA through the lens of hierarchical mixture of experts, our theoretical findings reveal that the latter achieves superior sample efficiency to the former. Furthermore, through extensive experiments across diverse language and vision benchmarks, we demonstrate that HoRA outperforms LoRA and other PEFT methods while requiring only a marginal increase in the number of trainable parameters.

Autoregressive (AR) models have shown great promise in image generation, yet they face a fundamental inefficiency stemming from their core component: a vast, unstructured vocabulary of visual tokens. This conventional approach treats tokens as a flat vocabulary, disregarding the intrinsic structure of the token embedding space where proximity often correlates with semantic similarity. This oversight results in a highly complex prediction task, which hinders training efficiency and limits final generation quality. To resolve this, we propose Manifold-Aligned Semantic Clustering (MASC), a principled framework that constructs a hierarchical semantic tree directly from the codebook's intrinsic structure. MASC employs a novel geometry-aware distance metric and a density-driven agglomerative construction to model the underlying manifold of the token embeddings. By transforming the flat, high-dimensional prediction task into a structured, hierarchical one, MASC introduces a beneficial inductive bias that significantly simplifies the learning problem for the AR model. MASC is designed as a plug-and-play module, and our extensive experiments validate its effectiveness: it accelerates training by up to 57% and significantly improves generation quality, reducing the FID of LlamaGen-XL from 2.87 to 2.58. MASC elevates existing AR frameworks to be highly competitive with state-of-the-art methods, establishing that structuring the prediction space is as crucial as architectural innovation for scalable generative modeling.