Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem.

Financial markets pose fundamental challenges for asset return prediction due to their high dimensionality, non-stationarity, and persistent volatility. Despite advances in large language models and multi-agent systems, current quantitative research pipelines suffer from limited automation, weak interpretability, and fragmented coordination across key components such as factor mining and model innovation. In this paper, we propose R&D-Agent for Quantitative Finance, in short R&D-Agent(Q), the first data-centric multi-agent framework designed to automate the full-stack research and development of quantitative strategies via coordinated factor-model co-optimization. R&D-Agent(Q)decomposes the quant process into two iterative stages: a Research stage that dynamically sets goal-aligned prompts, formulates hypotheses based on domain priors, and maps them to concrete tasks, and a Development stage that employs a code-generation agent, Co-STEER, to implement task-specific code, which is then executed in real-market backtests. The two stages are connected through a feedback stage that thoroughly evaluates experimental outcomes and informs subsequent iterations, with a multi-armed bandit scheduler for adaptive direction selection. Empirically, R&D-Agent(Q) achieves up to 2 higher annualized returns than classical factor libraries using 70% fewer factors, and outperforms state-of-the-art deep time-series models on real markets. Its joint factor-model optimization delivers a strong balance between predictive accuracy and strategy robustness.

Mixed-Integer Linear Programming (MILP) is a powerful framework used to address a wide range of NP-hard combinatorial optimization problems, often solved by Branch and bound (B&B). A key factor influencing the performance of B&B solvers is the variable selection heuristic governing branching decisions. Recent contributions have sought to adapt reinforcement learning (RL) algorithms to the B&B setting to learn optimal branching policies, through Markov Decision Processes (MDP) inspired formulations, and ad hoc convergence theorems and algorithms. In this work, we introduce BBMDP, a principled vanilla MDP formulation for variable selection in B&B, allowing to leverage a broad range of RL algorithms for the purpose of learning optimal B&B heuristics. Computational experiments validate our model empirically, as our branching agent outperforms prior state-of-the-art RL agents on four standard MILP benchmarks.

Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, referred to as the uncertainty set. However, the efficacy of DRO heavily depends on the design of the uncertainty set, and existing methods often perform suboptimally due to an inappropriate or inflexible uncertainty set. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: semantic calibration, which bootstraps semantically meaningful transport costs via inverse OT, and adaptive refinement, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis of this adaptive process and prove theoretical guarantees of convergence. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-ofthe-art robustness.

We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps: L(s) = L0 +A S α1 C S2, where L(s)is the validation loss at step s, S1 is the area under the LR curve, S2 is the LR annealing area, and L0, A, C, αare constant parameters.

Understanding complex systems by inferring trajectories from sparse sample snapshots is a fundamental challenge in a wide range of domains, e.g., single-cell biology, meteorology, and economics. Despite advancements in Bridge and Flow matching frameworks, current methodologies rely on pairwise interpolation between adjacent snapshots. This hinders their ability to capture long-range temporal dependencies and potentially affects the coherence of the inferred trajectories. To address these issues, we introduce Momentum Multi-Marginal Schrödinger Bridge Matching (3MSBM), a novel matching framework that learns smooth measure-valued splines for stochastic systems that satisfy multiple positional constraints. This is achieved by lifting the dynamics to phase space and generalizing stochastic bridges to be conditioned on several points, forming a multi-marginal conditional stochastic optimal control problem. The underlying dynamics are then learned by minimizing a variational objective, having fixed the path induced by the multi-marginal conditional bridge. As a matching approach, 3MSBM learns transport maps that preserve intermediate marginals throughout training, significantly improving convergence and scalability. Extensive experimentation in a series of real-world applications validates the superior performance of 3MSBM compared to existing methods in capturing complex dynamics with temporal dependencies, opening new avenues for training matching frameworks in multi-marginal settings.

Participating in efforts to endow generative AI with the 3D physical world perception, we propose I2-NeRF, a novel neural radiance field framework that enhances isometric and isotropic metric perception under media degradation. While existing NeRF models predominantly rely on object-centric sampling, I2-NeRF introduces a reverse-stratified upsampling strategy to achieve near-uniform sampling across 3D space, thereby preserving isometry. We further present a general radiative formulation for media degradation that unifies emission, absorption, and scattering into a particle model governed by the Beer-Lambert attenuation law. By composing the direct and media-induced in-scatter radiance, this formulation extends naturally to complex media environments such as underwater, haze, and even low-light scenes. By treating light propagation uniformly in both vertical and horizontal directions, I2-NeRF enables isotropic metric perception and can even estimate medium properties such as water depth. Experiments on real-world datasets demonstrate that our method significantly improves both reconstruction fidelity and physical plausibility compared to existing approaches.

In reinforcement learning, we typically refer to unsupervised pre-training when we aim to pre-train a policy without a priori access to the task specification, i.e., rewards, to be later employed for efficient learning of downstream tasks. In singleagent settings, the problem has been extensively studied and mostly understood. A popular approach casts the unsupervised objective as maximizing the entropy of the state distribution induced by the agent's policy, from which principles and methods follow. In contrast, little is known about state entropy maximization in multi-agent settings, which are ubiquitous in the real world. What are the pros and cons of alternative problem formulations in this setting? How hard is the problem in theory, how can we solve it in practice? In this paper, we address these questions by first characterizing those alternative formulations and highlighting how the problem, even when tractable in theory, is non-trivial in practice. Then, we present a scalable, decentralized, trust-region policy search algorithm to address the problem in practical settings. Finally, we provide numerical validations to both corroborate the theoretical findings and pave the way for unsupervised multi-agent reinforcement learning via state entropy maximization in challenging domains, showing that optimizing for a specific objective, namely mixture entropy, provides an excellent trade-off between tractability and performances.

Tokenization is the process of encoding strings into tokens of a fixed vocabulary size, and is widely utilized in Natural Language Processing applications. The leading tokenization algorithm today is Byte-Pair Encoding (BPE), which formulates the tokenization problem as a compression problem and tackles it by performing sequences of merges. In this work, we formulate tokenization as an optimization objective, show that it is NP-hard via a simple reduction from vertex cover, and propose a polynomial-time greedy algorithm GREEDTOK. Our formulation naturally relaxes to the well-studied weighted maximum coverage problem which has a simple (1 1/e)-approximation algorithm GREEDWMC. Through empirical evaluations on real-world corpora, we show that GREEDTOK outperforms BPE and UNIGRAM on compression and achieves a covering score comparable to GREEDWMC.

We study Transformers through the perspective of optimal control theory, using tools from continuous-time formulations to derive actionable insights into training and architecture design. This framework improves the performance of existing Transformer models while providing desirable theoretical guarantees, including generalization and robustness. Our framework is designed to be plug-and-play, enabling seamless integration with established Transformer models and requiring only slight changes to the implementation. We conduct seven extensive experiments on tasks motivated by text generation, sentiment analysis, image classification, and point cloud classification. Experimental results show that the framework improves the test performance of the baselines, while being more parameter-efficient. On character-level text generation with nanoGPT, our framework achieves a 46% reduction in final test loss while using 42% fewer parameters. On GPT-2, our framework achieves a 9.3% reduction in final test loss, demonstrating scalability to larger models. To the best of our knowledge, this is the first work that applies optimal control theory to both the training and architecture of Transformers. It offers a new foundation for systematic, theory-driven improvements and moves beyond costly trial-and-error approaches.