Aligning Large Language Models (LLMs) with human values often involves balancing multiple, conflicting objectives such as helpfulness and harmlessness. Training these models is computationally intensive, and centralizing the process raises significant data privacy concerns. Federated Learning (FL) offers a compelling alternative, but existing Federated Multi-Objective Optimization (FMOO) methods face severe communication bottlenecks as their reliance on transmitting multiple gradients to a server is unscalable for large models. We introduce FIRM (Federated In-client Regularized Multi-objective alignment), a novel algorithm that achieves both client disagreement drift mitigation and communication efficiency. In FIRM, each client locally solves a regularized multi-objective optimization problem. By directly mitigating client disagreement drift through in-client regularization, our method eliminates the need for the multi-gradient transmissions common in prior works. Consequently, clients need only to transmit a single set of adapted parameters, maintaining high communication efficiency. We prove that our algorithm converges to Pareto-stationary points and, to our knowledge, provide the first finite-time convergence guarantees for this federated multi-objective alignment setting. Empirically, we show that FIRM leads to smoother training dynamics, reduced client disagreement drift, and improved reward trade-offs compared to baselines. We further propose a method to incorporate a preference over the objectives and report empirical Pareto plots, demonstrating that FIRM can smoothly adapt trade-offs between objectives in response to specified preferences.

Group Relative Policy Optimization (GRPO) has shown promise in aligning image and video generative models with human preferences. However, applying it to modern flow matching models is challenging because of its deterministic sampling paradigm. Current methods address this issue by converting Ordinary Differential Equations (ODEs) to Stochastic Differential Equations (SDEs), which introduce stochasticity. However, this SDE-based GRPO suffers from issues of inefficient credit assignment and incompatibility with high-order solvers for fewer-step sampling. In this paper, we first reinterpret existing SDE-based GRPO methods from a distance optimization perspective, revealing their underlying mechanism as a form of contrastive learning. Based on this insight, we propose Neighbor GRPO, a novel alignment algorithm that completely bypasses the need for SDEs. Neighbor GRPO generates a diverse set of candidate trajectories by perturbing the initial noise conditions of the ODE and optimizes the model using a softmax distance-based surrogate leaping policy. We establish a theoretical connection between this distance-based objective and policy gradient optimization, rigorously integrating our approach into the GRPO framework. Our method fully preserves the advantages of deterministic ODE sampling, including efficiency and compatibility with high-order solvers. We further introduce symmetric anchor sampling for computational efficiency and group-wise quasi-norm reweighting to address reward flattening. Extensive experiments demonstrate that Neighbor GRPO significantly outperforms SDE-based counterparts in terms of training cost, convergence speed, and generation quality.

Macrocyclic peptides are an emerging modality that combines biologics-like affinity with small-molecule-like developability, but their vast combinatorial space and multi-parameter objectives make lead optimization slow and challenging. Prior generative approaches such as PepINVENT require chemists to pre-specify mutable positions for optimization, choices that are not always known a priori, and rely on static pretraining and optimization algorithms that limit the model's ability to generalize and effectively optimize peptide sequences. We introduce PepEVOLVE, a position-aware, dynamic framework that learns both where to edit and how to dynamically optimize peptides for multi-objective improvement. PepEVOLVE (i) augments pretraining with dynamic masking and CHUCKLES shifting to improve generalization, (ii) uses a context-free multi-armed bandit router that discovers high-reward residues, and (iii) couples a novel evolving optimization algorithm with group-relative advantage to stabilize reinforcement updates. During in silico evaluations, the router policy reliably learns and concentrates probability on chemically meaningful sites that influence the peptide's properties. On a therapeutically motivated Rev-binding macrocycle benchmark, PepEVOLVE outperformed PepINVENT by reaching higher mean scores (approximately 0.8 vs. 0.6), achieving best candidates with a score of 0.95 (vs. 0.87), and converging in fewer steps under the task of optimizing permeability and lipophilicity with structural constraints. Overall, PepEVOLVE offers a practical, reproducible path to peptide lead optimization when optimal edit sites are unknown, enabling more efficient exploration and improving design quality across multiple objectives.

Deep hashing improves retrieval efficiency through compact binary codes, yet it introduces severe and often overlooked privacy risks. The ability to reconstruct original training data from hash codes could lead to serious threats such as biometric forgery and privacy breaches. However, model inversion attacks specifically targeting deep hashing models remain unexplored, leaving their security implications unexamined. This research gap stems from the inaccessibility of genuine training hash codes and the highly discrete Hamming space, which prevents existing methods from adapting to deep hashing. To address these challenges, we propose DHMI, the first diffusion-based model inversion framework designed for deep hashing. DHMI first clusters an auxiliary dataset to derive semantic hash centers as surrogate anchors. It then introduces a surrogate-guided denoising optimization method that leverages a novel attack metric (fusing classification consistency and hash proximity) to dynamically select candidate samples. A cluster of surrogate models guides the refinement of these candidates, ensuring the generation of high-fidelity and semantically consistent images. Experiments on multiple datasets demonstrate that DHMI successfully reconstructs high-resolution, high-quality images even under the most challenging black-box setting, where no training hash codes are available. Our method outperforms the existing state-of-the-art model inversion attacks in black-box scenarios, confirming both its practical efficacy and the critical privacy risks inherent in deep hashing systems.

Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW. This paper presents theoretical analysis to support its practical success. We provide convergence proofs for Muon across four practical settings, systematically examining its behavior with and without the inclusion of Nesterov momentum and weight decay. Our analysis covers the standard configuration using both, thereby elucidating its real-world performance. We then demonstrate that the addition of weight decay yields strictly tighter theoretical bounds and clarify the interplay between the weight decay coefficient and the learning rate. Finally, we derive the critical batch size for Muon that minimizes the computational cost of training. Our analysis identifies the hyperparameters governing this value, and our experiments validate the corresponding theoretical findings across workloads including image classification and language modeling task.

Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through heuristic approaches. Recently, there has been growing interest in globally optimized trees, where the overall tree is trained by minimizing the error function over all its parameters. We propose a new soft survival tree model (SST), with a soft splitting rule at each branch node, trained via a nonlinear optimization formulation amenable to decomposition. Since SSTs provide for every input vector a specific survival function associated to a single leaf node, they satisfy the conditional computation property and inherit the related benefits. SST and the training formulation combine flexibility with interpretability: any smooth survival function (parametric, semiparametric, or nonparametric) estimated through maximum likelihood can be used, and each leaf node of an SST yields a cluster of distinct survival functions which are associated to the data points routed to it. Numerical experiments on 15 well-known datasets show that SSTs, with parametric and spline-based semiparametric survival functions, trained using an adaptation of the node-based decomposition algorithm proposed by Consolo et al. (2024) for soft regression trees, outperform three benchmark survival trees in terms of four widely-used discrimination and calibration measures. SSTs can also be extended to consider group fairness.

Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small outer-loop step sizes to handle the increased smoothness induced by large penalty terms, leading to suboptimal complexity. This work considers the general BLO problems with coupled constraints (CCs) and leverages a novel penalty reformulation that decouples the upper- and lower-level variables. This yields an improved analysis of the smoothness constant, enabling larger step sizes and reduced iteration complexity for Penalty-Based Gradient Descent algorithms in ALTernating fashion (ALT-PBGD). Building on the insight of reduced smoothness, we propose PBGD-Free, a novel fully single-loop algorithm that avoids inner loops for the uncoupled constraint BLO. For BLO with CCs, PBGD-Free employs an efficient inner-loop with substantially reduced iteration complexity. Furthermore, we propose a novel curvature condition describing the "flatness" of the upper-level objective with respect to the LL variable. This condition relaxes the traditional upper-level Lipschitz requirement, enables smaller penalty constant choices, and results in a negligible penalty gradient term during upper-level variable updates. We provide rigorous convergence analysis and validate the method's efficacy through hyperparameter optimization for support vector machines and fine-tuning of large language models.

We present a new algorithmic approach for the task of finding a chordal Markov network structure that maximizes a given scoring function. The algorithm is based on branch and bound and integrates dynamic programming for both domain pruning and for obtaining strong bounds for search-space pruning. Empirically, we show that the approach dominates in terms of running times a recent integer programming approach (and thereby also a recent constraint optimization approach) for the problem.

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the algorithms instead? In many real-world applications, it is typically the case that the same optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data. This provides an opportunity for learning heuristic algorithms that exploit the structure of such recurring problems. In this paper, we propose a unique combination of reinforcement learning and graph embedding to address this challenge. The learned greedy policy behaves like a meta-algorithm that incrementally constructs a solution, and the action is determined by the output of a graph embedding network capturing the current state of the solution. We show that our framework can be applied to a diverse range of optimization problems over graphs, and learns effective algorithms for the Minimum Vertex Cover, Maximum Cut and Traveling Salesman problems.

We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. Compared with recent advances in this vein, the differential equation considered here is the basic gradient flow, and we derive a class of multi-step schemes which includes accelerated algorithms, using classical conditions from numerical analysis. Multi-step schemes integrate the differential equation using larger step sizes, which intuitively explains the acceleration phenomenon.