T-GINEE: A Tensor-Based Multilayer Graph Representation Learning

Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by treating layers independently or aggregating them. To address this, we propose T-GINEE (Tensor-Based Generalized Multilayer-graph Estimating Equation), a statistical regularization framework combining tensor-based generalized estimating equations with task-specific loss to model cross-network correlations explicitly. Key innovations include: (1) CP tensor decomposition capturing structural dependencies via shared latent factors; (2) a generalized estimating equation framework modeling inter-layer correlations through working covariance matrices; and (3) a flexible link function accommodating characteristics like sparsity. Our theoretical analysis establishes consistency and asymptotic normality under mild conditions. Extensive experiments on synthetic and real-world datasets validate T-GINEE's effectiveness for multilayer network analysis.

Remember the Decision, Not the Description: A Rate-Distortion Framework for Agent Memory

Long-horizon language agents must operate under limited runtime memory, yet existing memory mechanisms often organize experience around descriptive criteria such as relevance, salience, or summary quality. For an agent, however, memory is valuable not because it faithfully describes the past, but because it preserves the distinctions between histories that must remain separated under a fixed budget to support good decisions. We cast this as a decision-centric rate-distortion problem, measuring memory quality by the loss in achievable decision quality induced by compression. This yields an exact forgetting boundary for what can be safely forgotten, and a memory-distortion frontier characterizing the optimal tradeoff between memory budget and decision quality. Motivated by this decision-centric view of memory, we propose DeMem, an online memory learner that refines its partition only when data certify that a shared state would induce decision conflict, and prove near-minimax regret guarantees. On both controlled synthetic diagnostics and long-horizon conversational benchmarks, DeMem yields consistent gains under the same runtime budget, supporting the principle that memory should preserve the distinctions that matter for decisions, not descriptions.

CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical Reasoning

Large Language Models (LLMs) exhibit strong mathematical reasoning when trained on high-quality Chain-of-Thought (CoT) that articulates intermediate steps, yet costly CoT curation hinders further progress. While existing remedies such as distillation from stronger LLMs and self-synthesis based on test-time search alleviate this issue, they often suffer from diminishing returns or high computing overhead.In this work, we propose CoTEvol, a genetic evolutionary framework that casts CoT generation as a population-based search over reasoning trajectories.Candidate trajectories are iteratively evolved through reflective global crossover at the trajectory level and local mutation guided by uncertainty at the step level, enabling holistic recombination and fine-grained refinement. Lightweight, task-aware fitness functions are designed to guide the evolutionary process toward accurate and diverse reasoning. Empirically, CoTEvol improves correct-CoT synthesis success by over 30% and enhances structural diversity, with markedly improved efficiency. LLMs trained on these evolutionary CoT data achieve an average gain of 6.6% across eight math benchmarks, outperforming previous distillation and self-synthesis approaches. These results underscore the promise of evolutionary CoT synthesis as a scalable and effective method for mathematical reasoning tasks.

X-GS: An Extensible Open Framework for Perceiving and Thinking via 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for novel view synthesis, subsequently extending into numerous spatial AI applications. However, most existing 3DGS methods operate in isolation, focusing on specific domains such as pose-free 3DGS, online SLAM, and semantic enrichment. In this paper, we introduce X-GS, an extensible open framework consisting of two major components: the X-GS-Perceiver, which unifies a broad range of 3DGS techniques to enable real-time online SLAM and distill semantic features; and the X-GS-Thinker, which interfaces with downstream multimodal models. In our implementation of the Perceiver, we integrate various 3DGS methods through three novel mechanisms: an online Vector Quantization (VQ) module, a GPU-accelerated grid-sampling scheme, and a highly parallelized pipeline design. The Thinker accommodates vision-language models and utilizes the resulting 3D semantic Gaussians, enabling downstream applications such as object detection, caption generation, and potentially embodied tasks. Experimental results on real-world datasets demonstrate the efficiency and newly unlocked multimodal capabilities of the X-GS framework.

DARC: Disagreement-Aware Alignment via Risk-Constrained Decoding

Preference-based alignment methods (e.g., RLHF, DPO) typically optimize a single scalar objective, implicitly averaging over heterogeneous human preferences. In practice, systematic annotator and user-group disagreement makes mean-reward maximization brittle and susceptible to proxy over-optimization. We propose **Disagreement-Aware Alignment via Risk-Constrained Decoding (DARC)**, a retraining-free inference-time method that frames response selection as distributionally robust, risk-sensitive decision making. Given multiple preference samples or scalable disagreement proxies, DARC reranks candidates by maximizing a *KL-robust (entropic)* satisfaction objective, and provides simple deployment controls that cap or penalize the corresponding entropic risk premium relative to the mean, enabling explicit risk budgets without retraining. We provide theoretical characterization linking this decoding rule to principled pessimism and KL-based distributionally robust optimization. Experiments on alignment benchmarks show that DARC reduces disagreement and tail risk while maintaining competitive average quality under noisy, heterogeneous feedback.

FinEvo: From Isolated Backtests to Ecological Market Games for Multi-Agent Financial Strategy Evolution

Conventional financial strategy evaluation relies on isolated backtests in static environments. Such evaluations assess each policy independently, overlook correlations and interactions, and fail to explain why strategies ultimately persist or vanish in evolving markets. We shift to an ecological perspective, where trading strategies are modeled as adaptive agents that interact and learn within a shared market. Instead of proposing a new strategy, we present FinEvo, an ecological game formalism for studying the evolutionary dynamics of multi-agent financial strategies. At the individual level, heterogeneous ML-based traders-rule-based, deep learning, reinforcement learning, and large language model (LLM) agents-adapt using signals such as historical prices and external news. At the population level, strategy distributions evolve through three designed mechanisms-selection, innovation, and environmental perturbation-capturing the dynamic forces of real markets. Together, these two layers of adaptation link evolutionary game theory with modern learning dynamics, providing a principled environment for studying strategic behavior. Experiments with external shocks and real-world news streams show that FinEvo is both stable for reproducibility and expressive in revealing context-dependent outcomes. Strategies may dominate, collapse, or form coalitions depending on their competitors-patterns invisible to static backtests. By reframing strategy evaluation as an ecological game formalism, FinEvo provides a unified, mechanism-level protocol for analyzing robustness, adaptation, and emergent dynamics in multi-agent financial markets, and may offer a means to explore the potential impact of macroeconomic policies and financial regulations on price evolution and equilibrium.

Renormalization Group Guided Tensor Network Structure Search

Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS methods face significant limitations in computational tractability, structure adaptivity, and optimization robustness across diverse tensor characteristics. They struggle with three key challenges: single-scale optimization missing multi-scale structures, discrete search spaces hindering smooth structure evolution, and separated structure-parameter optimization causing computational inefficiency. We propose RGTN (Renormalization Group guided Tensor Network search), a physics-inspired framework transforming TN-SS via multi-scale renormalization group flows. Unlike fixed-scale discrete search methods, RGTN uses dynamic scale-transformation for continuous structure evolution across resolutions. Its core innovation includes learnable edge gates for optimization-stage topology modification and intelligent proposals based on physical quantities like node tension measuring local stress and edge information flow quantifying connectivity importance. Starting from low-complexity coarse scales and refining to finer ones, RGTN finds compact structures while escaping local minima via scale-induced perturbations. Extensive experiments on light field data, high-order synthetic tensors, and video completion tasks show RGTN achieves state-of-the-art compression ratios and runs 4-600$\times$ faster than existing methods, validating the effectiveness of our physics-inspired approach.

A Polynomial-time Algorithm for Online Sparse Linear Regression with Improved Regret Bound under Weaker Conditions

In this paper, we study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ attributes per instance for prediction, which was proved to be NP-hard. Previous work gave polynomial-time algorithms assuming the data matrix satisfies the linear independence of features, the compatibility condition, or the restricted isometry property. We introduce a new polynomial-time algorithm, which significantly improves previous regret bounds (Ito et al., 2017) under the compatibility condition that is weaker than the other two assumptions. The improvements benefit from a tighter convergence rate of the $\ell_1$-norm error of our estimators. Our algorithm leverages the well-studied Dantzig Selector, but importantly with several novel techniques, including an algorithm-dependent sampling scheme for estimating the covariance matrix, an adaptive parameter tuning scheme, and a batching online Newton step with careful initializations. We also give novel and non-trivial analyses, including an induction method for analyzing the $\ell_1$-norm error, careful analyses on the covariance of non-independent random variables, and a decomposition on the regret. We further extend our algorithm to OSLR with additional observations where the algorithms can observe additional $k_0$ attributes after each prediction, and improve previous regret bounds (Kale et al., 2017; Ito et al., 2017).

SecFwT: Efficient Privacy-Preserving Fine-Tuning of Large Language Models Using Forward-Only Passes

Large language models (LLMs) have transformed numerous fields, yet their adaptation to specialized tasks in privacy-sensitive domains, such as healthcare and finance, is constrained by the scarcity of accessible training data due to stringent privacy requirements. Secure multi-party computation (MPC)-based privacy-preserving machine learning offers a powerful approach to protect both model parameters and user data, but its application to LLMs has been largely limited to inference, as fine-tuning introduces significant computational challenges, particularly in privacy-preserving backward propagation and optimizer operations. This paper identifies two primary obstacles to MPC-based privacy-preserving fine-tuning of LLMs: (1) the substantial computational overhead of backward and optimizer processes, and (2) the inefficiency of softmax-based attention mechanisms in MPC settings. To address these challenges, we propose SecFwT, the first MPC-based framework designed for efficient, privacy-preserving LLM fine-tuning. SecFwT introduces a forward-only tuning paradigm to eliminate backward and optimizer computations and employs MPC-friendly Random Feature Attention to approximate softmax attention, significantly reducing costly non-linear operations and computational complexity. Experimental results demonstrate that SecFwT delivers substantial improvements in efficiency and privacy preservation, enabling scalable and secure fine-tuning of LLMs for privacy-critical applications.

Efficient Network Automatic Relevance Determination

We propose Network Automatic Relevance Determination (NARD), an extension of ARD for linearly probabilistic models, to simultaneously model sparse relationships between inputs $X \in \mathbb R^{d \times N}$ and outputs $Y \in \mathbb R^{m \times N}$, while capturing the correlation structure among the $Y$. NARD employs a matrix normal prior which contains a sparsity-inducing parameter to identify and discard irrelevant features, thereby promoting sparsity in the model. Algorithmically, it iteratively updates both the precision matrix and the relationship between $Y$ and the refined inputs. To mitigate the computational inefficiencies of the $\mathcal O(m^3 + d^3)$ cost per iteration, we introduce Sequential NARD, which evaluates features sequentially, and a Surrogate Function Method, leveraging an efficient approximation of the marginal likelihood and simplifying the calculation of determinant and inverse of an intermediate matrix. Combining the Sequential update with the Surrogate Function method further reduces computational costs. The computational complexity per iteration for these three methods is reduced to $\mathcal O(m^3+p^3)$, $\mathcal O(m^3 + d^2)$, $\mathcal O(m^3+p^2)$, respectively, where $p \ll d$ is the final number of features in the model. Our methods demonstrate significant improvements in computational efficiency with comparable performance on both synthetic and real-world datasets.