arXiv subjects

Xuefeng Liu

Publications and source records attributed to Xuefeng Liu.

At least 19 recordsLinked to original sources

arXiv2026

Shared Actors Need Not Share Critics: Effects of Value Mismatch in Parallel Reinforcement Learning

When a single policy is trained in parallel across multiple environments of the same task, such as procedurally generated levels, randomized dynamics, or curricula, implementations commonly use one critic across all sampled environments. Yet different environments can assign different expected returns to the same input visible to the critic. A critic without environment information must then reconcile distinct value targets, systematically shifting the sampled advantages within individual environments. Using illustrative bandit models with multiple environments and a common optimal arm, we characterize how this value mismatch redistributes sampled policy updates, reinforcing unhelpful actions while attenuating or even reversing useful ones. The oracle processes using no baseline, the shared value, or the value specific to the sampled environment have the same mean logit update at a fixed policy and converge to the same optimal policy, yet their realized learning paths can differ sharply. The analysis motivates a minimal intervention: give only a logged environment index to the critic so that it can separate the value targets. Controlled CartPole and MuJoCo experiments expose the predicted shifted values, advantages, and performance gaps. In the more complex BipedalWalker and Procgen settings, the same intervention yields more stable learning and higher returns. Across all $16$ Procgen games, the multihead conditional critic improves aggregate normalized return on $600$ unseen levels per game by $40.8\%$. In conclusion, the theory identifies value mismatch as a direct mechanism through which critic sharing can degrade stochastic learning dynamics, not captured by scalar estimator variance alone, and the experiments show that conditioning on an index is broadly effective in parallel reinforcement learning.

cs.LG↗

arXiv2026

From estimate to proof: certified ground-state energy bounds for singular Schr\"odinger operators

Many predictions in quantum chemistry, materials science, and spectral geometry hinge on the lowest energy levels of a Schr\"odinger operator, yet standard simulations return approximations with no guarantee of how far they sit from the true value. We present a computational framework that returns mathematically certified bounds---an interval provably containing the exact energy---even for the singular, unbounded, sign-changing potentials of real molecules, where existing certified methods fail. For the hydrogen molecular ion this framework delivers, to our knowledge, the first guaranteed two-sided enclosure of the true infinite-domain ground-state energy: an interval of width below $5\times10^{-4}$ that provably contains the accepted reference value. The key that makes a whole-space guarantee possible is an \emph{explicit}, computable bound on the error of restricting the problem to a finite box---replacing the classical argument that the wavefunction merely decays---which brackets the true energy from both sides. Remarkably, the certified interval reproduces the uncertified numerical value to eleven digits, so mathematical rigor costs almost nothing in accuracy. The result turns eigenvalue computation from an estimate into a proof.

math.NA↗

arXiv2026

Leveraging generative hallucination and biophysics-informed modeling for unified biomolecular sequence-structure co-design

Biomolecular design underpins applications from molecular recognition to therapeutics and synthetic biology, yet de novo interaction design remains challenging-especially for DNA/RNA, underexplored non-protein modalities with scarce, heterogeneous complex data and sharper geometric and chemical constraints. We introduce MCTH (Monte Carlo Tree Hallucination), an inference-only framework that casts all-atom sequence-structure co-design as uncertainty-aware planning over hallucinated states from pretrained folding and inverse-folding models, with optional biophysical control within the same decision loop. MCTH treats these models as frozen black-box operators and uses Monte Carlo Tree Search to allocate a fixed inference budget across competing design trajectories, incorporating model confidence and uncertainty, as well as cross-expert consensus/disagreement when multiple predictors are available. Across protein-RNA, protein-DNA, protein-protein, and protein-ligand design, matched-budget experiments show that adaptive search improves over simpler sampling and cycling strategies, while held-out AlphaFold3 and Chai-1 evaluations demonstrate transfer beyond the search-time oracle. MCTH provides a shared planning layer across modalities while allowing task-specific folding, inverse-folding, and biophysical modules, requiring no fine-tuning or backpropagation through component models.

q-bio.QM↗

arXiv2026

Guaranteed Lower Eigenvalue Bounds for Spectral Galerkin Methods with Application to Schr\"odinger Operators

Spectral Galerkin methods are renowned for high-precision eigenvalue approximation, yet a rigorous lower bound obtained directly from a spectral discretisation has remained unavailable: the classical Kato and Weinstein--Temple enclosures do apply, but require a~priori information on a neighbouring eigenvalue. This paper resolves the issue by extending the author's projection-based framework for guaranteed lower eigenvalue bounds -- so far realised only through finite element methods -- to conforming spectral Galerkin methods. For trial spaces of exact eigenfunctions the required projection constant is the closed-form optimal value $C_N=\lambda_{M+1}^{-1/2}$, the inverse square root of the first omitted eigenvalue. For $-\Delta+V$ with $0\le V\in L^\infty$, a \emph{projection-gap estimate} yields an explicit constant for the standard Galerkin matrix (exact at $V=0$), and a composite discretisation removes the $||V||_{L^\infty}$-dependence for large potentials. With Neumann domain truncation these give certified two-sided bounds on $R^d$; for two benchmark potentials on $R^2$ the spectral enclosures match or surpass certified finite element ones at two orders of magnitude fewer degrees of freedom. The same auxiliary-projector mechanism extends to singular potentials with an unbounded $L^\infty$ norm -- in particular to attractive Coulomb singularities in three dimensions, via a localised Hardy inequality -- which we develop in a companion paper.

math.NA↗

arXiv2026

DL-SLAM: Enabling High-Fidelity Gaussian Splatting SLAM in Dynamic Environments based on Dual-Level Probability

Recent advances in 3D Gaussian Splatting (3DGS) have enabled significant progress in dense dynamic Simultaneous Localization And Mapping (SLAM). Prevailing methods typically discard predefined dynamic objects, ignoring that transiently static objects offer valuable geometric constraints for pose estimation. A recent work attempts to leverage this potential by employing per-pixel uncertainty maps to quantify the magnitude of motion. While this approach enables transiently static objects to enhance pose estimation, it erroneously integrates these objects into the static map, resulting in persistent artifacts. Moreover, its reliance on purely geometric information leads to ambiguous object boundaries in the uncertainty maps. To overcome these limitations, we present DL-SLAM, a monocular Gaussian Splatting SLAM system built upon a novel dual-level probabilistic framework. Our method computes dynamic probability maps by combining semantic and geometric information. These pixel-level probabilities are lifted to 3D and aggregated to derive an object-level dynamic probability for each instance. Object-level probability enables the categorical pruning of dynamic Gaussians, resulting in an artifact-free static map. The static map, in turn, provides a geometrically consistent guidance to refine the pixel-wise probabilities, enhancing their reliability. Experimental results demonstrate that DL-SLAM outperforms existing approaches, improving tracking accuracy by up to 13\% while generating high-fidelity semantic maps.

cs.RO↗

arXiv2026

Active-GRPO: Adaptive Imitation and Self-Improving Reasoning for Molecular Optimization

Scientific reasoning is an increasingly important capability of large language models, yet improving the robustness and efficiency of training such reasoning remains a key open challenge. We study this problem in instruction-based molecular optimization, where answer-only supervised fine-tuning (SFT) collapses multi-step reasoning and reinforcement learning with verifiable rewards (RLVR) suffers from sparse feedback. Reference-guided Policy Optimization mitigates both by anchoring policy updates to dataset-provided references, but its effectiveness is tightly coupled to reference quality: weak or misaligned references impose a performance ceiling. To overcome this ceiling, we propose active reasoning, a paradigm in which the policy actively decides, on a per-instance basis, when to imitate a reference and when to reinforce its own discoveries, while continuously upgrading what it imitates. We instantiate this paradigm as Active Group Relative Policy Optimization (Active-GRPO), realized through two coupled mechanisms: active imitate-reinforce and active referencing. The former performs imitation learning when the reference still outperforms the policy's own candidates, and shifts to self-improvement via reinforcement learning once the policy has generated molecules that surpass the reference. The latter continuously upgrades the reference itself by replacing it with the best policy-generated candidate discovered so far, progressively raising the imitation target and ensuring that reference guidance remains informative-rather than restrictive-throughout training. Across TOMG-Bench MOLOPT, Active-GRPO improves average SRxSim from 0.0959 for GRPO and 0.1665 for RePO to 0.1773 under matched three-seed evaluation, with statistically significant gains on LogP, MR, and QED.

cs.LG↗

arXiv2026

Protein Thoughts: Interpretable Reasoning with Tree of Thoughts and Embedding-Space Flow Matching for Protein-Protein Interaction Discovery

Protein-protein interactions (PPIs) govern nearly all cellular processes, yet computational methods for identifying binding partners typically produce ranked predictions without mechanistic justification. This creates a fundamental barrier to adoption because biologists cannot assess whether predictions reflect genuine biochemical insight or spurious correlations. We present \textbf{Protein Thoughts}, a framework that reformulates PPI discovery as an interpretable search problem with explicit reasoning. The system decomposes binding evidence into four biologically meaningful signals: sequence similarity reflecting evolutionary relationships, structural complementarity capturing geometric fit, interface balance, and chemical compatibility encoding residue-level interactions. Rather than collapsing these signals into an opaque score, we preserve their individual contributions through a transparent value function that enables both ranking and auditing. To navigate large candidate spaces efficiently, we introduce hypothesis-guided entropy-regularized Tree-of-Thoughts search. A fine-tuned language model generates search directives from embedding-derived features, classifying candidates as high-priority, exploratory, or skippable. These directives condition a Boltzmann policy that balances exploitation with entropy-driven exploration, while hypothesis-aware pruning prevents premature abandonment of promising candidates. For candidates exhibiting score disagreement, hypothesis-conditioned embedding-space flow matching transports protein embeddings toward the binder manifold. On the SHS148k benchmark, Protein Thoughts achieves mean best-binder rank of 11.2 versus 47.7 for an entropic tree search baseline, a 76% improvement, and for binding prediction the trained value function achieves $91.08 \pm 0.19$ Micro-F1, outperforming existing PPI methods on the same dataset.

q-bio.QM↗

arXiv2026

From Coordinate Matching to Structural Alignment: Rethinking Prototype Alignment in Heterogeneous Federated Learning

Heterogeneous federated learning (HtFL) aims to enable collaboration among clients that differ in both data distributions and model architectures. Prototype-based methods, which communicate class-level feature centers (prototypes) instead of full model parameters, have recently shown strong potential for HtFL. Existing prototype-based HtFL methods typically reuse the MSE-based or cosine-based alignment mechanism developed for homogeneous FL when aligning client-specific representations with global prototypes. These approaches are essentially coordinate alignment, where representations of clients are forced to match the global prototypes in the embedding space in an element-wise manner. Such alignment implicitly assumes that all clients should map their representations into the feature subspace defined by the global prototypes. This assumption is reasonable in homogeneous FL, where all clients share the same feature extractor. However, it becomes problematic in HtFL, since heterogeneous feature extractors naturally induce client-specific feature subspaces, and forcing all clients to optimize within a single global subspace unnecessarily suppresses their learning capacity. We observe that coordinate alignment implicitly couples two distinct objectives: aligning inter-class semantic structure, which is directly beneficial for classification, and enforcing a shared feature basis, which is unnecessary and even harmful under model heterogeneity. Building on this insight, we design FedSAF, which shifts the alignment objective from absolute coordinates to inter-class relational structure. We demonstrate that structural alignment consistently outperforms coordinate alignment in heterogeneous settings. Experiments on multiple benchmarks show that our structural alignment outperforms state-of-the-art prototype-based HtFL methods by up to 3.52\%.

cs.AI↗

arXiv2026

Explicit Two-Sided Eigenvalue Bounds for Schr\"odinger Operators with Singular Potentials via Finite Element Method

We present, to the best of our knowledge, the first numerical algorithm for explicit, computable two-sided eigenvalue bounds for Schr\"odinger operators H = -Delta + V on R^N, N = 2,3, in the presence of both an unbounded potential and an unbounded domain. "Explicit" here means that all constants and ingredients are derived in closed form from the mesh, the potential, and a small set of explicit inequalities (Payne-Weinberger, Hardy, and explicit bounded-domain Sobolev embeddings); the conversion to fully verified(IEEE-754-safe, interval-arithmetic) enclosures is a separate verification step and is left for future work. In particular, singular attractive potentials of Coulomb type, V(x) = -Z/|x|, which model the hydrogen atom and the H_2^+ molecular ion, are covered by the theory. The method combines domain truncation to a bounded domain D(R) containing {|x| <= R} with an extension of Liu's Composite Enriched Crouzeix-Raviart (CECR) finite element method to sign-indefinite potentials. Upper bounds come from the standard conforming Galerkin method; lower bounds come from the CECR construction, whose gap to the exact eigenvalue closes as the mesh is refined. Numerical experiments on the 2D single- and two-centred Coulomb potentials and on the 3D hydrogen atom and H_2^+ molecular ion illustrate the algorithm and confirm the predicted convergence.

math.NA↗

arXiv2026

Sharp Dirichlet eigenvalue inequalities on triangles

We prove sharp Dirichlet eigenvalue inequalities for planar triangles. We settle a conjecture of Laugesen and Siudeja by showing that the equilateral triangle uniquely minimizes a scale-invariant functional of the first Dirichlet eigenvalue, area, and perimeter. Consequences include an optimal two-term lower bound for the first Dirichlet eigenvalue in terms of area and perimeter. We also prove a Cheeger-type inequality with an explicit best constant considered by Parini. To prove these conjectures we propose a new method for proving Dirichlet eigenvalue inequalities on triangles. Our method is based on a new computable lower bound for second-order directional shape derivatives under vertex perturbations. It also uses validated finite-element error estimates and recently developed analytic estimates for eigenvalues of nearly degenerate triangles. The method is not specific to the functionals considered in this paper and it can be used to prove various other eigenvalue inequalities on triangles.

math.SP↗

arXiv2026

Rigorous Eigenvalue Bounds for Schr\"odinger Operators with Confining Potentials on $\mathbb{R}^2$

We propose a rigorous method for computing two-sided eigenvalue bounds of the Schr\"odinger operator $H=-\Delta+V$ with a confining potential on $\mathbb{R}^2$. The method combines domain truncation to a finite disk $D(R)$ on which the restricted eigenvalue problem is solved with a rigorous eigenvalue bound, where Liu's eigenvalue bound along with the Composite Enriched Crouzeix--Raviart (CECR) finite element method proposed plays a central role. Two concrete potentials are studied: the radially symmetric ring potential $V_1(x)=(|x|^2-1)^2$ and the Cartesian double-well $V_2(x)=(x_1^2-1)^2+x_2^2$. To author's knowledge, this paper reports the first rigorous eigenvalue bounds for Schr\"odinger operators on an unbounded domain.

math.NA↗

arXiv2026

Multi-Objective Coverage via Constraint Active Search

In this paper, we formulate the new multi-objective coverage (MOC) problem where our goal is to identify a small set of representative samples whose predicted outcomes broadly cover the feasible multi-objective space. This problem is of great importance in many critical real-world applications, e.g., drug discovery and materials design, as this representative set can be evaluated much faster than the whole feasible set, thus significantly accelerating the scientific discovery process. Existing works cannot be directly applied as they either focus on sample space coverage or multi-objective optimization that targets the Pareto front. However, chemically diverse samples often yield identical objective profiles, and safety constraints are usually defined on the objectives. To solve this MOC problem, we propose a novel search algorithm, MOC-CAS, which employs an upper confidence bound-based acquisition function to select optimistic samples guided by Gaussian process posterior predictions. For enabling efficient optimization, we develop a smoothed relaxation of the hard feasibility test and derive an approximate optimizer. Compared to the competitive baselines, we show that our MOC-CAS empirically achieves superior performances across large-scale protein-target datasets for SARS-CoV-2 and cancer, each assessed on five objectives derived from SMILES-based features.

cs.LG↗

arXiv2026

Learning to Optimize Job Shop Scheduling Under Structural Uncertainty

The Job-Shop Scheduling Problem (JSSP), under various forms of manufacturing uncertainty, has recently attracted considerable research attention. Most existing studies focus on parameter uncertainty, such as variable processing times, and typically adopt the actor-critic framework. In this paper, we explore a different but prevalent form of uncertainty in JSSP: structural uncertainty. Structural uncertainty arises when a job may follow one of several routing paths, and the selection is determined not by policy, but by situational factors (e.g., the quality of intermediate products) that cannot be known in advance. Existing methods struggle to address this challenge due to incorrect credit assignment: a high-quality action may be unfairly penalized if it is followed by a time-consuming path. To address this problem, we propose a novel method named UP-AAC. In contrast to conventional actor-critic methods, UP-AAC employs an asymmetric architecture. While its actor receives a standard stochastic state, the critic is crucially provided with a deterministic state reconstructed in hindsight. This design allows the critic to learn a more accurate value function, which in turn provides a lower-variance policy gradient to the actor, leading to more stable learning. In addition, we design an attention-based Uncertainty Perception Model (UPM) to enhance the actor's scheduling decisions. Extensive experiments demonstrate that our method outperforms existing approaches in reducing makespan on benchmark instances.

cs.LG↗

arXiv2026

Regime-Adaptive Bayesian Optimization via Dirichlet Process Mixtures of Gaussian Processes

Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications, including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design, demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.

cs.LG↗

arXiv2025

A Two-Stage Finite Element Approach for High-precision Guaranteed Lower Eigenvalue Bounds

Obtaining high-precision guaranteed lower eigenvalue bounds remains difficult, even though the standard high-order conforming finite element (FEM) easily yields extremely sharp upper bounds. Recently developed rigorous approaches using such as Crouzeix--Raviart or linear conforming elements do not extend well to high-order FEM. Some non-standard FEM approaches can provide sharp eigenvalue bounds but are technically involved. This persistent gap between accurate upper bounds and equally sharp rigorous lower bounds via standard high-order conforming FEMs makes the problem technically demanding and highly competitive. In this paper, we propose a new two-stage rigorous algorithm that closes this gap by employing high-order FEM on graded meshes and producing rigorous lower eigenvalue bounds as sharp as the corresponding high-order upper bounds, as demonstrated in our numerical examples. Numerical experiments for the Laplacian and Steklov eigenvalue problems on square and dumbbell domains show the accuracy and efficiency of the method, particularly on graded or highly nonuniform meshes. These results confirm that the proposed approach provides a practical and competitive solution to the long-standing difficulty of obtaining sharp, reliable lower eigenvalue bounds.

math.NA↗

arXiv2025

STED and Consistency Scoring: A Framework for Evaluating LLM Structured Output Reliability

Large Language Models (LLMs) are increasingly deployed for structured data generation, yet output consistency remains critical for production applications. We introduce a comprehensive framework for evaluating and improving consistency in LLM-generated structured outputs. Our approach combines: (1) STED (Semantic Tree Edit Distance), a novel similarity metric balancing semantic flexibility with structural strictness when comparing JSON outputs, and (2) a consistency scoring framework aggregating multiple STED measurements across repeated generations to quantify reliability. Through systematic experiments on synthetic datasets with controlled schema, expression, and semantic variations, we demonstrate STED achieves superior performance ($0.86-0.90$ similarity for semantic equivalents, $0.0$ for structural breaks) compared to existing metrics including TED, BERTScore, and DeepDiff. Applying our framework to benchmark six LLMs reveals significant variations: Claude-3.7-Sonnet demonstrates exceptional consistency, maintaining near-perfect structural reliability even at high temperatures ($T=0.9$), while models like Claude-3-Haiku and Nova-Pro exhibit substantial degradation requiring careful tuning. Our framework enables practical applications including targeted model selection for structured tasks, iterative prompt refinement for reproducible results, and diagnostic analysis to identify inconsistency root causes. This work provides theoretical foundations and practical tools for ensuring reliable structured output generation in LLM-based production systems.

cs.CL↗

arXiv2025

Can Federated Learning Safeguard Private Data in LLM Training? Vulnerabilities, Attacks, and Defense Evaluation

Fine-tuning large language models (LLMs) with local data is a widely adopted approach for organizations seeking to adapt LLMs to their specific domains. Given the shared characteristics in data across different organizations, the idea of collaboratively fine-tuning an LLM using data from multiple sources presents an appealing opportunity. However, organizations are often reluctant to share local data, making centralized fine-tuning impractical. Federated learning (FL), a privacy-preserving framework, enables clients to retain local data while sharing only model parameters for collaborative training, offering a potential solution. While fine-tuning LLMs on centralized datasets risks data leakage through next-token prediction, the iterative aggregation process in FL results in a global model that encapsulates generalized knowledge, which some believe protects client privacy. In this paper, however, we present contradictory findings through extensive experiments. We show that attackers can still extract training data from the global model, even using straightforward generation methods, with leakage increasing as the model size grows. Moreover, we introduce an enhanced attack strategy tailored to FL, which tracks global model updates during training to intensify privacy leakage. To mitigate these risks, we evaluate privacy-preserving techniques in FL, including differential privacy, regularization-constrained updates and adopting LLMs with safety alignment. Our results provide valuable insights and practical guidelines for reducing privacy risks when training LLMs with FL.

cs.LG↗

arXiv2025

Monte Carlo Tree Diffusion with Multiple Experts for Protein Design

The goal of protein design is to generate amino acid sequences that fold into functional structures with desired properties. Prior methods combining autoregressive language models with Monte Carlo Tree Search (MCTS) struggle with long-range dependencies and suffer from an impractically large search space. We propose MCTD-ME, Monte Carlo Tree Diffusion with Multiple Experts, which integrates masked diffusion models with tree search to enable multi-token planning and efficient exploration under the guidance of multiple experts. Unlike autoregressive planners, MCTD-ME uses biophysical-fidelity-enhanced diffusion denoising as the rollout engine, jointly revising multiple positions and scaling to large sequence spaces. It further leverages experts of varying capacities to enrich exploration, guided by a pLDDT-based masking schedule that targets low-confidence regions while preserving reliable residues. We propose a novel multi-expert selection rule ( PH-UCT-ME) extends Shannon-entropy-based UCT to expert ensembles with mutual information. MCTD-ME achieves superior performance on the CAMEO and PDB benchmarks, excelling in protein design tasks such as inverse folding, folding, and conditional design challenges like motif scaffolding on lead optimization tasks. Our framework is model-agnostic, plug-and-play, and extensible to denovo protein engineering and beyond.

cs.LG↗