arXiv subjects

Jia Liu

Publications and source records attributed to Jia Liu.

At least 19 recordsLinked to original sources

arXiv2026

The Assouad Dimension of Graphs: An Affirmative Answer to Fraser's Question

This article primarily investigates the Assouad dimension of graphs of continuous functions. Initially, the Assouad spectrum of the graph of a Hölder and count-Hölder continuous function has been derived. It has been shown that the Assouad dimension of the graph of a continuous function $f:[a,b]\to \mathbb{R}$ with the count-Hölder condition is at least $ 1 + \sup \left\{ \overline{\dim}_{\mathrm{B}}L_f(y) : y \in \mathscr{R}_f[a,b]\right\} $ where $\overline{\dim}_{\mathrm{B}}$ denotes the upper box dimension, $L_f(y)$ is the level set of $f$ at level $y$, and $\mathscr{R}_f[a,b]$ is the range of $f$ on $[a,b]$. As a consequence, non-trivial lower bounds are obtained for the Assouad dimension of the graphs of classical functions such as the Weierstrass and Takagi functions. We have also employed a unified projection solely in the direction of the $y$-axis to establish lower and upper bounds for the Assouad dimension. On this basis, we have shown that the lower bound is sharp in terms of level sets, namely the upper box dimension cannot be replaced by the Assouad dimension. This provides a partial positive answer to Question 17.11.1 posed by Fraser in~\cite{Fraser2021}, and to Question 2.2 posed by Yu in~\cite{Yu2020}. Building on this result, the analysis has been further extended to a broader class of Weierstrass-type functions and some self-affine functions like fractal interpolation functions. Moreover, we have discussed certain circumstances under which the Assouad dimension can reach 2 with several examples constructed. A supplementary explanation of why Brownian motion has the full Assouad dimension has also been provided based on the preceding work of Howroyd and Yu \cite{Howroyd2019}.

math.DS↗

arXiv2026

Democratizing LLM Training with the Edge: Challenges, Systems, and the Road Ahead

The growing computational power of modern GPU data centers has let a few industrial giants train and deploy large language models (LLMs) on massive amounts of data. Yet the sheer scale of these models and their training data makes centralized development increasingly hard to sustain, and at the same time shuts out smaller institutions that hold relevant private data but lack comparable infrastructure. In this paper, we organize our positions on distributed LLM training around the pretraining and fine-tuning paradigms, covering federated learning, split learning, and decentralized approaches, and we assess their readiness for geo-distributed settings with heterogeneous hardware and unreliable connectivity. We then present a {\em unified} system architecture built around a cloud-hosted parameter server that coordinates heterogeneous clients over outbound gRPC connections, reusing one communication, compression, and fault-tolerance stack for both pretraining and a family of fine-tuning methods. We validate the design with real geo-distributed experiments on GPT-2 Medium and Llama3-1B pretraining across multiple university sites, showing stable convergence under realistic conditions. Finally, we chart the road ahead, identifying open problems that span frontier model support, elastic fault tolerance, adaptive compression, federated alignment, privacy and trust, incentive design, and system--algorithm co-design, all of which must be addressed to make democratized LLM training a reality.

cs.DC↗

arXiv2026

Proper generalized decomposition with synthetic preconditioning for multiscale parametric phonon transport

Deterministic solution of the phonon Boltzmann transport equation is costly for two reasons: the distribution depends on high-dimensional phase space, and source iteration converges slowly when scattering is frequent. We address both for the steady linearized gray Callaway model in two dimensions by combining proper generalized decomposition (PGD) with the general synthetic iterative scheme (GSIS). The distribution is a sum of products of a space--azimuth factor and a polar factor. This splitting is intrinsically low-rank: along each characteristic the polar angle only stretches the in-plane optical depth, so the rank is bounded, uniformly in the Knudsen numbers, by the numerical rank of the kernel $\exp(-τ/\sinϕ)$. PGD--GSIS updates the factors against a macroscopic source frozen within each alternating step and refreshed by the GSIS moment equations. A Fourier analysis shows that pure PGD, although implicit in the polar factor, moves macroscopic information only through lagged spatial sweeps and stalls like source iteration, whereas the synthetic refresh sees only third-order moments of the representation error. On an isothermal cavity, cross-plane conduction and phonon Poiseuille flow, PGD--GSIS reproduces full-order solutions at ranks 3--14, with heat-flux errors below $6\times10^{-3}$ from the diffusive to the ballistic regime and memory independent of the polar resolution. Treating the inverse Knudsen numbers as coordinates of the polar factor yields one spatial basis over four decades of both; a joint update of all polar factors, which costs only small nodal linear systems, is required for accuracy at large Knudsen numbers.

physics.comp-ph↗

arXiv2026

SPRINT: Stochastic Performative Prediction With Variance Reduction

Performative prediction (PP) is an algorithmic framework for optimizing machine learning (ML) models where the model's deployment affects the distribution of the data it is trained on. Compared to traditional ML with fixed data, designing algorithms in PP converging to a stable point -- known as a stationary performative stable (SPS) solution -- is more challenging than the counterpart in conventional ML tasks due to the model-induced distribution shifts. While considerable efforts have been made to find SPS solutions using methods such as repeated gradient descent (RGD) and greedy stochastic gradient descent (SGD-GD), most prior studies assumed a strongly convex loss until a recent work established $O(1/\sqrt{T})$ convergence of SGD-GD to SPS solutions under smooth, non-convex losses. However, this latest progress is still based on the restricted bounded variance assumption in stochastic gradient estimates and yields convergence bounds with a non-vanishing error neighborhood that scales with the variance. This limitation motivates us to improve convergence rates and reduce error in stochastic optimization for PP, particularly in non-convex settings. Thus, we propose a new algorithm called stochastic performative prediction with variance reduction (SPRINT) and establish its convergence to an SPS solution at a rate of $O(1/T)$. Notably, the resulting error neighborhood is independent of the variance of the stochastic gradients. Experiments on multiple real datasets with non-convex models demonstrate that SPRINT outperforms SGD-GD in both convergence rate and stability.

cs.LG↗

arXiv2026

When Code Becomes an LLM Call: An Empirical Study of Call-Site Contracts in Agentic Systems

Software quality has long rested on specifications that state what code must do, and on testing and verification that check that the code does it. Agentic systems change this foundation: they replace parts of their logic, such as choosing the next tool, judging whether an action is allowed, or writing code to run, with calls to a large language model (LLM). The program still relies on what this logic must guarantee, but the model's behavior is not fixed by code, varies across runs, and can be steered by its input. The guarantee must therefore come from the program around each LLM call site, as a contract of pre-conditions, prompt constraints, and post-conditions. We present an empirical study of these contracts in 496 LLM call sites of 40 popular open-source agentic systems (13.4 MLOC, four languages). Using a multi-agent pipeline validated by 17,428 human judgments, we trace where every model output flows, derive an expected contract for each call site without access to its code, and compare it with the contract that the code implements. We find that 48% of LLM outputs reach control flow or execution, and 73% of these never reach a person. Programs enforce 78% of their constraints in code, but in the prompt, 67% of the constraints are only requested from the model. Although 82% of call sites are checked before and after the call, 63% of the expected constraints are unmet and only 5.3% of call sites satisfy their whole contract; ten recurring patterns explain 99% of the gaps. 38 mechanisms behind these gaps trigger at runtime, and a small code fix that enforces the expected constraint stops all 38. Our results show that the presence of checks says little about their adequacy, and we derive implications for agent developers, framework maintainers, and researchers.

cs.SE↗

arXiv2026

Selective spatiotemporal mode-locking in multimode Mamyshev oscillators

Spatiotemporal mode-locking (STML) in multimode fibers introduces spatial degrees of freedom for ultrashort pulse generation, yet flexible manipulation of transverse mode compositions within multimode solitons remains challenging. Here, we propose a spectrum-to-mode mapping strategy in multimode Mamyshev oscillators (MOs) to selectively synchronize specific transverse modes through synergistic cross-phase modulation and offset spectral filtering. Meanwhile, four-wave mixing acts to stabilize intermodal phase relationships, facilitating selective STML characterized by diverse mode compositions with matched group velocities. Spatiotemporal solitons containing the pure LP01 mode, degenerate LP11 modes, or LP02+LP21 composite modes are selectively realized and mapped across the parameter space spanned by intracavity gain and filter detuning. Furthermore, intracavity collisions between coexisting mode groups with disparate group velocities are demonstrated to enable dynamic mode selection. Beyond the simulation of six modes in graded-index multimode fibers, selective STML is also demonstrated in MOs based on step-index multimode fibers and fibers supporting more transverse modes, confirming the generality of our approach. This strategy offers a versatile and robust pathway for transverse mode regulation and provides new insights into full dimensional structured light manipulation in multimode ultrafast fiber lasers.

physics.optics↗

arXiv2026

Multi-flux Aharonov-Bohm caging with tunable couplings

Aharonov-Bohm (AB) caging is the complete wavefunction localization effect in translational-invariant lattices induced by destructive phase interference. These phases originate from the gauge fields such as the penetrated magnetic fields, which are directly related to several novel topological quantum states of matter. Recently, this effect has shown significant potential for applications in quantum simulation and topological quantum computation. Here, we propose a scalable protocol to derive universal conditions for AB caging with multi-flux. The numerical simulations validate the theoretical predictions by directly observing AB caging phenomena. We also investigate the breakage of the caging effect with onsite detuning, decoherence and non-Hermitian transitions. Our protocol provides an alternative approach for advancing quantum simulation of exotic states of matter.

quant-ph↗

arXiv2026

Parallelizable Gradient-Based Optimization For Multi-Objective MaxCut

Multi-objective combinatorial optimization arises in a wide range of problems and applications, including the canonical multi-objective MaxCut problem. Differentiable single-instance quadratic methods have recently achieved remarkable performance in single-objective combinatorial optimization. In this paper, we develop a differentiable framework for multi-objective MaxCut by combining an adjacency-based quadratic formulation with linear scalarization, thereby reducing the problem to a preference-conditioned single-objective signed-weight MaxCut problem. Theoretically, we characterize projected gradient ascent (PGA) fixed points and their local dynamics under the signed-weight adjacency formulation. We further characterize how these fixed points depend on preferences and establish their connection to Pareto optimality. Computationally, unlike conventional heuristics and branch-and-bound methods, our approach is GPU-parallelizable and can therefore benefit from substantial performance speedups. We term our algorithm Multi-objective QUadratic Combinatorial Optimization (MO-QUCO) and its parallelized variant pMO-QUCO. Empirically, we evaluate our methods on multi-layered graphs with different sizes and edge-weight distributions. Both our CPU-only and GPU-based algorithms outperform state-of-the-art exact and heuristic methods in terms of wall-clock runtime and objective quality. Despite operating under different computational settings, MO-QUCO also outperforms the SOTA quantum method.

cs.DM↗

arXiv2026

Beyond Type-checking: Towards Holistic Evaluation of Formal Specification Generation

When generating verifiable code, natural language requirements are mapped to machine checked code using LLMs and agentic workflows. A crucial component of this pipeline is specification generation (SpecGen), which produces a formal contract against which an agent can prove implementation correctness. Proof generation can obtain deterministic feedback from a theorem prover, but SpecGen lacks a definitive check that a generated specification captures the user's intent. A checked proof can therefore establish correctness against a specification that misrepresents the intended behaviour. We take a step towards holistic SpecGen evaluation with a unified dataset assembled from $350$ existing Lean tasks, including $189$ from VERINA and $161$ from CLEVER, and a framework covering formal validity, reference similarity and equivalence, and behavioural adequacy. We distinguish acceptance of required inputs from acceptance of valid outputs and rejection of invalid outputs, while making each metric's evidence scope explicit. Across four SpecGen configurations, restricting the generalized tree edit distance (GTED) comparison, a reference similarity measure, to $32$ jointly measurable VERINA tasks changes the VERINA configuration's position from second to fourth in mean similarity, showing the importance of measurement coverage. In an authored control, a specification achieves $100\%$ positive test recall and negative test rejection while accepting $0\%$ of required inputs. This demonstrates that perfect postcondition scores can miss an unusable input contract, motivating separate feedback on input coverage and output constraints.

cs.SE↗

arXiv2026

Foundation Model-Aided Multi-Agent Reinforcement Learning for Wireless Random Access Network Optimization

Random access (RA) is one of the most foundational medium access control (MAC) layer scheduling schemes for handling unpredictable data traffic from multiple terminals. While multi-agent reinforcement learning (MARL) has been explored to optimize RA-based wireless networks, its reliance on experience-driven, distributed policy learning incurs significant training overhead for each optimization task, limiting its feasibility in real-world applications. In this work, we propose to leverage a foundation model (FM) to improve MARL efficiency across diverse RA network optimization tasks. Specifically, we design an FM-aided actor-critic algorithm within a consensus-based decentralized MARL architecture and provide its convergence analysis under local reward exchanges and nonlinear value function approximations to show that our algorithm achieves the same convergence order as the conventional MARL with critic model exchanges and linear approximations. Our numerical results show that our FM-based approach significantly enhances MARL speed for RA network optimization.

cs.LG↗

arXiv2026

Towards One-for-All Foundation Model for Attributed Graph Clustering

Attributed graph clustering aims to discover node groups by jointly exploiting node attributes and graph topology, yet its unsupervised nature makes model selection and adaptation inherently difficult. Existing methods typically train and tune a separate model for each input graph, leading to costly and fragile pipelines that often fail to transfer across graphs with different feature spaces, structural patterns, and attribute-structure correlations. In this paper, we study a one-for-all alternative: can a single model be trained once and directly applied to diverse attributed graphs without graph-specific training, fine-tuning, or hyperparameter search? We propose OFAG, a foundation model for attributed graph clustering. Building upon Prior-data Fitted Networks, OFAG learns a reusable clustering inference strategy from synthetic attributed graphs generated under broad priors over latent clusters, node attributes, and graph structures. To handle incompatible feature spaces across graphs, OFAG adopts a dimension-agnostic signal-wise graph encoder that treats each feature channel as a graph signal and models its response to shared graph filters. The model is trained with a hyperspherical clustering objective, producing clustering-friendly node representations in a single forward pass at inference time. On ten datasets, one frozen OFAG model achieves the best mean performance and average rank across NMI, ACC, ARI, and F1, while completing all ten datasets in 12.43 minutes total---over 6* faster than the second-fastest baseline and nearly 28* faster than the second-best on clustering quality. Our code and pretrained checkpoint are available at https://github.com/Cloudy1225/OFAG, allowing practitioners to directly apply OFAG to their own attributed graph datasets without additional training or tuning.

cs.LG↗

arXiv2026

Probing anomalous $Wtb$ couplings through $bW$ spin correlations in top-quark pair production at the HL-LHC

We propose a spin-density-matrix framework for probing anomalous $Wtb$ interactions in top-quark pair production by exploiting the polarizations of the $b$ quark and the $W$ boson and their spin correlations. The $b$-quark spin is analyzed through angular distributions in semileptonic $Λ_b$ decay following fragmentation, while the leptonic $W$ decay serves as a $W$-polarization analyzer. We derive the $bW$ spin density matrix in the presence of anomalous $Wtb$ couplings and show that its polarization and spin-correlation parameters provide linear sensitivity to these couplings. We construct experimentally accessible angular observables associated with these parameters and evaluate their statistical sensitivities. For the HL-LHC at $\sqrt{s}=14~ \mathrm{TeV}$ with an integrated luminosity of $3000~ \mathrm{fb}^{-1}$, the proposed method yields improved constraints on most anomalous $W t b$ couplings, with the sensitivity to $V_R$ enhanced by a factor of 8 and that to $g_L$ by a factor of about 6.

hep-ph↗

arXiv2026

PMF-CL: Pareto-Minimal-Forgetting Continual Learner for Conflicting Tasks

In the literature, many continual learning (CL) algorithms have been proposed to address the issue of catastrophic forgetting in ML models (i.e., learning new tasks leads to the loss of performance on previously learned tasks). Although all CL approaches use some form of memory to retain information about past tasks, a grounded understanding of what information needs to be stored to minimize catastrophic forgetting remains elusive. Recently, it has been recognized that under the strong assumption of the existence of a common global minimizer over all tasks, catastrophic forgetting can be completely avoided. However, in practice, tasks rarely have a common global minimizer, and a certain amount of forgetting is inevitable. In this paper, we propose a foundational reframing of CL as balancing conflicting tasks in hindsight from a multi-task learning (MTL) perspective. The approach is based on finding Pareto-optimal solutions, i.e., the solutions which, by definition, minimally forget the previous tasks in the Pareto sense. We derive a Pareto-minimal-forgetting CL (PMF-CL) algorithm for linear and basis-function regression. Our algorithm naturally extends to loss functions with quadratic upper bounds around their minimizers, despite consuming only a static memory footprint of $O(d^2)$ for $d$ model parameters, independent of the number of sequentially occurring tasks $T$. In the quadratic-loss setting, we obtain exact hindsight Pareto-optimal guarantees on forgetting. In the quadratic-upper-bound setting, forgetting is provably bounded, with the tightness of the forgetting bound being directly determined by the tightness of the quadratic bound on the loss function. Our numerical results validate our theoretical claims of convergence to the Pareto-optimal solution, and demonstrate that we consistently out-perform prior empirical methods while occupying lesser memory.

cs.LG↗

arXiv2026

Who Owns That? Evaluating Ownership Intuitions in Large Language Models

Ownership establishes rights over the use, control, and transfer of objects. Understanding these relations is essential for AI systems to interact appropriately with people and their resources. Yet how large language models (LLMs) attribute ownership under competing claims remains unclear. We introduce the Competing Ownership Attribution Task (COAT), comprising 42 scenarios, and compare ownership allocations from 24 LLM configurations with those of 108 human participants. Overall, human-model similarity is close to human-human similarity, but models show greater homogeneity in their ownership judgments. Within individual answers, models also divide ownership more evenly among claimants than humans do. Pooling responses across model configurations reveals more scenarios with a shared judgment and fewer with distinct viewpoint groups than in humans. When humans form distinct groups, models may converge on one viewpoint or between competing viewpoints. Further comparisons reveal different contextual sensitivities. As material value increases across scenarios, allocations to creators decline less sharply in models than in humans. Across scenarios differing in public recognition of later holders as owners, allocations to these holders increase in models but decrease slightly in humans. Together, these findings suggest that the evaluated LLM responses do not fully capture the diversity of participants' ownership judgments or how those judgments vary across situations. Developing socially capable AI therefore requires moving beyond overall similarity to capture the diversity and context dependence of human judgments.

cs.AI↗

arXiv2026

Do Motion Tokenizers for Co-Speech Gesture Generation Encode Gesture Semantics?

Discrete motion tokenizers encode motion as atomic units and are widely used for co-speech gesture generation. It remains unclear which motion properties, especially those relevant to gesture semantics, are recoverable from these codebooks. We probe a reconstruction-trained codebook using 19 co-speech gesture descriptors spanning from raw motion to abstract communicative function. Results show that geometry and handedness are readily decodable from token embeddings, while motion category is only weakly decoded despite showing systematic differences in discrete code usage. This gap between reconstruction quality and descriptor decodability suggests that reconstruction objectives alone do not guarantee that gesture semantics are captured, and that evaluating codebooks on such properties can guide the design of more semantic motion tokenizers.

cs.CV↗

arXiv2026

DEALS: Decentralized Expertise-Aware Load Serving for Multi-Agent LLM Systems

Multi-agent systems (MAS) have recently emerged as an effective approach for coordinating large language model (LLM)-based agents to solve complex tasks through structured interactions. In practice, MASs often handle a stream of heterogeneous and complex tasks, requiring agents to decompose each task and then self-organize and self-evolve to adapt to incoming tasks while sharing execution resources. However, most early approaches to MASs rely on centralized controllers or fixed coordination patterns, which can limit scalability or adaptability. In contrast, existing decentralized and dynamic MASs often require training dedicated routers or invoking LLMs for agent selection, resulting in substantial computational costs and coordination overhead. To address these challenges and enable efficient task-level self-organization and self-evolution for task- and workload-level collaboration, we propose Decentralized Expertise-Aware Load Serving (DEALS), a decentralized and low-complexity framework that enables agents to self-organize and dynamically route concurrent tasks for processing. Specifically, each agent maintains local queues of incoming tasks, and its router decides whether to process a task locally or forward it to a neighbor based on differences in backlog and success rate. Meanwhile, executors process independent tasks concurrently within and across agents, and partially solved tasks can be resumed by other agents. Experiments show that DEALS not only improves performance along multiple dimensions (e.g., answer accuracy and task throughput) in both homogeneous and heterogeneous agent pools, but also balances agent expertise and workload in a self-organized manner, enabling effective decentralized coordination.

cs.LG↗

arXiv2026

Relative Mismatch: Local-Reference Calibration of Feature-Space Flows for Anomalous Sound Detection

Anomalous sound detection (ASD) has long been dominated by k-nearest-neighbor (KNN) based detectors, which essentially perform implicit likelihood estimation over normal samples. In this work, we investigate whether generative models can better serve this role. We propose Relative Mismatch, a generative ASD backend powered by flow matching, which learns a velocity field that transports Gaussian noise to a representative feature space of normality. During inference, it measures the mismatch between the oracle and predicted path velocities and aggregates them through a two-level design. To mitigate the inherent mismatch offsets incurred by domain shift, each query is further calibrated with the mismatch of its local normal reference, thereby exposing only its deviation beyond normality. Extensive experiments on DCASE 2020--2025 demonstrate that Relative Mismatch outperforms state-of-the-art backends with the highest score of 71.01, along with strong robustness and training stability. Furthermore, we show that curating a compact and discriminative feature space is the key to unleash the power of generative models for ASD.

cs.SD↗

arXiv2026

To Solve Bilevel Optimization with Nonconvex Lower Levels, We Need Second-Order Stationarity

Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.e., the lower-level objective function is assumed to be, at least, convex). While the LLSC/LLGC assumptions render more tractable algorithmic design and theoretical analysis, they are too rigid to encompass many machine learning problems in practice. The limitations of LLSC/LLGC assumptions in BLO motivate us to investigate solving the BLO problem in the general lower-level nonconvex (LLNC) settings, which remains in its infancy. In the literature on LLNC-BLO, most of the existing works either require additional structures in the lower-level objective function for tractable theoretical analysis, or adopt the first-order stationarity reformulation as a lower-level surrogate problem, which is inherited from the LLSC/LLGC settings but could lose their effectiveness in the LLNC setting. To bridge this gap, we propose to reformulate the nonconvex lower-level problem using a second-order stationarity-based surrogate, the solution of which guarantees a local optimal solution at the lower level. Based on this reformulation, we propose the PROBE (Perturbed gradient algorithm for bilevel problem) and show that it overcomes the limitations of prior works by probing and escaping lower-level saddle points. We prove that PROBE achieves a finite-time convergence rate of $O(T^{-2/5})$, where T denotes iterations. To our knowledge, this work is the first to establish the finite-time convergence for achieving lower-level second-order stationary solutions in general LLNC-BLO. Our experiments on both a large language model-based data curation task and a meta-learning task also show that PROBE outperforms SOTA methods.

cs.LG↗