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Yucheng Liu

Publications and source records attributed to Yucheng Liu.

At least 19 recordsLinked to original sources

Constructing stable Hilbert bundles via Diophantine approximation

On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian--Einstein metrics. Our main constructive step is by investigating the arithmetic property of the upper half plane in Bridgeland's definition of stability conditions and its homological countparts. The main analytic ingredient in our proof is a notion called a well-approximating sequence of stable bundles. This notion helps us to apply the Diophantine approximation to Donaldson's functional and bound the $L^\infty$ norm of Hermitian-Einstein metrics. We further study the continuous structures, smooth structures, and holomorphic structures on such Hilbert bundles. We hope that this construction can shed some new light on the geometric background of quantum field theory.

math.DG

Agentic ML Exploration (A-MLE) for Ads Ranking

Modern industrial ads ranking stacks are increasingly bottlenecked not by model capacity or training compute, but by the throughput of human ML iteration - the cycles of research, implementation, training, debugging, evaluation, and launch required to surface a single statistically significant improvement. A typical ranking stack contains numerous differentiated models with heterogeneous data, architectures, and infrastructure constraints, and each cycle takes days to weeks of senior engineer attention per model. As a result, techniques that have proven effective on one model diffuse into others slowly and unevenly, leaving substantial recoverable signal unexplored. We present Agentic ML Exploration (A-MLE), an autonomous LLM-agent system that systematically explores ML techniques across a portfolio of ads ranking models. A-MLE decomposes ML iteration into five stages involving hypothesis generation, exploration strategy, experiment execution, result analysis and shared knowledge substrate which are orchestrated by a single agent that invokes domain-specific skills and agentic workflows against a sandboxed execution layer, with human-in-the-loop checkpoints at each stage boundary. We deploy A-MLE across a representative set of large-scale ads ranking models and evaluate it along a tiered capability framework (tool availability, autonomous workflow execution, and open-ended exploration). We further report a controlled cross-LLM study using a fixed agent loop, which surfaces qualitative differences in execution reliability and exploration aggressiveness across the Claude Sonnet, Gemini, and GPT families. We discuss failure modes and the design choices that govern reliability. Our findings suggest that agentic exploration is a practical force multiplier for ML engineers in industrial recommenders, especially for the long tail of models that rarely receive expert attention.

cs.AI

A FEM-Based Surrogate Modelling and Optimization Framework for Physics-Constrained Electromagnetic Coil Design

This work evaluates surrogate-assisted optimization of a seven-parameter current-excited coil--core benchmark subject to geometric, manufacturing, and separate core and copper mass constraints. A Python--MPh--COMSOL workflow couples a two-dimensional axisymmetric finite-element method (FEM) model to a Matern 5/2 Gaussian-process (GP) probabilistic surrogate. Here, physics-constrained denotes a design problem evaluated by a governing-equation FEM model and restricted by explicit physical, geometric, manufacturing, and material-allocation constraints; it does not denote a physics-informed GP architecture. Sequential Bayesian optimization (BO) ranks candidates using expected improvement (EI), and every reported incumbent is verified by FEM. Five paired runs show that optimizer ranking depends on the available FEM-evaluation budget: EI--BO improves rapidly at small continuation budgets, COBYLA is stronger at the earliest checkpoint, and BOBYQA attains the highest mean terminal response. A retrospective finite-pool study further finds no robust endpoint advantage of EI over posterior-mean ranking on this smooth response surface. The broader result is that early progress, terminal response, information use, and wall-clock cost can favor different methods in simulation-driven design. A selected-design check at a common total current preserves the observed BOBYQA--COBYLA--EI-BO ordering. The conclusions nevertheless remain conditional on this axisymmetric benchmark and do not establish a fixed-current optimum, fixed-power performance, or electrical-efficiency superiority.

cs.LG

Continuum envelopes on Fargues-Fontaine curves and elliptic curves

In this paper, we apply the theory of Bridgeland stability conditions, which was motivated by ideas from string theory, to study the derived category of coherent sheaves on Fargues--Fontaine curves. This leads us to consider the quasi-coherent sheaves $\mathcal{O}(θ^{\pm})$ via the convergents of an irrational number $θ$. We define the continuum envelope $\mathrm{QCoh}_{\mathbb{R}}(X{FF})$ to be the smallest abelian subcategory of $\mathrm{QCoh}(X_{FF})$ containing $\mathrm{Coh}(X_{FF})$ and $\mathcal{O}(θ^{\pm})$. We study the homological algebra of $\mathrm{QCoh}_{\mathbb{R}}(X{FF})$ via Farey diagrams. We show that the homological properties of $\mathcal{O}(θ^{\pm})$ depend heavily on the Diophantine properties of $θ$. From this point of view, Fargues--Fontaine curves exhibit strong similarities to complex elliptic curves.

math.AG

Lehmer Codes and the Reverse-Complement Mapping from (32-1)-Avoiding Permutations to (3-21)-Avoiding Permutations

Let $S_n(32\text{-}1)$ and $S_n(3\text{-}21)$ denote the sets of $n$-permutations avoiding the vincular patterns $32\text{-}1$ and $3\text{-}21$, respectively. Using Lehmer codes, we realize these families as weighted posets $L_n(32\text{-}1)$ and $L_n(3\text{-}21)$, where the weight of a code is the inversion number of its permutation. We show that the maximal elements of each of these posets, $\operatorname{Max} L_n(32\text{-}1)$ and $\operatorname{Max} L_n(3\text{-}21)$, are enumerated by the Fibonacci numbers. We demonstrate that the classical reverse-complement map on permutations restricts to a natural bijection between these two sets of maximal elements, revealing a deep symmetry between their underlying poset structures.

math.CO

Modular variants of p-adic fundamental sequence

In this article, we relate any Farey triangle in the extended upper half-plane to a variant of Colmez--Fontaine's fundamental lemma in $p$-adic Hodge theory. In particular, their original fundamental lemma corresponds to the fundamental Farey triangle $(\frac{1}{0},\frac{1}{1},\frac{0}{1})$.

math.NT

LLM Retrieval for Stable and Predictable Ad Recommendations

Traditional ads recommendation systems have primarily focused on optimizing for prediction accuracy of click or conversion events using canonical metrics such as recall or normalized discounted cumulative gain (NDCG). With the hyper-growth of ads inventory and liquidity with generative AI technologies, the prediction stability and predictability is becoming increasingly critical. Intuitively, prediction stability and predictability can be defined to quantify system robustness with respect to minor/noisy input (ads, creatives) perturbations, the lack of which could lead to advertiser perceivable problems such as repeatability, cold start and under-exploration. In this paper, we introduce a new evaluation framework for quantifying stability and predictability of an ads recommender system, and present an online validated semantic candidate generation framework powered by fine-tuned Large Language Models (LLMs) that showed significant improvement along these metrics by fundamentally improving the semantic-awareness of the system. The approach extracts hierarchical semantic attributes from ad creatives to obtain LLM representations, which serve as the foundation for graph-based expansion, ensuring the retrieved candidates encapsulate semantic variants of an ad, guaranteeing that small creative variants from the advertiser yield consistent and explainable delivery results to the user. We tested this LLM ads retrieval framework in a large-scale industrial ads recommendation system, demonstrating significant improvements across offline and online A/B experiments, showcasing gains in both predictability and traditional performance metrics. Although evaluated in the ads stack, this is a general framework that can be applied broadly to any large-scale recommendation and retrieval systems facing similar scaling and predictability challenges.

cs.IR

Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation

The study of the Ornstein--Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossover from Ornstein--Zernike decay to critical power-law decay has received scant attention in the literature. We prove a general theorem which, under appropriate hypotheses, identifies the asymptotic behaviour of the solution to an Ornstein--Zernike equation on $\mathbb{Z}^d$ as that of the Green function for Brownian motion with drift, multiplied by an anisotropic exponentially decaying factor. The theorem applies to a wide class of random walks, to nearest-neighbour self-avoiding walk in dimensions $d \ge 5$, and to nearest-neighbour percolation in dimensions $d \ge 15$. Wide-ranging consequences follow, including details of the crossover from Ornstein--Zernike to critical decay on the scale of the correlation length, and the fact that all finite-order correlation lengths are equivalent up to universal constants. The proof is based on a variational characterisation of the direction-dependent rate of exponential decay and a major extension of Hara's 2008 Gaussian Lemma to noncentred kernels.

math.PR

Rethinking Model Selection in VLM Through the Lens of Gromov-Wasserstein Distance

Vision-Language Models (VLMs) have enhanced traditional LLMs with visual capabilities through the integration of vision encoders. While recent works have explored various combinations of vision encoders and LLMs, there still lacks a principled understanding of what makes a vision encoder suitable for VLM alignment. In this paper, we systematically investigate this question via comprehensive experiments on a curated collection of 19 pre-trained vision encoders from diverse sources. We first demonstrate that common practices, such as choosing encoders with the largest size or highest zero-shot accuracy, consistently fail to identify optimal models. In fact, these metrics show only weak to moderate correlation with VLM performance. This intriguing finding begs a fundamental question: What factors of vision-encoders matter in VLM? Through comprehensive analysis, we identify that the structural similarity across modalities plays a crucial but previously overlooked role in vision-encoder selection, which we measure using the Gromov-Wasserstein distance as a proxy. From a theoretical perspective, we show that the learnability of cross-modality mapping can be provably associated with the Gromov-Wasserstein distance. Empirical verification on 60+ full VLM training runs shows that our proposed inference-only metric performs significantly better than alternative model selection strategies and exhibits a much stronger correlation with final VLM performance, thereby enabling efficient and effective prediction of VLM performance before full training.

cs.CV

Decay of connection probability in high-dimensional continuum percolation

We study a percolation model on $\mathbb R^d$ called the random connection model. For $d$ large, we use the lace expansion to prove that the critical two-point connection probability decays like $|x|^{-(d-2)}$ as $|x| \to \infty$, with possible anisotropic decay. Our proof also applies to nearest-neighbour Bernoulli percolation on $\mathbb Z^d$ in $d \ge 11$ and simplifies considerably the proof given by Hara in 2008. The method is based on the recent deconvolution strategy of Liu and Slade and uses an $L^p$ version of Hara's induction argument.

math.PR

Graph-Based Meshfree Multi-scale Coarse Space Approximation for Two-Level Schwarz Methods

Efficient simulation of Darcy flow in highly heterogeneous porous media requires iterative solvers that remain robust under large permeability contrasts and mixed boundary conditions. Spectral coarse spaces in two-level overlapping Schwarz methods provide such robustness, but their practical use is often limited by an expensive setup phase dominated by many local generalized eigenvalue solves. We propose a purely algebraic, coarse-space approximation that avoids these repeated local eigensolves by using a graph neural network operating on the system-matrix graph. On the analysis side, we introduce a coefficient-weighted subspace-distance measure to quantify the discrepancy between the approximated and target local multiscale coarse spaces, and we derive a condition-number bound for the resulting preconditioned operator in terms of this distance. This bound yields a principled supervised-training objective and links learning error to solver performance. Numerical experiments on 2D and 3D high-contrast Darcy systems with varying mixed boundary conditions demonstrate that the proposed approach substantially reduces setup cost and improves end-to-end time-to-solution, while preserving robust convergence across the tested contrasts and boundary configurations.

math.NA

Universal finite-size scaling in high-dimensional critical phenomena

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results for linear and branched polymers, multi-component spin systems, and percolation. Both short-range and long-range interactions are included. The universal finite-size scaling is inherited from the scaling of the system unwrapped to the infinite lattice. We also present conjectures for universal scaling profiles for the susceptibility and two-point function plateau in a critical window. For free boundary conditions, the universal scaling has been proven to apply at a pseudocritical point for hierarchical spins, and we conjecture that this holds generally.

cond-mat.stat-mech

High-dimensional long-range statistical mechanical models have random walk correlation functions

We consider long-range percolation, Ising model, and self-avoiding walk on $\mathbb{Z}^d$, with couplings decaying like $|x|^{-(d+α)}$ where $0 < α\le 2$, above the upper critical dimensions. In the spread-out setting where the lace expansion applies, we show that the two-point function for each of these models exactly coincides with a random walk two-point function, up to a constant prefactor. Using this, for $0<α< 2$, we prove upper and lower bounds of the form $|x|^{-(d-α)} \min\{ 1, (p_c - p)^{-2} |x|^{-2α} \}$ for the two-point function near the critical point $p_c$. For $α=2$, we obtain a similar upper bound with logarithmic corrections. We also give a simple proof of the convergence of the lace expansion, assuming diagrammatic estimates.

math.PR

A general approach to massive upper bound for two-point function with application to self-avoiding walk torus plateau

We prove a sufficient condition for the two-point function of a statistical mechanical model on $\mathbb{Z}^d$, $d > 2$, to be bounded uniformly near a critical point by $|x|^{-(d-2)} \exp [ -c|x| / ξ]$, where $ξ$ is the correlation length. The condition is given in terms of a convolution equation satisfied by the two-point function, and we verify the condition for strictly self-avoiding walk in dimensions $d > 4$ using the lace expansion. As an example application, we use the uniform bound to study the self-avoiding walk on a $d$-dimensional discrete torus with $d > 4$, proving a ``plateau'' of the torus two-point function, a result previously obtained for weakly self-avoiding walk in dimensions $d > 4$ by Slade. Our method has the potential to be applied to other statistical mechanical models on $\mathbb{Z}^d$ or on the torus.

math.PR

Critical scaling profile for trees and connected subgraphs on the complete graph

We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a critical window. Our motivation comes from the analysis of the finite-size scaling of lattice trees and lattice animals on a high-dimensional discrete torus, for which we conjecture that the identical profile applies in dimensions $d \ge 8$.

math.PR

Computation and Communication Efficient Lightweighting Vertical Federated Learning for Smart Building IoT

With the increasing number and enhanced capabilities of IoT devices in smart buildings, these devices are evolving beyond basic data collection and control to actively participate in deep learning tasks. Federated Learning (FL), as a decentralized learning paradigm, is well-suited for such scenarios. However, the limited computational and communication resources of IoT devices present significant challenges. While existing research has extensively explored efficiency improvements in Horizontal FL, these techniques cannot be directly applied to Vertical FL due to fundamental differences in data partitioning and model structure. To address this gap, we propose a Lightweight Vertical Federated Learning (LVFL) framework that jointly optimizes computational and communication efficiency. Our approach introduces two distinct lightweighting strategies: one for reducing the complexity of the feature model to improve local computation, and another for compressing feature embeddings to reduce communication overhead. Furthermore, we derive a convergence bound for the proposed LVFL algorithm that explicitly incorporates both computation and communication lightweighting ratios. Experimental results on an image classification task demonstrate that LVFL effectively mitigates resource demands while maintaining competitive learning performance.

cs.LG

Passive Underwater Acoustic Signal Separation based on Feature Decoupling Dual-path Network

Signal separation in the passive underwater acoustic domain has heavily relied on deep learning techniques to isolate ship radiated noise. However, the separation networks commonly used in this domain stem from speech separation applications and may not fully consider the unique aspects of underwater acoustics beforehand, such as the influence of different propagation media, signal frequencies and modulation characteristics. This oversight highlights the need for tailored approaches that account for the specific characteristics of underwater sound propagation. This study introduces a novel temporal network designed to separate ship radiated noise by employing a dual-path model and a feature decoupling approach. The mixed signals' features are transformed into a space where they exhibit greater independence, with each dimension's significance decoupled. Subsequently, a fusion of local and global attention mechanisms is employed in the separation layer. Extensive comparisons showcase the effectiveness of this method when compared to other prevalent network models, as evidenced by its performance in the ShipsEar and DeepShip datasets.

cs.SD

The torus plateau for the high-dimensional Ising model

We consider the Ising model on a $d$-dimensional discrete torus of volume $r^d$, in dimensions $d>4$ and for large $r$, in the vicinity of the infinite-volume critical point $β_c$. We prove that for $β=β_c- {\rm const}\, r^{-d/2}$ (with a suitable constant) the susceptibility is bounded above and below by multiples of $r^{d/2}$. Additionally, again for $β=β_c- {\rm const}\, r^{-d/2}$, the two-point function has a ``plateau'': it decays like $|x|^{-(d-2)}$ when $|x|$ is small relative to the volume, but for larger $|x|$, it levels off to a constant value of order $r^{-d/2}$. We also prove that at $β=β_c- {\rm const}\, r^{-d/2}$ the renormalised coupling constant is nonzero, which implies a non-Gaussian limit for the average spin. The proof relies on near-critical estimates for the infinite-volume two-point function obtained recently by Duminil-Copin and Panis, and builds upon a strategy proposed by Papathanakos. The random current representation of the Ising model plays a central role in our analysis.

math-ph