arXiv subjects
Publications and source records attributed to Yipeng Zhang.
We prove that if the unit sphere of a separable infinite-dimensional real Banach space embeds uniformly into a Hilbert space, then the Banach space has Kasparov--Yu's Property (H).
Clinicians and neuroscientists have long analyzed intracranial electroencephalography (iEEG) through directly measurable physiological characteristics, which carry much of the information that downstream tasks depend on. Recent iEEG foundation models learn by reconstructing or predicting their inputs, which leaves the retention of these characteristics implicit. They are also evaluated mainly on cognitive decoding and a narrow clinical task, i.e., seizure detection. On a broad, clinically relevant benchmark such as Omni-iEEG, they remain below task-specific models when used frozen. We introduce PHASE, a physiology-guided foundation model that makes these characteristics explicit learning targets, pairing them with masked latent prediction in a temporal stage (PHASE-T) within each channel and a spatiotemporal stage (PHASE-ST) across synchronized channels. PHASE is pretrained on heterogeneous recordings from 222 participants at nine clinical sites. On all five Omni-iEEG clinical tasks, frozen PHASE-T outperforms every evaluated foundation model by up to 31\%, and fine-tuned PHASE-T surpasses the task-specific models, setting a new state of the art. PHASE-T benefits from physiological supervision, outperforming variants trained with latent prediction alone or auxiliary waveform reconstruction on every task in matched ablations. PHASE-T generalizes to unseen institutions, outperforming the compared models with few or no local labels. PHASE-ST further improves seizure-onset-zone identification over PHASE-T and, when frozen, decodes sound volume and pitch on BrainTreebank better than published models. Beyond task performance, PHASE learns to encapsulate the physiological characteristics clinicians recognize, from seizure onset and its propagation to anatomical region identity, even though its pretraining contains no ictal recordings or anatomical labels.
Multimodal intracranial EEG (iEEG) research for epilepsy surgery combines anatomical and functional imaging, implanted electrode locations, interictal biomarkers, and functional mapping--outputs produced by different applications and reconciled by hand before they can be viewed on the same anatomy. Omni-iEEG Planner is an open-source Python platform that brings these inputs into one patient coordinate frame for research data analysis. The workflow starts from the preoperative T1-weighted MRI, from which FreeSurfer provides the cortical surface and anatomical labels; CT, PET and diffusion MRI are then co-registered to that reference, electrode contacts are detected automatically on the postimplantation CT and reviewed by the analyst, and tractography is reconstructed within the application. Channel-indexed results computed outside the platform, such as high-frequency oscillation counts from pyHFO or time-resolved gamma responses, are projected onto the contacts and the cortical surface with their source units preserved, and interictal and functional evidence remain separate layers. We describe the design and demonstrate representative workflows on de-identified patient data. The platform is not proposed as a method for every laboratory; it is a worked example of how one research group combined multimodal integration with an AI-assisted iEEG analysis tool, pyHFO, in a single open environment that others can adapt to their own pipelines. The design will accommodate further evidence types--model-derived contact scores, virtual implantation and hypothetical resection studies, group-level analyses--as they are implemented. The software is released under the MIT license for research and educational use, not clinical decision-making.
Generative AI systems are increasingly deployed to address domain problems. These systems operate under technical, regulatory, institutional, and normative constraints that define acceptable AI behaviour and outcomes within their domains. We observe a recurring pattern in our industry engagement: partners often arrive with a functioning but relatively generic AI solution. The challenge is no longer to build an AI system from scratch, but to improve the quality and domain appropriateness of an AI-generated solution. In these settings, the limiting factor is often the quality, scope, and structure of the context available to the system. Yet, existing context engineering approaches primarily focus on supplying domain knowledge through retrieval, memory, and tools, with limited support for systematically identifying and operationalising the constraints that govern AI systems in their operational environments. This paper proposes Constraint-Driven Context Engineering (CDCE), a design approach for engineering domain interfaces for AI systems. Drawing on software architecture design and Domain-Driven Design (DDD), CDCE treats domain constraints as first-class design drivers. It identifies and characterises constraints, determines the required context assets, and designs representations through which these assets are made available to AI systems. We conducted a comparative multiple-case study with industry and public-sector partners across educational assessment, healthcare decision support, and financial-distress prediction. Depending on their characteristics, constraints can guide AI behaviour, enforce permissible boundaries, or support verification of AI-generated outcomes. The cases demonstrate CDCE's applicability across contrasting domains and show how constraint characteristics shape the resulting domain interfaces.
We show that there exist two separable real Banach spaces $X$ and $Y$ such that, for every $\varepsilon>0$, there is a standard exact $\varepsilon$-isometry $f_\varepsilon: X\to Y$ whose distortion of every distance is between $0$ and $\varepsilon$, whereas no isometric embedding of $X$ into $Y$ exists, even without a linearity assumption. This gives a negative answer to \cite[Problem 1 and Problem 2]{cheng4} of Cheng and Zhou. The construction combines a snowflaked Lipschitz-free space with the Schur-property theorem of Kalton and the isometric linearization theorem of Godefroy and Kalton.
We determine the optimal order of the scaling parameter in the metric cotype $2$ inequality for complete Alexandrov spaces of nonnegative curvature. It grows linearly with the dimension $n$ of the discrete torus. This answers Question 17 of Eskenazis, Mendel, and Naor. In their sign-vector normalization on $\bigl(\mathbb{Z}/(2m\mathbb{Z})\bigr)^n$, the square of the optimal metric cotype $2$ constant for this class lies between $\max\{1,n/m\}$ and $e\lceil n/m\rceil$ for every dyadic $m\geq 2$. The upper bound follows from a dyadic Bernoulli-thinning argument using only the Lang--Schroeder--Sturm inequality. Snowflake universality of the fixed Wasserstein space $\mathcal{P}_2(\mathbb{R}^3)$ gives the $n/m$ lower bound.
We study the quadratic convexification of the compact nonconvex set ${G} := \left[1/2,2\right]^2 \cap \{(x_1,x_2)\in\mathbb R^2\mid x_1x_2\leq1\}, $ which is a square truncated by a hyperbolic arc. Although the ordinary convex hull of ${G}$ is a triangle, its lifted convex hull in the complete quadratic space retains the nontrivial geometry of the curved boundary. We characterize all extreme rays of the cone of quadratic polynomials nonnegative on $G$, including parameterized families of bounded tangent and bitangent rays. Using this classification and conic duality, we derive an exact finite semidefinite representation of the lifted convex hull of ${G}$. The analysis follows the general framework of our earlier work on an unbounded product-constrained region, but the bounded geometry creates new boundary-contact patterns and leads to a different finite organization of the nonnegative-quadratic cone.
We study quadratic polynomials that are nonnegative on the non-compact set \[ F:=\{(x_1,x_2)\in\mathbb R^2:\ x_1\ge 0,\ x_2\ge 0,\ x_1x_2\le 1\}. \] All extreme rays of the cone of nonnegative quadratic polynomials are characterized on this set. The characterization allows us to study parameterized valid inequalities for quadratic convexifications involving $F$, which yields a semidefinite representation of its lifted convex hull in the quadratic space. Our analysis on extreme ray characterization separates the positive-semidefinite (PSD) and non-PSD branches, reduces the latter to boundary nonnegativity, and classifies the boundary contacts of the relevant extreme rays. By reparameterization, we also find a non-trivial and non-permutation-symmetric six-dimensional linear section of the cone of nonnegative homogeneous ternary octics that are sum-of-squares. We also show that our lifted convex hull result yields a degree-bounded preordering certificate of nonnegative quadratics on $F$ and a degree-bounded certificate for a family of nonnegative quartics on the half-strip.
Joint-embedding self-supervised learning (SSL), the key paradigm for unsupervised representation learning from visual data, learns from invariances between semantically-related data pairs. We study the one-to-many mapping problem in SSL, where each datum may be mapped to multiple valid targets. This arises when data pairs come from naturally occurring generative processes, e.g., successive video frames. We show that existing methods struggle to flexibly capture this conditional uncertainty. As a remedy, we introduce a latent variable to account for this uncertainty and derive a variational lower bound on the mutual information between paired embeddings. Our derivation yields a simple regularization term for standard SSL objectives. The resulting method, which we call AdaSSL, applies to both contrastive and distillation-based SSL objectives, and we empirically show its versatility in causal representation learning, fine-grained image understanding, and world modeling on videos.
Positional encodings (PEs) are essential for Transformers. Yet designing effective PEs for non-Euclidean graphs remains challenging. Such encodings should ideally induce an Attention-Compatible Geometry for self-attention: not merely describing graph structure, but defining a geometry whose inner products reflect meaningful structural relatedness. To realize this geometry, we propose Communicability-Inspired Positional Encoding (CIPE), built from communicability, a measure between pairs of nodes that aggregates contributions from paths of all lengths. By construction, CIPE inner products recover communicability, converting global multi-path connectivity into an attention-ready similarity geometry. For practical Transformer training, we introduce dimensionality alignment, mapping graph-size-dependent CIPE representations to prescribed dimensions while faithfully preserving the induced geometry. Empirically, CIPE improves structure-agnostic Transformers by 35.5% on average across seven benchmarks, outperforming representative PEs; it also consistently improves structure-biased graph Transformers, where competing PEs often yield only marginal benefits. These results position CIPE as a principled framework for attention-compatible graph positional encodings.
Reconstructing Hyperspectral Images (HSI) from RGB images can yield high spatial resolution HSI at a lower cost, demonstrating significant application potential. This paper reveals that local correlation and global continuity of the spectral characteristics are crucial for HSI reconstruction tasks. Therefore, we fully explore these inter-spectral relationships and propose a Correlation and Continuity Network (CCNet) for HSI reconstruction from RGB images. For the correlation of local spectrum, we introduce the Group-wise Spectral Correlation Modeling (GrSCM) module, which efficiently establishes spectral band similarity within a localized range. For the continuity of global spectrum, we design the Neighborhood-wise Spectral Continuity Modeling (NeSCM) module, which employs memory units to recursively model the progressive variation characteristics at the global level. In order to explore the inherent complementarity of these two modules, we design the Patch-wise Adaptive Fusion (PAF) module to efficiently integrate global continuity features into the spectral features in a patch-wise adaptive manner. These innovations enhance the quality of reconstructed HSI. We perform comprehensive comparison and ablation experiments on the mainstream datasets NTIRE2022 and NTIRE2020 for the spectral reconstruction task. Compared to the current advanced spectral reconstruction algorithms, our designed algorithm achieves State-Of-The-Art (SOTA) performance.
Standard reinforcement learning (RL) for large language model (LLM) agents primarily optimizes extrinsic task rewards, often favoring isolated task completion over continual adaptation. This paradigm can cause premature convergence to suboptimal policies and leaves useful experience only implicitly encoded in model parameters, limiting its retrieval and reuse for future decisions. We introduce RetroAgent, an online RL framework that trains agents to master interactive environments not merely by solving tasks, but by evolving across episodes. Inspired by human retrospective self-improvement, RetroAgent augments extrinsic rewards with hindsight-generated dual intrinsic feedback: (1) Intrinsic Numerical Feedback, which rewards beneficial exploration by measuring incremental subtask progress relative to prior attempts; and (2) Intrinsic Language Feedback which distills successes and failures into reusable textual lessons for explicit experience reuse. To leverage these lessons effectively, we propose Similarity & Utility-Aware Upper Confidence Bound (SimUtil-UCB), a retrieval strategy that balances semantic relevance, historical utility, and exploration. Across four challenging agentic benchmarks, RetroAgent achieves new state-of-the-art performance, outperforming GRPO by +18.3% on ALFWorld, +15.4% on WebShop, +27.1% on Sokoban, and +8.9% on MineSweeper, while demonstrating strong test-time adaptation and out-of-distribution generalization.
Recent advances in reinforcement learning (RL) using numerical rewards have significantly enhanced the complex reasoning capabilities of large language models (LLMs). However, we identify three fundamental limitations of purely numerical feedback: performance plateaus, ineffective spontaneous self-reflection, and persistent failures. We show that plateaued RL models can successfully refine failed solutions when given natural language critiques. Motivated by this, we propose Critique-GRPO, an online RL framework that integrates both natural language and numerical feedback for policy optimization. This approach enables LLMs to learn simultaneously from initial responses and critique-guided refinements, effectively internalizing the exploration benefits of both stages. Extensive experiments show that Critique-GRPO outperforms all compared supervised and RL-based fine-tuning methods, achieving average Pass@1 improvements of approximately +15.0-21.6% on various Qwen models and +7.3% on Llama-3.2-3B-Instruct across eight challenging reasoning tasks. Notably, Critique-GRPO facilitates effective self-improvement through self-critiquing, achieving substantial gains over GRPO, e.g., a +16.7% Pass@1 improvement on AIME 2024. The code and models are released at: https://github.com/zhangxy-2019/critique-GRPO
Nesterov's accelerated gradient descent method (AGD) is a seminal deterministic first-order method known to achieve the optimal order of iteration complexity for solving convex smooth optimization problems. Two distinct sequences of iterates are included in the description of AGD: gradient evaluations are performed at one sequence, while approximate solutions are selected from the other. The iteration complexity on minimizing objective function value has been well-studied in the literature, but such analysis is almost always performed only at the approximate solution sequence. To the best of our knowledge, for projection-based AGD that solves problems with feasible sets, it is still an open research question whether the gradient evaluation sequence (when treated as approximate solutions) could also achieve the same optimal order of iteration complexity. It is also unknown whether such results still hold in the non-Euclidean setting. Motivated by computer-aided algorithm analysis, we provide positive results that answer the open problems affirmatively. Specifically, for (possibly constrained) problem $f^*:=\min_{x\in X}f(x)$ where $f$ is convex and $L$-smooth and $X$ is closed, convex and projection friendly, we prove that the gradient-evaluation sequence $\{\underline{x}_k\}$ in AGD satisfies that $f(\underline{x}_k) - f^*\le \mathcal O(L/k^2)$.
Epilepsy affects over 50 million people worldwide, and one-third of patients suffer drug-resistant seizures where surgery offers the best chance of seizure freedom. Accurate localization of the epileptogenic zone (EZ) relies on intracranial EEG (iEEG). Clinical workflows, however, remain constrained by labor-intensive manual review. At the same time, existing data-driven approaches are typically developed on single-center datasets that are inconsistent in format and metadata, lack standardized benchmarks, and rarely release pathological event annotations, creating barriers to reproducibility, cross-center validation, and clinical relevance. With extensive efforts to reconcile heterogeneous iEEG formats, metadata, and recordings across publicly available sources, we present $\textbf{Omni-iEEG}$, a large-scale, pre-surgical iEEG resource comprising $\textbf{302 patients}$ and $\textbf{178 hours}$ of high-resolution recordings. The dataset includes harmonized clinical metadata such as seizure onset zones, resections, and surgical outcomes, all validated by board-certified epileptologists. In addition, Omni-iEEG provides over 36K expert-validated annotations of pathological events, enabling robust biomarker studies. Omni-iEEG serves as a bridge between machine learning and epilepsy research. It defines clinically meaningful tasks with unified evaluation metrics grounded in clinical priors, enabling systematic evaluation of models in clinically relevant settings. Beyond benchmarking, we demonstrate the potential of end-to-end modeling on long iEEG segments and highlight the transferability of representations pretrained on non-neurophysiological domains. Together, these contributions establish Omni-iEEG as a foundation for reproducible, generalizable, and clinically translatable epilepsy research. The project page with dataset and code links is available at omni-ieeg.github.io/omni-ieeg.
Infrared small object detection urgently requires semi-supervised paradigms due to the high cost of annotation. However, existing methods like SAM face significant challenges of domain gaps, inability of encoding physical priors, and inherent architectural complexity. To address this, we designed a Hierarchical MoE Adapter consisting of four white-box neural operators. Building upon this core component, we propose a two-stage paradigm for knowledge distillation and transfer: (1) Prior-Guided Knowledge Distillation, where we use our MoE adapter and 10% of available fully supervised data to distill SAM into an expert teacher (Scalpel-SAM); and (2) Deployment-Oriented Knowledge Transfer, where we use Scalpel-SAM to generate pseudo labels for training lightweight and efficient downstream models. Experiments demonstrate that with minimal annotations, our paradigm enables downstream models to achieve performance comparable to, or even surpassing, their fully supervised counterparts. To our knowledge, this is the first semi-supervised paradigm that systematically addresses the data scarcity issue in IR-SOT using SAM as the teacher model.
Quantum Machine Learning (QML) offers a new paradigm for addressing complex financial problems intractable for classical methods. This work specifically tackles the challenge of few-shot credit risk assessment, a critical issue in inclusive finance where data scarcity and imbalance limit the effectiveness of conventional models. To address this, we design and implement a novel hybrid quantum-classical workflow. The methodology first employs an ensemble of classical machine learning models (Logistic Regression, Random Forest, XGBoost) for intelligent feature engineering and dimensionality reduction. Subsequently, a Quantum Neural Network (QNN), trained via the parameter-shift rule, serves as the core classifier. This framework was evaluated through numerical simulations and deployed on the Quafu Quantum Cloud Platform's ScQ-P21 superconducting processor. On a real-world credit dataset of 279 samples, our QNN achieved a robust average AUC of 0.852 +/- 0.027 in simulations and yielded an impressive AUC of 0.88 in the hardware experiment. This performance surpasses a suite of classical benchmarks, with a particularly strong result on the recall metric. This study provides a pragmatic blueprint for applying quantum computing to data-constrained financial scenarios in the NISQ era and offers valuable empirical evidence supporting its potential in high-stakes applications like inclusive finance.
User queries in e-commerce search are often vague, short, and underspecified, making it difficult for retrieval systems to match them accurately against structured product catalogs. This challenge is amplified by the one-to-many nature of user intent, where a single query can imply diverse and competing needs. Existing methods, including neural query expansion and prompting-based LLM approaches, fall short in real-world settings: they struggle to capture nuanced user intent, often generate outputs that violate platform constraints, and rely on workflows that are difficult to scale in production. We propose Learning to Expand via Search Engine-feedback Reinforcement (LESER), a novel framework that fine-tunes a context-aware LLM using real-time search engine feedback as supervision. LESER formulates query expansion as a retrieval optimization task and leverages Group Relative Policy Optimization to learn directly from relevance and coverage metrics. LESER is trained to reason over search results and produce high quality query expansions that align with platform rules and retrieval objectives. We evaluate LESER on large-scale, real-world e-commerce datasets, demonstrating substantial improvements in both offline and online settings. Our results show that LESER not only enhances semantic coverage and retrieval relevance but also delivers measurable gains in user engagement, making it a practical and scalable solution for modern search systems.