arXiv subjects

Ziheng Chen

Publications and source records attributed to Ziheng Chen.

At least 37 records · Page 2Linked to original sources

arXiv2026

Weak order one convergence of structure-preserving stochastic theta methods for stochastic differential algebraic equations with time-dependent singular matrices

This paper studies the weak convergence order of structure-preserving stochastic theta methods for a class of index-$1$ stochastic differential algebraic equations with time-dependent singular matrices. The singular matrix is allowed to vary in time but preserves a fixed differential-algebraic splitting, thereby extending the constant singular-matrix setting while retaining the projector structure required for constraint preservation. By exploiting the index-$1$ algebraic-differential decomposition of the exact solution, we establish an abstract weak convergence theorem for constraint-preserving one-step approximations and apply it to the stochastic theta method with $θ\in (0,1]$. Under global Lipschitz, linear growth, and suitable smoothness assumptions, the considered method is proved to be well posed, to preserve the algebraic constraints at all time levels, and to converge with weak order one. Numerical experiments are finally presented to confirm the structure-preserving property and the theoretical convergence order.

math.NA↗

arXiv2026

Disentangling Language Roles in Multilingual LLM Task Execution

Multilingual LLMs are increasingly used when instruction, source content, and required response languages do not coincide. Existing benchmarks have expanded multilingual instruction-following evaluation, but they rarely isolate these three roles within a fully crossed design. We introduce MTM-Bench, a controlled benchmark for language-conditioned task execution in which each instance is defined by a triplet $(L_{\text{instr}}, L_{\text{content}}, L_{\text{resp}})$. Across English, Spanish, and Chinese, MTM-Bench enumerates all 27 triplets and contains 2{,}430 instances per model across semantic reversal, final-state extraction, and language purity with update realization. We evaluate 20 frontier and open-weight LLMs using decomposed metrics for semantic correctness, target-language adherence, constraint satisfaction, contamination ratio, and joint success, with scoring validated by a targeted human audit. The fully crossed design reveals that degradation is organized by the role a language occupies in the task structure, not merely by mismatch count. The response-language role is the dominant axis of variation, and a single response-slot mismatch accounts for most degradation. The response-only and full-mismatch comparison suggests that mismatch count is not a monotonic predictor of difficulty, with model-level ordering varying across systems. Task families fail through distinct channels, showing that semantic correctness alone does not capture reliable multilingual task execution.

cs.CL↗

arXiv2026

Relative Repairability: A Calibration-Based Diagnostic for High-Sparsity Post-Pruning Allocation

At very high sparsity, neural network pruning does more than decide which weights remain. It also determines where pruning induced damage is placed across the network, and whether that damage can be recovered by a fixed lightweight repair procedure. We study this problem through the lens of repair conditioned sparsity allocation. We introduce Relative Repairability (RR), a calibration based diagnostic that compares the raw activation distortion caused by layerwise pruning with the residual distortion left after channelwise variance matching repair. RR estimates the fraction of local damage that remains after repair, using only unlabeled calibration data. Across ResNet18, ResNet34, and VGG16 BN on CIFAR10 and CIFAR100, we find that RR is not a universally dominant allocation rule. Instead, it is most useful near an architecture dependent recoverability transition, where standard structural or magnitude based allocation priors begin to lose reliability but post repair recovery has not yet fully collapsed. On CIFAR100 ResNet18, a fine grained sweep shows that RR improves over ERK across the central transition band and surpasses LAMP near the upper part of this band. A projection forced ablation further shows that capped ERK can over protect projection layers, shifting excessive sparsity onto regular convolutions and reducing post repair recovery. These results suggest that high sparsity pruning should allocate not only retained weights, but also repairable damage.

cs.LG↗

arXiv2026

Adaptive Signal Resuscitation: Channel-wise Post-Pruning Repair for Sparse Vision Networks

One-shot magnitude pruning can cause severe accuracy collapse in the high-sparsity regime, even when the pruning mask preserves the largest weights. We argue that this failure reflects a granularity mismatch in post-pruning repair. Under global magnitude pruning, nearly collapsed channels can coexist with channels that retain informative activation variance within the same layer. Existing layer-wise activation repair methods apply a single correction to the whole layer, and can therefore over-amplify damaged channels while trying to restore the layer-level signal. We propose Adaptive Signal Resuscitation (ASR), a training-free channel-wise repair method that matches the granularity of repair to the granularity of damage. ASR estimates a variance-matching correction for each output channel and stabilizes it with a data-driven shrinkage rule, suppressing unreliable corrections for channels with weak post-pruning signal while preserving corrections for healthier channels. Applied before BatchNorm recalibration, ASR requires only forward passes on a small calibration set and no retraining. Across three datasets, four convolutional architectures, and both unstructured and structured sparsity settings, ASR generally improves over layer-wise repair, with the clearest gains in high-sparsity regimes. On ResNet-50 at 90% sparsity, ASR recovers 55.6% top-1 accuracy on CIFAR-10, compared with 41.0% for layer-wise repair and 28.0% for BatchNorm-only recalibration. Ablations show that naive channel-wise variance matching is insufficient, and that shrinkage stabilizes post-pruning repair.

cs.LG↗

arXiv2026

Riemannian Networks over Full-Rank Correlation Matrices

Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.

cs.LG↗

arXiv2026

ESG as Priced Crash Insurance: State-Dependent Tail Risk and Deconfounding Evidence

This research establishes ESG as a state dependent insurance mechanism against equity crashes by addressing the decoupling of unconditional alpha from tail risk resilience. By validating market stress regimes as distinct economic states through a drawdown-based truncation rule, the study demonstrates that high ESG ratings materially reduce the incidence of discrete crash events during systemic drawdowns. To address the selection bias and high-dimensional confounding inherent in traditional linear frameworks, we implement Double Machine Learning as a structural deconfounding layer. Unlike simple predictive modeling, the Double Machine Learning framework utilizes machine learning to handle complex nuisance parameters, allowing us to isolate the asymmetric treatment effects of ESG across different market states. Distributional analysis reveals the underlying mechanism as ESG specifically attenuates the severity of realized tail losses at the most adverse quantiles instead of shifting the entire return distribution. Confirmed by structural estimates, this protection functions as priced insurance that incurs performance drags during stable periods while providing critical resilience when tail risks are most acute.

q-fin.MF↗

arXiv2026

MeSH: Memory-as-State-Highways for Recursive Transformers

Recursive transformers reuse parameters and iterate over hidden states multiple times, decoupling compute depth from parameter depth. However, under matched compute, recursive models with fewer parameters often lag behind non-recursive counterparts. By probing hidden states, we trace this performance gap to two primary bottlenecks: undifferentiated computation, where the core is forced to adopt a similar computational pattern at every iteration, and information overload, where long-lived and transient information must coexist in a single hidden state. To address the issues, we introduce a Memory-as-State-Highways (MeSH) scheme, which externalizes state management into an explicit memory buffer and employs lightweight routers to dynamically diversify computation across iterations. Probing visualizations confirm that MeSH successfully resolves the pathologies by inducing functional specialization across iterations. On the Pythia suite (160M-6.9B), MeSH-enhanced recursive transformers consistently improve over recursive baselines and outperforms its larger non-recursive counterpart at the 1.4B scale, improving average downstream accuracy by +1.06% with 33% fewer non-embedding parameters. Our analysis establishes MeSH as a scalable and principled architecture for building stronger recursive models. Our code is available at https://github.com/LivingFutureLab/MeSH/ .

cs.LG↗

arXiv2026

SpiralFormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion

Recursive (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures.

cs.LG↗

arXiv2026

YOCO++: Enhancing YOCO with KV Residual Connections for Efficient LLM Inference

Cross-layer key-value (KV) compression has been found to be effective in efficient inference of large language models (LLMs). Although they reduce the memory consumption of the KV cache, such methods usually introduce non-negligible performance degradation. In this work, we aim to enhance the performance of YOCO, a cross-layer KV compression method that shares the KVs of the middle layer with the top-half layers. We propose YOCO++, an enhanced YOCO that incorporates a weighted residual connection between the KVs of each bottom-half layer and the bottom layer. Compared to YOCO, YOCO++ increases model capacity while maintaining the same training and inference efficiency. Our experiments show that YOCO++ achieves state-of-the-art performance among the cross-layer KV compression methods at a 50% KV cache compression rate, outperforming the standard Transformer.

cs.CL↗

arXiv2026

CRAB: Codebook Rebalancing for Bias Mitigation in Generative Recommendation

Generative recommendation (GeneRec) has introduced a new paradigm that represents items as discrete semantic tokens and predicts items in a generative manner. Despite its strong performance across multiple recommendation tasks, existing GeneRec approaches still suffer from severe popularity bias and may even exacerbate it. In this work, we conduct a comprehensive empirical analysis to uncover the root causes of this phenomenon, yielding two core insights: 1) imbalanced tokenization inherits and can further amplify popularity bias from historical item interactions; 2) current training procedures disproportionately favor popular tokens while neglecting semantic relationships among tokens, thereby intensifying popularity bias. Building on these insights, we propose CRAB, a post-hoc debiasing strategy for GeneRec that alleviates popularity bias by mitigating frequency imbalance among semantic tokens. Specifically, given a well-trained model, we first rebalance the codebook by splitting over-popular tokens while preserving their hierarchical semantic structure. Based on the adjusted codebook, we further introduce a tree-structured regularizer to enhance semantic consistency, encouraging more informative representations for unpopular tokens during training. Experiments on real-world datasets demonstrate that CRAB significantly improves recommendation performance by effectively alleviating popularity bias.

cs.IR↗

arXiv2026

CURE:Circuit-Aware Unlearning for LLM-based Recommendation

Recent advances in large language models (LLMs) have opened new opportunities for recommender systems by enabling rich semantic understanding and reasoning about user interests and item attributes. However, as privacy regulations tighten, incorporating user data into LLM-based recommendation (LLMRec) introduces significant privacy risks, making unlearning algorithms increasingly crucial for practical deployment. Despite growing interest in LLMRec unlearning, most existing approaches formulate unlearning as a weighted combination of forgetting and retaining objectives while updating model parameters in a uniform manner. Such formulations inevitably induce gradient conflicts between the two objectives, leading to unstable optimization and resulting in either ineffective unlearning or severe degradation of model utility. Moreover, the unlearning procedure remains largely black-box, undermining its transparency and trustworthiness. To tackle these challenges, we propose CURE, a circuit-aware unlearning framework that disentangles model components into functionally distinct subsets and selectively updates them. Here, a circuit refers to a computational subgraph that is causally responsible for task-specific behaviors. Specifically, we extract the core circuits underlying item recommendation and analyze how individual modules within these circuits contribute to the forget and retain objectives. Based on this analysis, these modules are categorized into forget-specific, retain-specific, and task-shared groups, each subject to function-specific update rules to mitigate gradient conflicts during unlearning. Experiments on real-world datasets show that our approach achieves more effective unlearning than existing baselines.

cs.IR↗

arXiv2026

Weak convergence order of stochastic theta method for SDEs driven by time-changed Lévy noise

This paper studies the weak convergence order of the stochastic theta method for stochastic differential equations (SDEs) driven by time-changed Lévy noise under global Lipschitz and linear growth conditions. In contrast to classical Lévy-driven SDEs, the presence of a random time change makes the weak error analysis involve both the discretization error of the underlying equation and the approximation error of the random clock. Moreover, compared with explicit Euler--Maruyama method, the implicit drift correction in the stochastic theta method makes the associated weak error analysis substantially more delicate. To address these difficulties, we first establish a global weak convergence estimate of order one for the stochastic theta method applied to the corresponding non-time-changed Lévy SDEs on the infinite time interval by means of the Kolmogorov backward partial integro differential equations. Incorporating the approximation of the inverse subordinator together with the duality principle, we derive the weak convergence order of the stochastic theta method with $θ\in [0,1]$ in the time-changed Lévy setting. The result advances the currently available weak convergence analysis beyond the Euler--Maruyama method to the more general class of stochastic theta method, and establishes a workable route from the weak analysis of the underlying non-time-changed Lévy equation to the corresponding time-changed problem. Finally, numerical experiments are presented to further support the theoretical findings.

math.NA↗

arXiv2026

MIBench: Evaluating LMMs on Multimodal Interaction

In different multimodal scenarios, it needs to integrate and utilize information across modalities in a specific way based on the demands of the task. Different integration ways between modalities are referred to as "multimodal interaction". How well a model handles various multimodal interactions largely characterizes its multimodal ability. In this paper, we introduce MIBench, a comprehensive benchmark designed to evaluate the multimodal interaction capabilities of Large Multimodal Models (LMMs), which formulates each instance as a (con_v , con_t, task) triplet with contexts from vision and text, necessitating that LMMs employ correct forms of multimodal interaction to effectively complete the task. MIBench assesses models from three key aspects: the ability to source information from vision-centric or text-centric cues, and the ability to generate new information from their joint synergy. Each interaction capability is evaluated hierarchically across three cognitive levels: Recognition, Understanding, and Reasoning. MIBench comprises over 10,000 vision-text context pairs spanning 32 distinct tasks. Evaluation of state-of-the-art LMMs show that: (1) LMMs' ability on multimodal interaction remains constrained, despite the scaling of model parameters and training data; (2) they are easily distracted by textual modalities when processing vision information; (3) they mostly possess a basic capacity for multimodal synergy; and (4) natively trained multimodal models show noticeable deficits in fundamental interaction ability. We expect that these observations can serve as a reference for developing LMMs with more enhanced multimodal ability in the future.

cs.CV↗

arXiv2026

Intrinsic Lorentz Neural Network

Real-world data frequently exhibit latent hierarchical structures, which can be naturally represented by hyperbolic geometry. Although recent hyperbolic neural networks have demonstrated promising results, many existing architectures remain partially intrinsic, mixing Euclidean operations with hyperbolic ones or relying on extrinsic parameterizations. To address it, we propose the \emph{Intrinsic Lorentz Neural Network} (ILNN), a fully intrinsic hyperbolic architecture that conducts all computations within the Lorentz model. At its core, the network introduces a novel \emph{point-to-hyperplane} fully connected layer (FC), replacing traditional Euclidean affine logits with closed-form hyperbolic distances from features to learned Lorentz hyperplanes, thereby ensuring that the resulting geometric decision functions respect the inherent curvature. Around this fundamental layer, we design intrinsic modules: GyroLBN, a Lorentz batch normalization that couples gyro-centering with gyro-scaling, consistently outperforming both LBN and GyroBN while reducing training time. We additionally proposed a gyro-additive bias for the FC output, a Lorentz patch-concatenation operator that aligns the expected log-radius across feature blocks via a digamma-based scale, and a Lorentz dropout layer. Extensive experiments conducted on CIFAR-10/100 and two genomic benchmarks (TEB and GUE) illustrate that ILNN achieves state-of-the-art performance and computational cost among hyperbolic models and consistently surpasses strong Euclidean baselines. The code is available at \href{https://github.com/Longchentong/ILNN}{\textcolor{magenta}{this url}}.

cs.LG↗

arXiv2026

Hyperbolic Busemann Neural Networks

Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural networks require intrinsic and efficient components that operate directly in hyperbolic space. In this work, we lift two core components of neural networks, Multinomial Logistic Regression (MLR) and Fully Connected (FC) layers, into hyperbolic space via Busemann functions, resulting in Busemann MLR (BMLR) and Busemann FC (BFC) layers with a unified mathematical interpretation. BMLR provides compact parameters, a point-to-horosphere distance interpretation, batch-efficient computation, and a Euclidean limit, while BFC generalizes FC and activation layers with comparable complexity. Experiments on image classification, genome sequence learning, node classification, and link prediction demonstrate improvements in effectiveness and efficiency over prior hyperbolic layers. The code is available at https://github.com/GitZH-Chen/HBNN.

cs.LG↗

arXiv2026

Fast and Stable Riemannian Metrics on SPD Manifolds via Cholesky Product Geometry

Recent advances in Symmetric Positive Definite (SPD) matrix learning show that Riemannian metrics are fundamental to effective SPD neural networks. Motivated by this, we revisit the geometry of the Cholesky factors and uncover a simple product structure that enables convenient metric design. Building on this insight, we propose two fast and stable SPD metrics, Power--Cholesky Metric (PCM) and Bures--Wasserstein--Cholesky Metric (BWCM), derived via Cholesky decomposition. Compared with existing SPD metrics, the proposed metrics provide closed-form operators, computational efficiency, and improved numerical stability. We further apply our metrics to construct Riemannian Multinomial Logistic Regression (MLR) classifiers and residual blocks for SPD neural networks. Experiments on SPD deep learning, numerical stability analyses, and tensor interpolation demonstrate the effectiveness, efficiency, and robustness of our metrics. The code is available at https://github.com/GitZH-Chen/PCM_BWCM.

math.DG↗

arXiv2026

HEEGNet: Hyperbolic Embeddings for EEG

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underlying task-relevant information would mitigate these shifts and improve generalization. One promising approach is to exploit the underlying hierarchical structure in EEG, as recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. While many decoding methods still rely on Euclidean embeddings, recent work has begun exploring hyperbolic geometry for EEG. Hyperbolic spaces, regarded as the continuous analogue of tree structures, provide a natural geometry for representing hierarchical data. In this study, we first empirically demonstrate that EEG data exhibit hyperbolicity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure in EEG and learn domain-invariant hyperbolic embeddings. To this end, HEEGNet combines both Euclidean and hyperbolic encoders and employs a novel coarse-to-fine domain adaptation strategy. Extensive experiments on multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEGNet achieves state-of-the-art performance. The code is available at https://github.com/fightlesliefigt/HEEGNet

cs.LG↗

arXiv2026

Autonomous AI Agents for Option Hedging: Enhancing Financial Stability through Shortfall Aware Reinforcement Learning

The deployment of autonomous AI agents in derivatives markets has widened a practical gap between static model calibration and realized hedging outcomes. We introduce two reinforcement learning frameworks, a novel Replication Learning of Option Pricing (RLOP) approach and an adaptive extension of Q-learner in Black-Scholes (QLBS), that prioritize shortfall probability and align learning objectives with downside sensitive hedging. Using listed SPY and XOP options, we evaluate models using realized path delta hedging outcome distributions, shortfall probability, and tail risk measures such as Expected Shortfall. Empirically, RLOP reduces shortfall frequency in most slices and shows the clearest tail-risk improvements in stress, while implied volatility fit often favors parametric models yet poorly predicts after-cost hedging performance. This friction-aware RL framework supports a practical approach to autonomous derivatives risk management as AI-augmented trading systems scale.

cs.AI↗