arXiv subjects

Wenlong Wang

Publications and source records attributed to Wenlong Wang.

At least 19 recordsLinked to original sources

arXiv2026

The metric extension problem under positive and negative curvature conditions

We first prove that every smooth boundary metric on a compact manifold extends to a metric with any prescribed positive lower bound for Ricci curvature, whereas extensions under stronger positive $k^{\mathrm{th}}$-intermediate Ricci curvature conditions may fail due to local obstructions. For negative sectional curvature, we identify a global obstruction to extension. We then consider the class of compact manifolds defined by the existence of a metric with negative sectional curvature and boundary index at most one. On every manifold in this class, we prove that any smooth boundary metric extends to a metric with negative sectional curvature and strictly convex umbilical boundary. We further show that every such initial metric admits a complete asymptotically hyperbolic isometric extension with the same curvature condition and any prescribed conformal infinity. This class of manifolds is closed under boundary connected sums. As a geometric application of these extension results, every smooth metric on $\mathbb S^n$ admits a strictly convex isometric embedding into $\mathbb R^{n+1}$ equipped with a complete metric of negative sectional curvature. The proofs combine neck constructions with corner smoothing for upper curvature bounds.

math.DG↗

arXiv2026

Diffusion and reaction in the quasi-spherical equation: mean curvature deformations for fill-Ins

We study the diffusion and reaction effects of Bartnik's quasi-spherical equation to deform boundary mean curvature in fill-in problems with scalar curvature bounded below. The diffusion effect yields an explicit $L^p$-to-$L^\infty$ estimate for $\partial_tu=u^2Δu$, thereby extending the known upper bound for the minimum boundary mean curvature of fill-ins to a quantitative upper bound for its harmonic mean. For spin fill-ins, this bound is explicit and involves only coarse intrinsic boundary data. By introducing an absorbing reaction term, we also construct a deformation that transforms any nonnegative initial mean curvature into a terminal mean curvature with a uniform positive lower bound. For Gromov's conjecture on total mean curvature, this reduces the $H\geq 0$ case to Theorem A of Frenck, Hanke, and Hirsch \cite{FHH}, which assumes $H\geqκ>0$. This covers the case of non-spin boundaries, complementing their result for spin boundaries (Theorem B) for this conjecture.

math.DG↗

arXiv2026

Looped Transformers under the Jacobian Lens: Does the Global Workspace Survive Recurrence?

Recent work identifies a mid-depth band of verbalisable, causally potent representations in a standard feedforward transformer --- a functional analogue of a global workspace. Whether the same workspace functionality emerges when depth is implemented through recurrence rather than a stack of distinct layers remains unknown. Looped and depth-recurrent transformers provide a direct test of this question because they reuse the same weights across depth. We extend the Jacobian lens to iterated architectures using a virtual-unrolling adapter. We apply the full workspace suite --- lens fitting, readout, and eleven causal experiment families --- to Ouro-2.6B (48 layers looped 4 times, deeply supervised) and Huginn-0125 (a 4-layer core recurred 16 times, trained for latent reasoning), using Qwen3.6-27B (64 untied layers) as the standard baseline. We find that a workspace forms in the iterated part of each architecture, but that recurrence changes how it can be accessed. Ouro reconstructs workspace content in every loop, and linear transport cannot carry that content across loop boundaries; writes and ablations must therefore span every remaining loop. Huginn carries content forward across all sixteen recurrences, while reads, writes, and ablations act only within a sliding window of roughly two recurrences. Whether newly injected content can be verbalised tracks explicit per-iteration supervision; whether existing content can be steered does not.

cs.AI↗

arXiv2026

Jointly Sparse Blind Deconvolution via Riemannian Optimization

Blind deconvolution has been widely applied in system identification and signal processing. While joint sparsity commonly arises in practical scenarios, effectively exploiting this structure to enhance recovery performance remains a challenging and largely open problem. In this paper, we propose a joint-sparsity-promoting optimization problem and develop a Riemannian optimization algorithm for its accurate and efficient solution. We further establish theoretical guarantees that characterize the non-asymptotic relationship between the estimation error and the sample complexity, showing that exploiting joint sparsity can significantly reduce the sample complexity required for successful recovery. Numerical experiments are provided that validate the theoretical results and demonstrate the effectiveness of the proposed approach.

math.OC↗

arXiv2026

Does Verbose Chain-of-Thought Really Help? In-Distribution Evidence that Content, Not Length, Matters

Chain-of-thought (CoT) prompting improves LLM reasoning, but the source is contested: do the intermediate steps help because they carry useful semantic content, or because conditioning on more tokens buys extra computation before the model commits to an answer? We bring two lines of evidence to bear. First, in distribution: we repeatedly sample each model on the same question and pair a shorter with a longer of its own natural generations that follow the same reasoning plan, so nothing is rewritten and both traces are genuinely in-distribution. Across 25 models the extra tokens leave accuracy essentially unchanged for every independently-trained reasoner, and a blind analysis of the surplus tokens shows that what gain exists elsewhere tracks validation- and checking-content, not verbosity per se. Second, as a controlled intervention, we ask whether two traces expressing the same semantic content (the same facts, operations, and intermediate values, verified through directed acyclic graph equivalence) produce different outcomes when one is more verbose, using a dual-validator design across four targets and eight benchmarks with number-redacted completion and stratified bootstrap confidence intervals. Verbose traces do improve accuracy (25 of 32 benchmark-target cells are positive under at least one validator), but the effects are modest (typically 1-4 points) and depend on the quality of the verbose prose, not merely its length. Under maximum numerical redaction the effect is amplified (median 3.24x across four arithmetic benchmarks), and length-matched non-reasoning filler recovers none of it. Both lines converge: what matters is what the extra tokens do (the reasoning and validation content they carry), not how many there are, a picture neither a pure forward-pass-compute nor a pure semantic-content account fully explains.

cs.AI↗

arXiv2026

A Bernstein Theorem for the Self-Shrinking $J$-Equation and Some Generalizations

We prove that every entire smooth plurisubharmonic solution of the self-shrinking $J$-equation on $\mathbb{C}^n$ is a quadratic polynomial. This removes the asymptotic lower bound assumption on the complex Hessian in \cite[Theorem 4]{HJ}. The result also recovers the corresponding real rigidity theorem in \cite[Theorem 1.1]{HOW} as a special case. More generally, our method applies to a broad class of fully nonlinear elliptic operators satisfying suitable structural conditions, including the inverse complex Hessian quotient operators $-σ_{k-1}/σ_{k}$ for $1\leq k\leq n$.

math.DG↗

arXiv2026

Systematic solitary waves by linear limit continuation from two anisotropic traps in two-dimensional Bose-Einstein condensates

Linear limit continuation was recently developed as a systematic and effective method for constructing numerically exact solitary waves from their respective linear limits. In this work, we apply the technique to two typical anisotropic harmonic traps in two-dimensional Bose-Einstein condensates to further establish the method and also to find more solitary waves. Many wave patterns are identified in the near-linear regime and they are subsequently continued into the Thomas-Fermi regime, and then they are further continued into the isotropic trap if possible. Finally, the parametric connectivity of the pertinent solitary waves is also discussed.

cond-mat.quant-gas↗

arXiv2026

Tiny Recursive Reasoning with Mamba-2 Attention Hybrid

Recent work on recursive reasoning models like TRM demonstrates that tiny networks (7M parameters) can achieve strong performance on abstract reasoning tasks through latent recursion -- iterative refinement in hidden representation space without emitting intermediate tokens. This raises a natural question about operator choice: Mamba-2's state space recurrence is itself a form of iterative refinement, making it a natural candidate for recursive reasoning -- but does introducing Mamba-2 into the recursive scaffold preserve reasoning capability? We investigate this by replacing the Transformer blocks in TRM with Mamba-2 hybrid operators while maintaining parameter parity (6.83M vs 6.86M parameters). On ARC-AGI-1, we find that the hybrid improves pass@2 (the official metric) by +2.0\% (45.88\% vs 43.88\%) and consistently outperforms at higher K values (+4.75\% at pass@100), whilst maintaining pass@1 parity. This suggests improved candidate coverage -- the model generates correct solutions more reliably -- with similar top-1 selection. Our results validate that Mamba-2 hybrid operators preserve reasoning capability within the recursive scaffold, establishing SSM-based operators as viable candidates in the recursive operator design space and taking a first step towards understanding the best mixing strategies for recursive reasoning.

cs.AI↗

arXiv2026

Kinetics of Stacking Order Evolution During Heterogeneous Ice Formation

The selection of stacking order in a broad range of close-packed polymorphic materials remains a challenging enigma. Using in situ cryogenic transmission electron microscopy, we uncover the atomistic mechanisms governing the vapour deposition growth of ice. We find that the heterogeneous ice nucleation and growth undergoes recrystallization accompanied by bifurcation, reflecting a coherent epitaxial transition from a cubic-ice embryonic core to hexagonal-ice prismatic dendrites, with intermediate stacking-disordered layers serving as a dynamic fluctuating bridge. Supported by molecular dynamics simulations, these phenomena are attributed to a surface-constrained, symmetry-breaking crystallization preference aligned with the principle of minimizing free energy. Our results highlight the critical role of the combined effects of surface and symmetry in shaping ice crystallization, providing fresh insights into crystal growth mechanisms and guiding principles for the design of advanced materials.

cond-mat.mtrl-sci↗

arXiv2026

TCDA: Robust 2D-DOA Estimation for Defective L-Shaped Arrays

While tensor-based methods excel at Direction-of-Arrival (DOA) estimation, their performance degrades severely with faulty or sparse arrays that violate the required manifold structure. To address this challenge, we propose Tensor Completion for Defective Arrays (TCDA), a robust algorithm that reformulates the physical imperfection problem as a data recovery task within a virtual tensor space. We present a detailed derivation for constructing an incomplete third-order Parallel Factor Analysis (PARAFAC) tensor from the faulty array signals via subarray partitioning, cross-correlation, and dimensional reshaping. Leveraging the tensor's inherent low-rank structure, an Alternating Least Squares (ALS)-based algorithm directly recovers the factor matrices embedding the DOA parameters from the incomplete observations. This approach provides a software-defined 'self-healing' capability, demonstrating exceptional robustness against random element failures without requiring additional processing steps for DOA estimation.

cs.IT↗

arXiv2025

Quotient Manifold Optimization for Spectral Compressed Sensing

Spectral compressed sensing involves reconstructing a spectral-sparse signal from a subset of uniformly spaced samples, with applications in radar imaging and wireless channel estimation. By fully exploiting the signal structures, this problem is formulated as a rank-constrained semidefinite program subject to Hankel-Toeplitz structural constraints in our previous work. To further enhance computational efficiency, this paper proposes a quotient-manifold-based optimization framework that leverages the underlying Riemannian geometry in a matrix factorization space. Specifically, we establish an equivalence between spectral-sparse signals and matrix equivalence classes under the action of the real orthogonal group, where each class member corresponds to a rank-constrained positive-semidefinite Hankel-Toeplitz structured matrix. The associated quotient manifold geometry--including the Riemannian metric, horizontal space, retraction, and vector transport--is rigorously derived. Based on these results, we develop a Riemannian conjugate gradient descent algorithm, where each iteration is efficiently implemented using fast Fourier transforms (FFTs) by exploiting the Hankel and Toeplitz structures. Extensive numerical experiments demonstrate the superior performance of the proposed algorithm in both computational speed and accuracy compared to state-of-the-art methods.

math.OC↗

arXiv2025

An Automated Classifier of Harmful Brain Activities for Clinical Usage Based on a Vision-Inspired Pre-trained Framework

Timely identification of harmful brain activities via electroencephalography (EEG) is critical for brain disease diagnosis and treatment, which remains limited application due to inter-rater variability, resource constraints, and poor generalizability of existing artificial intelligence (AI) models. In this study, a convolutional neural network model, VIPEEGNet, was developed and validated using EEGs recorded from Massachusetts General Hospital/Harvard Medical School. The VIPEEGNet was developed and validated using two independent datasets, collected between 2006 and 2020. The development cohort included EEG recordings from 1950 patients, with 106,800 EEG segments annotated by at least one experts (ranging from 1 to 28). The online testing cohort consisted of EEG segments from a subset of an additional 1,532 patients, each annotated by at least 10 experts. For the development cohort (n=1950), the VIPEEGNet achieved high accuracy, with an AUROC for binary classification of seizure, LPD, GPD, LRDA, GRDA, and "other" categories at 0.972 (95% CI, 0.957-0.988), 0.962 (95% CI, 0.954-0.970), 0.972 (95% CI, 0.960-0.984), 0.938 (95% CI, 0.917-0.959), 0.949 (95% CI, 0.941-0.957), and 0.930 (95% CI, 0.926-0.935). For multi classification, the sensitivity of VIPEEGNET for the six categories ranges from 36.8% to 88.2% and the precision ranges from 55.6% to 80.4%, and performance similar to human experts. Notably, the external validation showed Kullback-Leibler Divergence (KLD)of 0.223 and 0.273, ranking top 2 among the existing 2,767 competing algorithms, while we only used 2.8% of the parameters of the first-ranked algorithm.

cs.LG↗

arXiv2025

Pursuing the limit of chirp parameter identifiability: A computational approach

In this paper, it is shown that a necessary condition for unique identifiability of $K$ chirps from $N$ regularly spaced samples of their mixture is $N\geq 2K$ when $K\geq 2$. A necessary and sufficient condition is that a rank-constrained matrix optimization problem has a unique solution; this is the first result of such kind. An algorithm is proposed to solve the optimization problem and to identify the parameters numerically. The lower bound of $N=2K$ is shown to be tight by providing diverse problem instances for which the proposed algorithm succeeds to identify the parameters. The advantageous performance of the proposed algorithm is also demonstrated compared with the state of the art.

eess.SP↗

arXiv2025

Drama: Mamba-Enabled Model-Based Reinforcement Learning Is Sample and Parameter Efficient

Model-based reinforcement learning (RL) offers a solution to the data inefficiency that plagues most model-free RL algorithms. However, learning a robust world model often requires complex and deep architectures, which are computationally expensive and challenging to train. Within the world model, sequence models play a critical role in accurate predictions, and various architectures have been explored, each with its own challenges. Currently, recurrent neural network (RNN)-based world models struggle with vanishing gradients and capturing long-term dependencies. Transformers, on the other hand, suffer from the quadratic memory and computational complexity of self-attention mechanisms, scaling as $O(n^2)$, where $n$ is the sequence length. To address these challenges, we propose a state space model (SSM)-based world model, Drama, specifically leveraging Mamba, that achieves $O(n)$ memory and computational complexity while effectively capturing long-term dependencies and enabling efficient training with longer sequences. We also introduce a novel sampling method to mitigate the suboptimality caused by an incorrect world model in the early training stages. Combining these techniques, Drama achieves a normalised score on the Atari100k benchmark that is competitive with other state-of-the-art (SOTA) model-based RL algorithms, using only a 7 million-parameter world model. Drama is accessible and trainable on off-the-shelf hardware, such as a standard laptop. Our code is available at https://github.com/realwenlongwang/Drama.git.

cs.LG↗

arXiv2025

Temperature chaos may emerge many thermodynamic states in spin glasses

We present a large-scale simulation of the three-dimensional and mean-field spin glasses down to a very low but finite temperature. We extrapolate pertinent observables, e.g., the disorder-averaged central weight to zero temperature, finding that many thermodynamic states at a finite temperature and two ground states at zero temperature are fully compatible. While the disorder-averaged central weight monotonically decreases with decreasing temperature, this is far from true for individual samples. This motivates us to link this behaviour with the well-known temperature chaos. At an observing temperature, a sample may or may not have pure state coexistence depending on whether it is undergoing temperature chaos, which is a random process. Therefore, temperature chaos is likely responsible for the emergence of many pure states, providing a natural and intuitive explanation for the coexistence of expensive domain-wall excitations and many pure states at the disorder-averaged level.

cond-mat.dis-nn↗

arXiv2025

Improved impedance inversion by the iterated graph Laplacian

We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic exploration. Our method initiates from an impedance estimate derived using either traditional inversion techniques or neural network-based methods. This initial estimate guides the construction of a graph Laplacian operator, effectively capturing structural characteristics of the impedance profile. Utilizing a Tikhonov-inspired variational framework with this graph-informed prior, our approach iteratively updates and refines the impedance estimate while continuously recalibrating the graph Laplacian. This iterative refinement shows rapid convergence, increased accuracy, and enhanced robustness to noise compared to initial reconstructions alone. Extensive validation performed on synthetic and real seismic datasets across varying noise levels confirms the effectiveness of our method. Performance evaluations include four initial inversion methods: two classical techniques and two neural networks - previously established in the literature.

math.NA↗

arXiv2025

LearnedKV: Integrating LSM and Learned Index for Superior Performance on Storage

We present LearnedKV, a novel tiered key-value store that seamlessly integrates a Log-Structured Merge (LSM) tree with a Learned Index to achieve superior read and write performance on storage systems. While existing approaches use learned indexes primarily as auxiliary components within LSM trees, LearnedKV employs a two-tier design where the LSM tree handles recent write operations while a separate Learned Index accelerates read performance. Our design includes a non-blocking conversion mechanism that efficiently transforms LSM data into a Learned Index during garbage collection, maintaining high performance without interrupting operations. LearnedKV dramatically reduces LSM size through this tiered approach, leading to significant performance gains in both reads and writes. Extensive evaluations across diverse workloads show that LearnedKV outperforms state-of-the-art LSM-based solutions by up to 4.32x for read operations and 1.43x for writes. The system demonstrates robust performance across different data distributions, access patterns, and storage media including both SSDs and HDDs.

cs.DB↗

arXiv2025

BLI: A High-performance Bucket-based Learned Index with Concurrency Support

Learned indexes are promising to replace traditional tree-based indexes. They typically employ machine learning models to efficiently predict target positions in strictly sorted linear arrays. However, the strict sorted order 1) significantly increases insertion overhead, 2) makes it challenging to support lock-free concurrency, and 3) harms in-node lookup/insertion efficiency due to model inaccuracy.\ In this paper, we introduce a \textit{Bucket-based Learned Index (BLI)}, which is an updatable in-memory learned index that adopts a "globally sorted, locally unsorted" approach by replacing linear sorted arrays with \textit{Buckets}. BLI optimizes the insertion throughput by only sorting Buckets, not the key-value pairs within a Bucket. BLI strategically balances three critical performance metrics: tree fanouts, lookup/insert latency for inner nodes, lookup/insert latency for leaf nodes, and memory consumption. To minimize maintenance costs, BLI performs lightweight bulk loading, insert, node scaling, node split, model retraining, and node merging adaptively. BLI supports lock-free concurrency thanks to the unsorted design with Buckets. Our results show that BLI achieves up to 2.21x better throughput than state-of-the-art learned indexes, with up to 3.91x gains under multi-threaded conditions.

cs.DB↗