arXiv subjects

Enhan Zhao

Publications and source records attributed to Enhan Zhao.

4 recordsLinked to original sources

arXiv2026

Generic Nullity of Generalized Commutators

We study the generic nullity of generalized commutator operators \[L_{\mathbf{A}}(X)=s_{k+1}(A_1,\cdots,A_k,X)\] on matrix algebras, where $s_{k+1}$ denotes the standard polynomial. Dixon and Pressman conjectured an explicit formula for the generic nullity of $L_{\mathbf{A}}$, and Brassil and Reichstein proved the conjecture when $k$ is even. In this paper, we settle the remaining case where $k$ is odd. Our proof first treats the boundary cases $k=2n-3$ in dimensions $n$ and $n+1$ using degree decompositions and graph-theoretic interpretations of alternating trace forms, and then establishes a dimension-extension argument from $n$ to $n+2$. Consequently, together with the result of Brassil and Reichstein, we obtain a complete proof of the Dixon-Pressman generic nullity conjecture over any field of characteristic zero.

math.RA↗

arXiv2026

Ouroboros-Spatial: Closing the Data-Model Loop for Spatial Reasoning

Spatial reasoning remains a persistent challenge for multimodal large language models (MLLMs). Existing approaches largely rely on large-scale, statically curated datasets, where all training samples are treated uniformly regardless of the model's evolving capabilities. This static paradigm is inherently data-inefficient: training capacity is often spent on samples that are either trivial or overly difficult for the model at its current stage. To address this limitation, we propose Ouroboros-Spatial, a self-evolving training framework in which the model plays dual roles as a proposer and a solver. In each iteration, a frozen proposer generates spatial question-answer (QA) pairs from 3D scene metadata and raw video frames, together with executable code for deriving reliable ground truth. A learnable solver is then fine-tuned on the accepted samples, and its per-sample prediction confidence is used as a difficulty signal. This signal is fed back to the proposer in the next iteration, guiding it to generate questions better matched to the solver's current capabilities. Through this closed-loop design, the training distribution co-evolves with model ability, reducing redundant trivial examples while filtering out ambiguous or uninformative samples with limited learning value. Across six spatial reasoning benchmarks, Ouroboros-Spatial substantially improves Qwen3-VL-4B and Qwen3-VL-8B while using an order of magnitude fewer training examples than recent large-scale curated datasets. On VSI-Bench, it yields absolute gains of 9.9 and 6.8 points for the 4B and 8B models, respectively, enabling both to outperform a wide range of strong open-source and proprietary baselines.

cs.CV↗

arXiv2026

SWE-MiniSandbox: Container-Free Reinforcement Learning for Building Software Engineering Agents

Reinforcement learning (RL) has become a key paradigm for training software engineering (SWE) agents, but existing pipelines typically rely on per-task containers for isolation. At scale, pre-built container images incur substantial storage overhead, slow environment setup, and require container-management privileges. We propose SWE-MiniSandbox, a lightweight, container-free method that enables scalable RL training of SWE agents without sacrificing isolation. Instead of relying on per-instance containers, SWE-MiniSandbox executes each task in an isolated workspace backed by kernel-level mechanisms, substantially reducing system overhead. It leverages lightweight environment pre-caching techniques to eliminate the need for bulky container images. As a result, our approach lowers disk usage to approximately 5\% of that required by container-based pipelines and reduces environment preparation time to about 25\% of the container baseline. Empirical results demonstrate that SWE-MiniSandbox achieves evaluation performance comparable to standard container-based pipelines. By removing the dependency on heavy container infrastructure, SWE-MiniSandbox offers a practical and accessible foundation for scaling RL-based SWE agents, particularly in resource-constrained research environments.

cs.SE↗

arXiv2022

A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics

A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics is proposed and validated using high-temperature auto-ignitions, perfectly stirred reactors (PSR), and one-dimensional freely propagating flames of n-heptane/air mixtures. The mechanism reduction is modeled as an optimization problem on Boolean space, where a Boolean vector, each entry corresponding to a species, represents a reduced mechanism. The optimization goal is to minimize the reduced mechanism size given the error tolerance of a group of pre-selected benchmark quantities. The key idea of the DeePMR is to employ a deep neural network (DNN) to formulate the objective function in the optimization problem. In order to explore high dimensional Boolean space efficiently, an iterative DNN-assisted data sampling and DNN training procedure are implemented. The results show that DNN-assistance improves sampling efficiency significantly, selecting only $10^5$ samples out of $10^{34}$ possible samples for DNN to achieve sufficient accuracy. The results demonstrate the capability of the DNN to recognize key species and reasonably predict reduced mechanism performance. The well-trained DNN guarantees the optimal reduced mechanism by solving an inverse optimization problem. By comparing ignition delay times, laminar flame speeds, temperatures in PSRs, the resulting skeletal mechanism has fewer species (45 species) but the same level of accuracy as the skeletal mechanism (56 species) obtained by the Path Flux Analysis (PFA) method. In addition, the skeletal mechanism can be further reduced to 28 species if only considering atmospheric, near-stoichiometric conditions (equivalence ratio between 0.6 and 1.2). The DeePMR provides an innovative way to perform model reduction and demonstrates the great potential of data-driven methods in the combustion area.

cs.LG↗