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arXiv

Agentic Router: An Execution-Grounded Continual Learning Approach With Memory

Yuxuan Chen, Rongpeng Li, Zhifeng Zhao, Yuntao Liu, Xing Xu, Honggang Zhang

Large language model (LLM) agents provide a promising interface for command-line-based network operations, but a plausible command may still fail or introduce operational risk after execution. Existing approaches mainly focus on command generation or final configuration correctness, and do not use execution-grounded experience to jointly improve candidate coverage and action selection. We propose an execution-grounded dual-path consequence-aware agent for CLI-based SONiC operations, which generates multiple complete actions, predicts their execution consequences, and selects the final action through utility- and risk-aware reranking. The proposal-side path abstracts reusable operational lessons into retrievable guidance to improve feasible-action coverage without modifying the proposal LLM, while the selection-side path adapts the consequence predictor through session-level LoRA updates using real SSH feedback to improve conditional selection quality. Experiments over multi-turn SONiC operation sessions with different Qwen3 proposal models show that the framework improves feasible-action coverage and top-1 execution success, and that the two adaptation paths provide complementary gains over interaction.

arXiv

From Relevance to Execution Utility: Reward-Aware Dynamic Execution Gating for Skill-Based LLM Agents

Liang He, Jingbo Wen, Hongyu Gu, Hao Li, Haoyu Wang, Yixiong Chen, Kangning Cui, Xilu Wang

Agent skills are increasingly used to equip large language model (LLM) agents with reusable procedural knowledge. Although recent work has substantially improved skill retrieval due to the increasing skill libraries, retrieving a plausible skill bundle does not guarantee that executing it is worthwhile. Since every skill-conditioned rollout is computationally expensive, deciding whether a retrieved bundle should be executed has become an increasingly important challenge. To this end, we introduce the Reward-Aware Dynamic Execution Gate (RADEG), a lightweight, retriever-agnostic decision layer between skill retrieval and agent execution. RADEG learns a low-cost surrogate model that predicts the execution utility of a query--bundle pair before the expensive rollout is launched. To obtain informative supervision while controlling for task difficulty, we locally perturb each retrieved bundle by deleting, adding, or replacing one skill, producing matched same-query rollouts that isolate the effect of bundle composition on verifier reward. During deployment, RADEG updates only a warm-started logistic head as new verifier feedback becomes available, enabling inexpensive adaptation of the execute/skip boundary without retraining either the retriever or the agent. Under a query-level held-out evaluation on 288 collected rollouts, RADEG substantially reduces unnecessary agent executions while preserving a large fraction of the downstream verifier reward. It consistently outperforms relevance-based and random gating across different execution budgets, demonstrating that execution-aware surrogate modeling provides a practical and cost-effective complement to skill retrieval.

arXiv

From Inaudible Inputs to Model Failures: Low-Frequency Safety Risks in LALMs

Yuanhe Zhang, Weiliu Wang, Jie Ren, Liang Lin, Zhenhong Zhou, Haoran Gao, Kun Wang, Chen Li, Li Sun, Sen Su

Large audio-language models (LALMs) have demonstrated strong capabilities in understanding diverse audio inputs. This diversity includes low-frequency signals that are inaudible to humans but can still enter the model and influence its generation. However, the practical impact of such low-frequency inputs on LALMs remains largely unexplored. In this paper, we propose Intermittent Low-Frequency Lockout (ILL), an inaudible red teaming method that evaluates this risk using a universal waveform template in a black box setting. ILL uses Sentence Attention Scale Estimation to determine active intervals and Frequency Confusion Transfer to construct a low-frequency waveform with continuous phase from corpus spectral variation. To mitigate this risk, we propose Distributional Requery Guard (DRG) to detect low-frequency distribution shifts and conditionally request a second recording for semantic recovery. Across six LALMs and multiple audio understanding tasks, ILL reduces accuracy by up to 67 percentage points while receiving a mean human audibility rating of 1.33, close to 1.17 for clean audio; DRG raises mean attacked accuracy from 28.5\% to 46.1\% after clean reacquisition. These findings identify a previously overlooked safety risk for LALMs and provide a foundation for future research on robust audio understanding.

arXiv

Stochastic Emulation of a Fully Coupled Preindustrial E3SMv3 Simulation

Elynn Wu, James P. C. Duncan, Troy Arcomano, Jeremy McGibbon, Oliver Watt-Meyer, Christopher S. Bretherton, Naser Mahfouz, Claudia Tebaldi, Luke Van Roekel, Andrew Roberts, Wuyin Lin, Finn Rebassoo, Jean-Christophe Golaz, Peter M. Caldwell

We present a stochastic coupled emulator of E3SM version 3, built on the SamudrACE framework, which couples an atmosphere emulator (ACE2) with a full-depth ocean emulator (Samudra). We replace the deterministic atmosphere emulator with its stochastic counterpart, ACE2S, and fine-tune the coupled system with a probabilistic objective, so that the atmosphere acts as a source of internal variability for the ocean. Trained on 105 years of a pre-industrial control simulation and evaluated on an independent 400 years, the emulator reproduces E3SMv3's mean climate state with biases much smaller than existing model-to-observation differences. Relative to a deterministic baseline, stochastic training maintains internal variability across timescales, most notably in the ENSO power spectrum, eddy-rich SST anomalies, and sea ice variability in the marginal ice zone. The emulator captures daily precipitation accurately up to the 99.99th percentile, but underestimates the rarest tropical extremes. These results show that stochastic coupled emulators can reproduce long-timescale variability with high fidelity, while extrapolation to unseen extremes remains a key challenge.

arXiv

ChronoState: Hidden Elapsed-Time Conditioning for Temporal-State Action Selection in Frozen-Backbone Language Models

Sam Siavoshian, Omar Ramadan, Amir K. Saeed, Benjamin A. Johnson, Amin Mohamed El-Amin Diab, Benjamin M. Rodriguez

Temporal decisions in language-model systems often depend on both symbolic task state and elapsed wall-clock time, such as cache expiration, job completion, quota resets, deadlines, or stale sessions. We study whether elapsed time can be supplied as a non-token, system-side scalar and composed with visible symbolic state by a frozen-backbone language model. We introduce ChronoState, a compositional temporal-state benchmark in which symbolic state appears in the prompt, elapsed seconds tau are supplied through a hidden chronometric-injection channel, and the model selects a forced-choice temporal action. Here, "hidden" means hidden from the user-visible token sequence, not from model computation. Using Qwen2.5-3B-Instruct as a frozen bf16 backbone with a 31-dimensional sinusoidal-plus-log time encoding, gated FiLM residual modulation, and a rank-8 LoRA action surface, hidden-time CI reaches 0.9305 +/- 0.0134 accuracy and 0.9410 +/- 0.0103 balanced accuracy. No-time and shuffled-time controls fall to 0.5511 +/- 0.0042 and 0.3323 +/- 0.0097, respectively, with high shuffled-time wrong-state consistency supporting causal dependence on the injected scalar within the trained distribution. Generalization remains strong for held-out templates, durations, and multi-constraint compositions, but held-out quota-family transfer is weak at 0.5065 +/- 0.0559, while a fair prompt+LoRA timestamp baseline reaches 0.9893 +/- 0.0052. Thus, ChronoState supports a narrow conclusion: hidden elapsed time can be composed with symbolic task state under direct supervision, but does not establish autonomous time tracking, broad unseen-family abstraction, or superiority over prompt-injected timestamps.

arXiv

BreastMammo and DenseMammo: Benchmarks for Mammography Domain Generalization

Hongyi Pan, Gorkem Durak, Halil Ertugrul Aktas, Andrea Mia Bejar, Mustafa Ege Seker, Nebile Alibeyoglu, Rumeysa Guclu, Rana Gunoz Comert Bozkurt, Sibel Ozkan Gurdal, Neslihan Cabioglu, Beyza Ozcinar, Ravza Yilmaz, Vahit Ozmen, Erkin Aribal, Sukru Mehmet Erturk, Yalda Zafari, Mohamed Mabrok, Kayhan Batmanghelich, Mohammad Yaqub, Ziyue Xu, Ulas Bagci

Breast density classification is a critical component of breast cancer risk assessment, yet AI models often struggle to generalize across clinical sites due to vendor-specific acquisition styles. In this work, we introduce two new datasets, BreastMammo and DenseMammo, to facilitate robust multi-view mammography research. We propose a domain generalization framework that utilizes a foreground-only histogram matching protocol to resolve the domain shift issue arising from disparate clinical sources. Internal evaluation using a 5-fold cross-validation protocol demonstrates the efficacy of our approach, with the Swin Transformer backbone achieving a peak AUC of 98.32% for density classification. External evaluation on the TNMammo and LUMINA datasets demonstrates that the proposed approach consistently reduces domain shift, significantly outperforming prominent domain generalization paradigms, including MixStyle and Discrete-Fourier-Transform-based frameworks.

arXiv

Toward Human Rights Benchmarking for LLMs: A Pilot Methodology

Savannah Thais, Wm. Matthew Kennedy, Abhigyan Acherjee, Matilda Wysocki, Malcolm Langford, Caitlin Kraft Buchman

Large language models (LLMs) increasingly mediate legal determinations over what human rights are realized, and how. Yet, no evaluation benchmark exists to assess whether they can reason correctly about human rights law. To this end, we report our efforts to develop a robust and scalable methodology for creating HumRightsBench: the first expert-validated, scenario-based benchmark for evaluating reasoning grounded in the obligation structure of international human rights law. We adapt the IRAC framework for legal reasoning to better suit the unique reasoning patterns of human rights work (substituting P, "proposing remedies," for C, "legal conclusion," yielding IRAP) to structure our evaluation heuristics. We also produce a pilot series of authentic scenarios designed to implicate the many dimensions of real-world human rights issues and annotated by human rights lawyers and professionals across the world. Ultimately, we find that model accuracy scores range considerably across legal reasoning tasks (overall model performance ranges from 0.339 to 0.577, task min-max ranges from 0.025 to 0.774), which strongly implies that HumRightsBench is a capable instrument for advancing this emerging subfield of AI evaluations science at a critical moment in its evolution.

arXiv

CRHT: A Continuous Regression Hybrid Transformer for Vessel Trajectory Prediction with Online Cluster Sampling

Alexander Schiøtz, Bertram Hage, Christian Rand, Felix Thomsen, Peder Heiselberg

Accurate vessel trajectory prediction is critical for maritime safety and anomaly detection, yet existing models often struggle with geographic bias and navigational realism. We propose the Continuous Regression Hybrid Transformer (CRHT), a deep learning framework designed to forecast vessel motion using Automatic Identification System (AIS) data. To mitigate spatial data imbalance, we introduce an online K-means cluster sampling strategy that ensures diverse exposure to rare maneuvers during training. Our hybrid architecture integrates 1D convolutional layers for local kinematic feature extraction with a multi-head attention mechanism for global temporal context. CRHT demonstrates superior performance in short-term forecasting, achieving the lowest errors at the 1-hour horizon. The results demonstrate that while discrete models provide high navigational stability over long horizons, CRHT offers an optimal balance of precision and maneuver tracking for real-time maritime surveillance.

arXiv

RISE-RL: Rubric-Informed Selective Exploration for Open-Ended Reinforcement Learning

Jinkun Hou, Zhuo Liu, Huimin Ren, Hongsheng Xin, Pan Zhou, Kun Zhan

Aligning Large Language Models (LLMs) for open-ended tasks is challenging because responses must satisfy multidimensional criteria without following a single correct generation trajectory. Existing rubric-based reinforcement learning (RL) methods compress fine-grained criterion-level feedback into scalar rewards, making persistent capability gaps difficult to target under limited on-policy exploration. We propose $\textbf{RISE-RL}$ (Rubric-Informed Selective Exploration), which uses repeatedly missed rubric criteria to elicit privileged trajectories that are difficult to discover through unguided exploration alone. RISE-RL retains only trajectories whose complete-rubric reward exceeds the mean reward of natural rollouts, and then re-evaluates them under the original prompt to emphasize behaviors that remain weakly supported by the natural policy. The resulting guidance signal is optimized through a separate auxiliary objective and removed once its additional benefit diminishes. Experiments with 4B and 14B models across writing, chat, health, and science show that RISE-RL achieves the highest mean score on every evaluated benchmark under guidance-free evaluation. Compared with standard Rubric-RL, it improves the average score by 1.3 points at the 4B scale and $\textbf{3.3 points at the 14B scale}$, including a $\textbf{6.0-point}$ gain on CreativeWriting-V3. It also improves creative-writing diversity and yields gains on objectively scored medical and scientific benchmarks. These results indicate that selective internalization through reward filtering and policy support shaping is effective for open-ended reinforcement learning.

arXiv

MELLON - Multimodal Enhanced LLM for Online Navigation

Ruiyu Li, Haoyang Cai, Zhitong Guo, Tong Hu

Web navigation agents are capable of addressing various types of tasks on different websites. Current baselines on web navigation are either unimodal or lack strong reasoning abilities given multimodal inputs. Focusing on the WebShop benchmark, a real-world website simulation, we explore the alignment of text and images, as well as multimodal reasoning and planning abilities, to enhance the performance of web navigation agents. We propose three innovative multimodal enhancements: Multimodal Enhanced LLM for Online Navigation (MELLON), VQAgent, and Multimodal Ranker. MELLON demonstrates a significant improvement in task completion accuracy, with a 9.26% increase after just one epoch of training. Our findings suggest the necessity of further exploration into multimodal approaches, with a focus on more extensive training and alignment strategies to enhance the effectiveness of web navigation agents.

arXiv

Motif 3: Technical Report

Junghwan Lim, Joon Son Chung, Sungmin Lee, Wai Ting Cheung, Gihun Cho, Minsu Ha, Sangho Kang, Beomgyu Kim, Dongseok Kim, Jangwoong Kim, Taehyun Kim, Taewhan Kim, Jeesoo Lee, Jeongdoo Lee, Junhyeok Lee, Dongpin Oh, Hyeyeon Cho, Dahye Choi, Jaeheui Her, Hanbin Jung, Changjin Kang, Minjae Kim, Youngrok Kim, Hyukjin Kweon, Hongjoo Lee, Yeongjae Park, Bokki Ryu

We introduce Motif 3, a decoder-only Mixture-of-Experts language model with 314 billion total parameters and 13.2 billion activated per token. Each sparse MoE layer contains 384 routed experts, with eight selected per token. This fine-grained sparsity provides substantial expert capacity while limiting computation. Motif 3 is built around Grouped Differential Latent Attention (GDLA), which integrates grouped differential attention with the compressed key-value representation of Multi-head Latent Attention. The architecture further incorporates modified manifold-constrained hyper-connections, Expert Specific PolyNorm activations, and multi-token prediction to improve optimization stability, expert specialization, and inference efficiency. We pretrain Motif 3 on approximately 12.5 trillion tokens spanning web documents, STEM, code, mathematics, multilingual content, and domain-specialized corpora. Expert-balancing and numerical-stabilization techniques support stable training at scale, while selective MXFP8 computation and communication, memory-efficient fused kernels, and window-aware context parallelism enable training with context lengths up to 256K tokens. Our post-training pipeline combines general supervised fine-tuning, six specialist teachers trained with reinforcement learning, a software-engineering teacher trained with supervised fine-tuning, and Multi-teacher On-Policy Distillation. The resulting unified model consolidates complementary capabilities in reasoning, coding, tool use, professional work, long-context understanding, calibrated abstention, and instruction following. Across a broad evaluation suite, Motif 3 demonstrates competitive performance against leading open weight models, including strong results on long-horizon agentic tasks, mathematical reasoning, scientific knowledge, and hallucination-sensitive evaluation.

arXiv

STCAD: Scalable Trajectory Clustering and Anomaly Detection on Terabyte-Scale AIS Data

Bertram Hage, Alexander Schiøtz, Felix Thomsen, Christian Rand, Peder Heiselberg

We present a scalable framework for unsupervised clustering of maritime trajectories derived from terabyte-scale Automatic Identification System (AIS) archives. Variable-length trajectories are encoded with a custom BERT-based model trained via masked token modeling and clustered using CURE hierarchical clustering, producing physically interpretable trajectory groups without requiring a predefined number of clusters. An intrinsic unsupervised anomaly detection method based on reconstruction loss and clustering noise assignment identifies irregular navigation patterns. The framework is demonstrated on a national-scale AIS dataset comprising billions of messages spanning one year, yielding stable trajectory clusters and a clear separation between nominal and anomalous vessel behavior.

arXiv

DualSpectralCF: Training-Free Sign-Aware Spectral Collaborative Filtering

Guanqun Yang, Tong Qi, Xiaoxue Han

Real-world recommendation platforms routinely collect explicit negative feedback such as 1-star reviews, hate-button clicks, distrust between users, and very-low watch-ratio videos. Learned sign-aware recommenders exploit this signal for clear accuracy gains, but only at the cost of gradient-based training. In parallel, a line of training-free spectral collaborative filtering methods matches or beats learned graph recommenders at a fraction of the cost, yet operates on positive interactions alone. We bridge these two lines with DualSpectralCF, a training-free framework of two components that attach to any spectral backbone of the form $\hat{\mathbf{r}}_u = F(\mathbf{M}) \mathbf{r}_u$: a signed input signal $\mathbf{r}_u^{\pm}$ that encodes the user's explicit dislikes, and a signed item-item operator $\mathbf{M}^{\pm}$ that blends like-together and dislike-together similarity. The framework is backbone-agnostic and adds just two scalar hyperparameters. We instantiate DualSpectralCF on ChebyCF, GF-CF, and Turbo-CF, and evaluate on five sign-aware benchmarks: every instance matches or beats its unsigned backbone on all 5 datasets, with Recall@20 lifts up to +32.6% with backbone-specific $(γ, κ)$ tuning and +1.9% to +16.0% for DualSpectralCF-Cheby at the fixed default $(γ= -0.5, κ= 0.1)$, and the family runs 7.7 to 155.3$\times$ faster than SIGformer while reaching 70.7% to 90.7% of its accuracy. Sign-awareness helps most for cold-start users, with up to +29.2% Recall@20 on Epinions users with 1 to 5 training items.

arXiv

A Graph Neural Network--Guided Genetic Algorithm for Physical Internet Supply Chain Optimization under Cost Uncertainty

Faezeh Ardali, Gerald M. Knapp

Inventory and distribution planning in Physical Internet networks requires coordinating factory-hub assignments, factory supply, lateral transshipment among collaborative hubs, retailer deliveries, and shortages. The problem combines discrete assignment decisions with interdependent continuous flows, while uncertain operating costs make robust planning more difficult. This study formulates deterministic and min-max regret models for a three-echelon network of factories, hubs, and retailers and develops a graph neural network-guided genetic algorithm (GNN-GA) for the assignment decisions. The GNN estimates hub-specific factory-selection probabilities that are used to construct the initial GA population and adapt mutation according to prediction uncertainty. Each previously unseen candidate assignment is evaluated by solving the remaining continuous-flow problem to LP optimality. Simulated annealing, a standard GA, and GNN-GA are compared on 15 instances using matched random seeds and fixed limits on distinct assignment evaluations. Because the evaluation budgets for test Instances 13-15 are smaller than the nominal population size, these experiments primarily assess the quality of learned initialization rather than multi-generation evolutionary search. A separate 400-evaluation experiment on exact test Instance 13 permits three complete offspring generations and a partial fourth pass, with GNN-GA outperforming GA in all 10 matched runs. Three independently generated exact-solvable instances provide a separate test of transfer. Ablation results show that learned initialization provides most of the improvement, while entropy-guided mutation has a smaller, instance-dependent effect. Per-instance solution times include GNN inference and search but exclude model training and one-time model setup.

arXiv

RAVEN-Eval: Rubric-Guided Automatic Evaluation for AI Video Generation Models Based on LMM Preference Judgement

Ziheng Jia, Jiaying Qian, Zicheng Zhang, Xiaorong Zhu, Lancheng Gao, Xiongkuo Min

AI video generation has advanced rapidly and entered widespread commercial use. As a result, quality differences among videos produced by state-of-the-art AI video generation models~(AIVGMs) have become increasingly difficult to discern using conventional evaluation criteria, such as visual fidelity and semantic instruction following. Meanwhile, human evaluation now requires more expertise and sustained attention, substantially increasing annotation costs. This calls for automated evaluation that can reliably distinguish fine-grained differences among advanced AIVGMs with minimal human intervention. To address this challenge, we present RAVEN-Eval, a rubric-guided automated evaluation framework for AIVGMs, built primarily on the LMM-as-a-judge paradigm. Through an automatic task curation and quality-filtering pipeline, RAVEN-Eval curates 150 text-to-video~(T2V) tasks and 100 image-to-video~(I2V) tasks, and systematically collects more than 4,500 AIGVs. At its core, RAVEN-Eval adopts rubric-guided automated LMM preference judgement, in which LMM judges conduct pairwise comparisons according to task-specific rubrics. It further introduces an anchor-based model insertion approach to reduce the evaluation cost of incorporating new models. Finally, we evaluate 20 high-performance AIVGMs, as well as the judging capabilities of 13 LMM judges, and establish the RAVEN-Eval Leaderboards. Overall, RAVEN-Eval paves a scalable path for automatic and trustworthy evaluation of rapidly evolving AIVGMs.

arXiv

Different Feedback, Different Updates: Selective Self-Learning from User Interactions for Large Language Models

Xuanchen Li, Haitao Li, Yujia Zhou, Qingyi Pan, Heng Wang, Yiqun Liu, Min Zhang, Qingyao Ai

User feedback offers natural supervision for persistent LLM improvement, but a single message may support multiple behavioral changes with different scopes of generalization. We introduce SLIFT, a selective self-learning framework built on a task-relative view of user feedback. SLIFT decomposes each feedback message into atomic components and interprets each component relative to the original task as Fix, Spec, or Null: requirements for task validity, compatible condition-specific refinements, or content with no reliable positive update direction. To incorporate each change at the appropriate scope, SLIFT trains two complementary LoRA adapters on a shared frozen backbone: a Generalist that consolidates Fix requirements into default behavior through feedback-conditioned self-distillation, and a Specialist that observes only the task and Generalist response to supply residual guidance for applicable, unmet Spec refinements. Null components induce no positive update. Across backbones, SLIFT achieves strong performance on both MemoryBench and WildFB, with targeted analyses further examining its underlying mechanisms. We release our code at https://anonymous.4open.science/r/SLIFT.

arXiv

Who Bridges Safety? Identifying and Targeting Cross-Lingual Shared Safety Pathways

Shuyi Miao, Wangjie Qiu, Pengyang Shao, Canran Xiao, Fei Shen, Zhiming Zheng, Tat-Seng Chua

Uncovering the internal mechanisms underlying the safety capabilities of large language models (LLMs) is crucial for developing trustworthy artificial intelligence. Currently, mechanistic interpretability studies on multilingual safety are largely confined to local components, such as isolated neurons. However, this static and fragmented perspective overlooks the synergy among components and fails to elucidate how safety signals dynamically propagate within the model to drive safety decisions ultimately. In this work, we move beyond isolated neurons to identify and target the cross-layer functional pathways formed during safety signal propagation, thereby uncovering the mechanisms driving the cross-lingual safety gap. Specifically, we first identify monolingual safety pathways and validate their impact on refusing harmful requests. Subsequent cross-lingual analyses reveal a sparse subset of cross-lingual shared safety pathways, confirming that this intersection acts as the internal bridge transferring safety capabilities from high-resource (HR) languages to non-high-resource (NHR) languages. Building on these mechanistic findings, we propose a pathways-targeted alignment method based on the cross-lingual shared safety pathways. Experimental results show that updating only a small fraction of pathway parameters significantly improves safety in NHR languages while largely preserving the model's general capabilities.

arXiv

Sequential Modality Dropout for Robust Multi-Modal Sequential Recommendation

Guanqun Yang, Wenlong Zhang

Multi-modal sequential recommenders assume every item carries every modality, but real product catalogs often miss images or text, and a model trained on complete data loses much of its recommendation accuracy when a modality is unavailable at serving time. We propose Sequential Modality Dropout (SMD): during training, each modality stream (image and text) is independently erased with probability p for an entire user interaction history, so the model learns to predict the next item without relying on any single modality. We measure robustness by retention, the fraction of a model's full-modality accuracy (HR@10) that survives when a modality is removed at test time. Across four backbones (MM-SASRec, IISAN, MISSRec, and fMRLRec) on four Amazon domains, SMD raises text retention by 1.0 to 3.2x at essentially no cost to full-modality accuracy; under an extreme 95% per-item missing rate, it retains 61% of HR@10 versus 22% without (a 2.8x improvement). An optional cross-modal reconstruction loss further lifts retention from 90% to 98% on a simple additive backbone under severe text missingness. SMD is a four-line, architecture-agnostic change that makes multi-modal sequential recommenders robust to the missing modalities they actually encounter in deployment.

arXiv

A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim Tewe

Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks. We evaluate this prior under a controlled protocol in which an HNN and a parameter-matched feedforward baseline are trained on the same RK4-generated trajectories, use the same central-difference derivative targets and optimization settings, and are integrated at inference with the same RK4 scheme. Results are reported over five independent training seeds. On the nonlinear pendulum, the HNN reduces mean energy drift by 42-fold and mean trajectory MSE by 15.8-fold at T = 100, approximately 16 pendulum periods. Its energy drift also remains bounded and exhibits substantially lower seed-to-seed variability than the standard-network baseline. An energy-stratified analysis shows that the difference becomes more pronounced as trajectories explore more nonlinear regions of phase space. As an additional diagnostic, we examine an explicit Störmer--Verlet-style rollout of the learned HNN. Because the learned Hamiltonian is not constrained to the separable form H(q,p) = T(p) + V(q), the standard symplecticity guarantee of velocity Verlet does not directly apply. We further apply the same matched-integrator protocol to the three-dimensional Kepler two-body problem. The HNN again exhibits lower trajectory, energy, and angular-momentum drift than the parameter-matched baseline. These experiments provide a controlled study of how Hamiltonian parameterization affects long-horizon prediction and physical consistency across two conservative dynamical systems.

arXiv

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics

Petr Badolia, Leonid Obukhov, Dmitry Bylinkin, Aleksandr Beznosikov

Operator learning is a rapidly advancing area of computational science. It is particularly well suited to problems where a partial differential equation (PDE) must be solved repeatedly under varying physical configurations. Most existing architectures represent the solution operator in a fixed basis. While this assumption is well aligned with global structures, it is less suitable for phenomena governed by local interactions in physical space. We explore an alternative perspective motivated by the observation that the continuum limit of coupled oscillator systems can describe a broad class of PDEs. Building on this idea, we introduce the Kuramoto Neural Operator (KNO), which represents the solution through the evolution of a latent field of interacting oscillators. Across a diverse collection of PDE benchmarks, KNO achieves strong predictive performance, with improvements over competing approaches. Our experimental evaluation also includes an extensive ablation study that quantifies the contribution of each architectural component incorporated into KNO. Furthermore, we show that the model's prediction error is closely linked to the collective dynamics of the latent oscillators. It varies systematically with their degree of synchronization, providing insights into the underlying mechanisms.

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