#01Oct 16, 2026
cs.LG
LagNet: Lag-Structured Operators for Long-Term Time Series Forecasting
Zhenan Yu, Guangxin Jiang, Jiuyun Jiang and 1 more
Long-term time series forecasting maps a finite history window to an extended future horizon. Many existing models focus primarily on the design of input representations and model structures, while paying less attention to the structural form of the history-to-future forecasting operator itself. We examine this operator directly and find that, across model families, sensitivity matrices exhibit recurring diagonal patterns whose diagonals correspond to relative temporal lags. Motivated by this observation, we develop a framework for direct multi-step forecasting based on lag-structured temporal operators. Its basic building block, LagLayer, constructs a Toeplitz matrix by tying history-to-future connections with the same relative lag and incorporates horizon-wise and history-wise scaling coefficients to relax exact sharing. This design enables LagLayer to serve as an effective replacement for temporal linear layers in existing forecasting models. Stacking LagLayer modules with activations and multiple feature maps yields LagNet. Experiments on long-term time series forecasting benchmarks show that our method is competitive with strong baselines, while sensitivity matrix diagnostics and limited-data experiments demonstrate that LagLayer provides an effective and sample-efficient alternative to a linear layer.
#02Oct 16, 2026
cs.LG
Escaping Parameter Space: Tight Generalization Bounds via Representation Quality
Niclas Göring, Shuofeng Zhang, Branton DeMoss and 1 more
We derive a tight generalization bound for deterministic neural We derive a tight generalization bound for deterministic neural networks based on their last hidden layer representations. By evaluating representation quality with a parameter-free $k$-nearest-neighbor ($k$-NN) classifier, our certificate avoids traditional parameter-space complexity measures, KL divergences to a posterior, weight norms, and compression. The bound is tight: trained from scratch, it reaches an 8.0 percentage point gap to test error on CIFAR-10 (ResNet-18) and yields the first non-vacuous certificates we are aware of on CIFAR-100; with frozen DINOv2 representations, it certifies at 1.4\% on CIFAR-10 and 23.1\% on 1,000-class ImageNet. It decomposes additively into three empirical, independently measurable quantities: local class geometry ($k$-NN decoder error), decoder-network agreement, and training stability. This allows the bound to act as a diagnostic tool: we demonstrate that actively destroying local class geometry eliminates generalization while leaving dataset memorization intact, identifying class geometry as a causally relevant mechanism for generalization. Finally, we show that learned representations are significantly less sensitive to weight noise than linear readouts, suggesting why parameter-space certificates often struggle to remain tight.
#03Oct 16, 2026
cs.LG
CocoRNA: Collective RNA Design with Cooperative Multi-agent Reinforcement Learning
Tianmeng Hu, Biao Luo, Ke Li
Designing RNA sequences that reliably fold into specific secondary structures is essential for understanding their biological functions but remains a challenging computational problem. We propose CocoRNA, a cooperative multi-agent reinforcement learning framework for RNA inverse design. CocoRNA simplifies the design task by decomposing it into smaller sub-problems, each solved collaboratively by multiple agents. This approach reduces the complexity of the problem and improves the exploration of design policies. During training, a centralized critic uses global structural information to guide the agents, enabling them to jointly optimize their design strategies. As a result, CocoRNA learns high-quality RNA design policies that generalize effectively to unseen structures without additional training. Experiments on the Rfam dataset demonstrate that CocoRNA substantially outperforms state-of-the-art methods in both success rate and design speed. Further experiments on other biological sequence design tasks highlight the effectiveness and broad potential of CocoRNA for complex design tasks.
#04Oct 16, 2026
cs.LG
Logic-Guided Graph Denoising Diffusion Models
Samuel Cognolato, Luciano Serafini, Alessandro Sperduti and 1 more
Graph diffusion models are competitive approaches for generating complex graph-structured data. However, when such distributions have strict structural constraints, diffusion models may fail to capture them exactly, resulting in the generation of invalid graphs. In this paper, we propose a method for grounding graph diffusion models in domain-specific knowledge via First Order Logic (FOL), leveraging its expressive and interpretable formalism to impose structural constraints on the generative process. We incorporate domain knowledge using classifier guidance, a technique that conditions the diffusion model's distribution on external variables to exert control over the sampled data. During the generative process, classifier guidance steers the denoising trajectory to optimize an objective function, which we define as a fuzzy and differentiable relaxation of the logical rules. Our methodology requires only the specification of constraints in FOL, whose satisfaction is encouraged at inference time to guide a pre-trained generative model. We evaluate our approach by comparing the unconditional generation of knowledge graphs with our logic-guided framework, which incorporates domain ontologies as structural constraints during inference. This approach significantly increases the proportion of generated graphs that satisfy the ontological constraints.
#05Oct 16, 2026
nlin.CD
From Flow-Box Invariants to Global Conservation Laws: Machine Learning-Assisted Detection of Singularities and Near-Integrability
Jimmie Adriazola, Ioannis G. Kevrekidis, Panayotis G. Kevrekidis and 1 more
Conservation laws reveal invariant structure in dynamical systems and constrain their evolution to lower-dimensional level sets. Locally, however, per the flow-box theorem, every $d$-dimensional system generically admits $d-1$ functionally independent conservation laws near a regular point even though, generically, only a few such laws persist globally. Data-driven methods typically learn conservation laws on a prescribed region of phase space from which training samples are drawn, leaving their behavior beyond that region unresolved. We formulate this local-to-global continuation problem and develop an {expanding-domain neural deflation} framework that tracks the number of independent conservation laws over nested domains. The method recovers the expected $d-1$ local invariants and detects their successive breakdown as the domain expands, relaxing to the expected global conservation law limit. It distinguishes the local invariants (associated with Frobenius integrability) from persistent global structure and shows that the domain scale over which additional laws survive reflects proximity to Liouville integrability. Pointwise losses can localize isolated obstructions, whereas in more complicated dynamics the breakdown of our loss functions is gradual and spatially diffuse. The framework thus provides a data-driven approach for studying the persistence and breakdown of (so-far-learned) conservation laws across phase space.