arXiv:2506.06454v2 Announce Type: cross Abstract: Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

arXiv:2510.15514v3 Announce Type: replace Abstract: Reinforcement Learning from AI Feedback (RLAIF) relies on LLM judges as preference measurement instruments, yet these instruments are fundamentally limited by random measurement errors -- stochastic fluctuations that manifest as preference cycles (e.g., $A \succ B \succ C \succ A$), occurring in 5-9% of evaluations across state-of-the-art models. While repeated sampling mitigates noise by averaging multiple judgments, it treats each comparison in isolation and fails to exploit the structural constraints that distinguish systematic signals from random noise. We introduce Topological Consensus Rewards (TCR), a framework that leverages transitivity as a denoising mechanism via topological majority voting: systematic signals reinforce each other through transitive chains, while random errors cluster into topologically exposed cycles. TCR approximates the Maximum Acyclic Subgraph to filter stochastic noise from preference signals. We also propose Cycle Incidence Rate (CIR) as a diagnostic metric that measures the proportion of samples containing preference cycles. Under our noise model, these cycles arise primarily from stochastic measurement errors rather than genuine intransitivity. Experiments on Arena-Hard, MT-Bench, and WritingBench demonstrate that TCR consistently outperforms pairwise baselines and classical ranking algorithms, while exhibiting robust performance across different judge models.