Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate tasks, ignoring the inherent coupling between them. To address this, we propose residual-loss anomaly analysis of physics-informed neural networks, a unified framework that leverages dynamical consistency within the physics-informed learning paradigm. This approach jointly infers piecewise parameters and transition points under a single set of constraints. The method follows a two-stage strategy: First, local physical residuals are analyzed through overlapping subinterval decomposition. When a subinterval spans a true transition point, the residual exhibits a distinct structural elevation in noise-free conditions, which has a non-zero lower bound, enabling effective localization of potential transition intervals. Second, within our framework, change-point locations and piecewise parameters are integrated into a unified physical loss function for joint optimization, enabling simultaneous identification. Experiments on benchmark nonlinear dynamical systems, including Malthusian and logistic growth models, Van der Pol oscillator, Lotka-Volterra model and Lorenz system, demonstrate that the proposed method outperforms traditional decoupled approaches in both change-point localization and parameter estimation accuracy. This study provides an efficient, unified solution for structurally coupled inverse problems in nonlinear dynamical systems with regime switching.

Training language models via reinforcement learning often relies on imperfect proxy rewards, since ground truth rewards that precisely define the intended behavior are rarely available. Standard metrics for assessing the quality of proxy rewards, such as ranking accuracy, treat incorrect rewards as strictly harmful. In this work, however, we highlight that not all deviations from the ground truth are equal. By theoretically analyzing which outputs attract probability during policy gradient optimization, we categorize reward errors according to their effect on the increase in ground truth reward. The analysis establishes that reward errors, though conventionally viewed as harmful, can also be benign or even beneficial by preventing the policy from stalling around outputs with mediocre ground truth reward. We then present two practical implications of our theory. First, for reinforcement learning from human feedback (RLHF), we develop reward model evaluation metrics that account for the harmfulness of reward errors. Compared to standard ranking accuracy, these metrics typically correlate better with the performance of a language model after RLHF, yet gaps remain in robustly evaluating reward models. Second, we provide insights for reward design in settings with verifiable rewards. A key theme underlying our results is that the effectiveness of a proxy reward function depends heavily on its interaction with the initial policy and learning algorithm.

"Never talk about goblins, gremlins, raccoons, trolls, ogres, pigeons, or other animals or creatures unless it is absolutely and unambiguously relevant," reads OpenAI's coding agent instructions. OpenAI has a goblin problem. Instructions designed to guide the behavior of the company's latest model as it writes code have been revealed to include a line, repeated several times, that specifically forbids it from randomly mentioning an assortment of mythical and real creatures. "Never talk about goblins, gremlins, raccoons, trolls, ogres, pigeons, or other animals or creatures unless it is absolutely and unambiguously relevant to the user's query," read instructions in Codex CLI, a command-line tool for using AI to generate code. It is unclear why OpenAI felt compelled to spell this out for Codex --or indeed why its models might want to discuss goblins or pigeons in the first place.

Musk testifies at OpenAI trial it's not OK to'loot a charity' Elon Musk has taken the stand at a high-stakes trial over the future of OpenAI, casting his lawsuit against the ChatGPT maker as a defence of charitable giving. The world's richest person is suing OpenAI, its cofounder and chief executive officer, Sam Altman, and its president, Greg Brockman, and said on the stand on Tuesday that they betrayed him and the public by abandoning OpenAI's mission to be a benevolent steward of AI for humanity and transforming the nonprofit into a profit-seeking juggernaut. Musk, who founded carmaker Tesla and rocket company SpaceX, also said he is committed to serving the public by working 80-to 100-hour weeks and generally not taking vacations. "I like working and solving problems that make people's lives better," he said. Before Musk began testifying, Bill Savitt, a lawyer for OpenAI and Altman, told jurors during his opening statement it was Musk who saw dollar signs as he helped finance OpenAI's early growth and pushed it to become a for-profit business, one he might eventually lead as CEO.

Global military spending is up again, according to SIPRI's latest report showing the 11th consecutive year of growth. But it's based on open data and not everything makes the list. Ukrainian drones strike Russia's Tuapse refinery for third time

In this supplementary material, we provide the proofs of convergence analysis in Section 1, 1-vs-1 transformation employed in the classification and semantic segmentation tasks in Section 2, the coordinate-wise and the preprocessing method of the LSTM teacher in Section 3, the loss functions of YOLO-v3 in Section 4, more experiments of image classification in Section 5, and the inferences of semantic segmentation in Section 6. A differentiable function e()is L-smooth with gradient Lipschitz constant C (uniformly Lipschitz continuous), if e(x) e(y) C x y, x,y. The function is called block-wise smooth with gradient Lipschitz Ci, if i e(x i,xi) ie(x i,x i) Ci xi x i, x,x (1) or with gradient Lipschitz constants { Ci}, if i e(x i,xi) ie(x i,xi) Ci x i x i, x,x (2) Further, Let Gmax max{Ci, Ci, k} C. Definition 2. For a differentiable function e(), if e(x) = 0, then x is a first-order stationary solution (SS1). For a differentiable function e(), if x is a SS1, and there exists ϵ > 0 so that for any y in the ϵ-neighborhood of x, we have e(x) e(y), then xis a local minimum. A saddle point xis an SS1 that is not a local minimum. If λmin( 2e(x)) < 0, x is a strict (non-degenerate) saddle point.

With the concept of teaching being introduced to the machine learning community, a teacher model start using dynamic loss functions to teach the training of a student model. The dynamic intends to set adaptive loss functions to different phases of student model learning. In existing works, the teacher model 1) merely determines the loss function based on the present states of the student model, i.e., disregards the experience of the teacher; 2) only utilizes the states of the student model, e.g., training iteration number and loss/accuracy from training/validation sets, while ignoring the states of the loss function. In this paper, we first formulate the loss adjustment as a temporal task by designing a teacher model with memory units, and, therefore, enables the student learning to be guided by the experience of the teacher model. Then, with a dynamic loss network, we can additionally use the states of the loss to assist the teacher learning in enhancing the interactions between the teacher and the student model. Extensive experiments demonstrate our approach can enhance student learning and improve the performance of various deep models on real-world tasks, including classification, objective detection, and semantic segmentation scenarios.

US lawmakers gave King Charles III a standing ovation upon mentioning the importance of "checks and balances" on executive power during his historic speech to Congress. Ukrainian drones strike Russia's Tuapse refinery for third time

Why is Israel still in southern Lebanon? A war to shape Lebanon's future Video captured massive explosions in southern Lebanon in what the Israeli military called strikes on a Hezbollah tunnel. Other attacks happened nearby, as Israeli Defence Minister Israel Katz vowed that southern Lebanon's fate will be like Gaza's. Ukrainian drones strike Russia's Tuapse refinery for third time Qatar says using Hormuz Strait as political weapon is'unacceptable' Australia's top diplomat visits China to talk energy security