Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative models remains poorly understood: after a task change, what aspects of the learned distribution are most easily lost, and what replay samples should be prioritized? We address these questions through the modern Hopfield energy. Recent links between modern Hopfield networks (MHNs) and diffusion models allow analyses in MHNs to be transferred to diffusion models. We introduce intrinsic forgetting as an increase in Hopfield energy after the task change. In tractable settings in an MHN, we prove that high-energy, outlier-like samples undergo a larger energy increase than cluster-like samples, implying that samples located in sharp, isolated basins are more forgettable. We further analyze memory replay and show that replay is particularly effective for high-energy samples, enabling an energy-based selection of replay samples. We validate these predictions in experiments on MHNs and two diffusion models under continual-learning settings: Stable Diffusion and a pixel-space DDPM. In these diffusion models, Hopfield energy tracks reconstruction-based forgetting, and replay experiments reveal energy-dependent mitigation of forgetting that is consistent with the MHN analysis.

Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in the over-parameterized regime by showing that the prediction induced by continuous-time neural tangent kernel (NTK) gradient flow is exactly equivalent to that from a classical random-effects model. In this framework, training time acts as a variance component, or equivalently an empirical Bayes covariance hyperparameter, governing the allocation of variation from noise to structured signal. This equivalence reveals an optimization-inference duality: the gradient-flow path is both an optimization trajectory and an empirical Bayes random-effects inference path. Conditional on training time, the network output is the posterior mean of the latent signal, and estimating training time by restricted maximum likelihood (REML) turns early stopping into likelihood-based empirical Bayes inference rather than external tuning. This perspective yields a two-stage inferential procedure. First, a variance-component test determines whether DNN training captures statistically significant structure beyond initialization. Second, conditional on training being warranted, REML provides a likelihood-based early stopping rule. The resulting stopping time admits a spectral interpretation in the NTK eigenbasis, where training proceeds until spectral loss decorrelation is achieved. We further establish that REML-guided early stopping achieves asymptotically optimal prediction error for fixed-design in-sample prediction and, under additional random-design regularity conditions, for out-of-sample prediction. This work reframes DNN training as statistical inference and provides a principled foundation for deciding whether and how long to train deep neural networks.

The use of residential photovoltaics has increased dramatically in recent years. With battery systems becoming more affordable, the optimal operation of a photovoltaic-battery system can bring significant savings to households. Optimal control requires correct forecasts of underlying parameters, such as photovoltaic power generation, to schedule the battery. While forecasting models have become increasingly accurate due to algorithmic advances and data availability, accuracy is typically measured in generic metrics which might not align with the downstream application. This study proposes a decision-focused learning framework that integrates optimization and prediction by training a Long Short-Term Memory photovoltaic energy forecaster on the downstream optimal scheduling of a battery system. The proposed methodology is compared against a standard two-phase approach. Across a 14-month evaluation period, the decision-focused method reduced average electricity costs across twenty buildings by 3.6% when normalized against performance bounds defined by a perfect forecast and a baseline of no optimization. Critically, this financial improvement was achieved despite the model exhibiting a root mean squared error of 19.9%, significantly higher than the decoupled model's 8.2%. Warm-starting the decision-focused model further improves results, lowering average cost by approximately 8%, while also mitigating the negative impact on statistical accuracy (root mean squared error of 13.7%). The findings are statistically significant at the 0.001 level across the twenty households and for each household individually. These results demonstrate that aligning forecast models with optimization goals is key for achieving cost advantages in PV-battery systems. Future research should replicate these findings on other datasets, alternate forecasting models and alternate optimization algorithms.

Integrating probability and nonprobability survey samples is an important problem in modern survey sampling. Nonprobability samples often contain rich outcome information but may lack population representativeness, whereas probability samples provide design-based auxiliary information but may not contain the study variable. We propose a deep neural network (DNN)-assisted doubly robust framework for estimating the finite population mean from these two data sources. The proposed method models the logit sampling score for the nonprobability sample as an unknown nonparametric function and estimates it by maximizing a pseudo-likelihood that combines information from the nonprobability sample and a reference probability sample. The DNN parameters are optimized using the ADAM algorithm. The resulting DNN-estimated sampling scores are incorporated into a DNN-assisted inverse-probability weighted estimator and a deep doubly robust estimator. We establish consistency and convergence rates under regularity conditions and evaluate the finite-sample performance of the proposed estimators through simulation studies and an empirical application using Pew Research Center and Behavioral Risk Factor Surveillance System data. The results suggest that the proposed estimators can improve robustness to parametric propensity-score misspecification, especially when the true selection mechanism is nonlinear.

Many real-world classification tasks require predicting multiple labels per instance, necessitating the optimization of complex evaluation metrics such as the $F$-measure and Jaccard index. While the Empirical Utility Maximization (EUM) framework is natural for these population-level metrics, existing theoretical results are largely limited to asymptotic Bayes-consistency. In this paper, we develop principled learning algorithms for optimizing a broad class of generalized metrics within the EUM framework, grounded in the stronger notion of $H$-consistency. Our key contribution is the design of novel surrogate loss functions for multi-label learning that admit provable $H$-consistency bounds, enabling optimization with non-asymptotic guarantees tailored to the hypothesis class and finite samples. Crucially, we prove these combinatorially formulated surrogates decompose exactly, operating in strictly $O(l)$ time without approximations. Building on this foundation, we introduce MMO (Multi-Label Metric Optimization), a new family of algorithms for optimizing generalized linear-fractional metrics. We validate our approach through extensive experiments, demonstrating robust scalability and superior performance over state-of-the-art continuous baselines on large-scale datasets (MS-COCO, Reuters-21578) in high-sparsity, deep learning regimes. Our results offer both theoretical rigor and practical effectiveness for general multi-label metric optimization.

The Chinese company is adapting to the demise of Moore's Law, which guides chip production. It could complicate US chip dominance. Tingbo He, president of Huawei's chip-design subsidiary HiSilicon, says her company's engineers have developed a novel way to optimize semiconductors--and she believes it will close the performance gap between Chinese and Western chips over the next few years. Huawei's method, in short, focuses on speeding up computations across chips, circuits, and entire computing systems, rather than squeezing ever-more components onto a single piece of silicon. "We found a new path," He said at the IEEE International Symposium on Circuits and Systems in Shanghai last weekend.

Trajectory is betting the rapid iteration cycle that supercharged vibe-coding can help all kinds of companies build AI products that learn continuously. Trajectory founders, Ronak Malde (left), Michael Elabd(center), and Arjun Karanam (right). A group of AI researchers who previously worked at Google DeepMind, Apple, OpenAI, and Meta Superintelligence Labs announced on Wednesday they're launching a new startup called Trajectory, which aims to help companies regularly improve their AI products by training on real-world user interactions. Trajectory wants to build a platform for AI that can learn continuously, a capability that researchers have long held up as a major barrier to further AI progress. OpenAI, Google, and Anthropic have found success training increasingly capable versions of AI models, especially for domains such as coding, math, and science.

You probably wouldn't notice if an AI chatbot slipped ads into its responses Hundreds of millions of people consult artificial intelligence chatbots on a daily basis for everything from product recommendations to romance, making them a tempting audience to target with potentially below-the-radar advertising. Indeed, our research suggests AI chatbots could easily be used for covert advertising to manipulate their human users. We are computer scientists who have been tracking AI safety and privacy for several years. In a study we published in an Association for Computing Machinery journal, we found that chatbots trained to embed personalized product ads in replies to queries influenced people's choices about products. And most participants didn't recognize that they were being manipulated.

Former Giants manager's daughter consulted ChatGPT before reporting altercation The 18-year-old daughter of former Yomiuri Giants manager Shinnosuke Abe said she consulted ChatGPT before reporting an alleged altercation with her father to a child guidance center. The 18-year-old daughter of former Yomiuri Giants manager Shinnosuke Abe said in a letter released on Tuesday that she had consulted ChatGPT before reporting an alleged physical altercation with her father to the child guidance center. Abe resigned from his position on Tuesday following his arrest on suspicion of physically assaulting his daughter . He has been released from police custody. According to reports, two of his daughters had been involved in an argument the previous day.

Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering mechanism remains unclear. This paper proves that this phenomenon is a result of floating-point arithmetic precision limits. As training enters a high-confidence stage, the difference between the correct-class logit and the other logits may exceed the absorption-error threshold. Then during backpropagation, the gradient of the correct class is rounded exactly to zero, while the gradients of the incorrect classes remain nonzero. This breaks the zero-sum constraint of gradients across classes and introduces a systematic drift in the parameter update of the classifier layer. We prove that this drift forms a positive feedback loop with the feature, causing the global classifier mean and the global feature mean to grow exponentially. We call this mechanism Numerical Feature Inflation (NFI). This mechanism explains the rapid norm growth before a Slingshot spike, the subsequent reappearance of gradients, and the resulting loss spike. We further show that NFI is not equivalent to an observed loss spike: in more practical tasks, partial absorption may not produce visible spikes, but it can still break the zero-sum constraint and drive rapid growth of parameter norms. Our results reinterpret Slingshot as a numerical dynamic of finite-precision training, and provide a testable explanation for abnormal parameter growth and logit divergence in late-stage training.