We analyze neural scaling laws in a solvable model of last-layer fine-tuning where targets have intrinsic, instance-heterogeneous difficulty. In our Latent Instance Difficulty (LID) model, each input's target variance is governed by a latent ``precision'' drawn from a heavy-tailed distribution. While generalization loss recovers standard scaling laws, our main contribution connects this to inference. The pass@$k$ failure rate exhibits a power-law decay, $k^{-β_\text{eff}}$, but the observed exponent $β_\text{eff}$ is training-dependent. It grows with sample size $N$ before saturating at an intrinsic limit $β$ set by the difficulty distribution's tail. This coupling reveals that learning shrinks the ``hard tail'' of the error distribution: improvements in the model's generalization error steepen the pass@$k$ curve until irreducible target variance dominates. The LID model yields testable, closed-form predictions for this behavior, including a compute-allocation rule that favors training before saturation and inference attempts after. We validate these predictions in simulations and in two real-data proxies: CIFAR-10H (human-label variance) and a maths teacher-student distillation task.

This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms.

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Large language models (LLMs) have achieved remarkable performance on various natural language tasks. However, they are trained on static corpora and their knowledge can become outdated quickly in the fast-changing world. This motivates the development of knowledge editing methods designed to update certain knowledge in LLMs without changing unrelated others. To make selective edits, previous efforts often sought to update a small amount of parameters in some specific layer(s) of a LLM. Nonetheless, in challenging scenarios, they still fall short in making successful edits while preserving knowledge irrelevant to the updates simultaneously, resulting in a notable editing-locality trade-off. In this work, we question if the trade-offs are caused by the fact that parameter-based updates have a global effect, i.e., edited parameters affect all inputs indiscriminately. In light of this, we explore the feasibility of representation fine-tuning, which applied some linear update to a few representations in a learned subspace, for knowledge editing. While being effective to enhance an LLM's general ability as demonstrated in the previous work, we theoretically show that this linear update imposes a tension in editing-locality trade-off. Subsequently, BaFT is proposed to break the linearity. BaFT computes a weight for each basis that spans a dimension of the subspace based on the input representation. This input-dependent weighting mechanism allows BaFT to manage different types of knowledge in an adaptive way, thereby achieving a better editing-locality trade-off. Experiments on three LLMs with five editing benchmarks in diverse scenarios show the superiority of our method.

Generative AI is reshaping the media landscape, enabling unprecedented capabilities in video creation, personalization, and scalability. This paper presents a comprehensive SWOT analysis of Metas Movie Gen, a cutting-edge generative AI foundation model designed to produce 1080p HD videos with synchronized audio from simple text prompts. We explore its strengths, including high-resolution video generation, precise editing, and seamless audio integration, which make it a transformative tool across industries such as filmmaking, advertising, and education. However, the analysis also addresses limitations, such as constraints on video length and potential biases in generated content, which pose challenges for broader adoption. In addition, we examine the evolving regulatory and ethical considerations surrounding generative AI, focusing on issues like content authenticity, cultural representation, and responsible use. Through comparative insights with leading models like DALL-E and Google Imagen, this paper highlights Movie Gens unique features, such as video personalization and multimodal synthesis, while identifying opportunities for innovation and areas requiring further research. Our findings provide actionable insights for stakeholders, emphasizing both the opportunities and challenges of deploying generative AI in media production. This work aims to guide future advancements in generative AI, ensuring scalability, quality, and ethical integrity in this rapidly evolving field.

Synthetic data has become a pivotal resource in post-training tasks for large language models (LLMs) due to the scarcity of high-quality, specific data. While various methods have been developed to generate synthetic data, there remains a discernible gap between the practical effects of synthetic data and our theoretical comprehension. To address this challenge, we commence by presenting a detailed modeling of the prevalent synthetic data generation process. Building upon this modeling, we demonstrate that the generalization capability of the post-trained model is critically determined by the information gain derived from the generative model, as analyzed from a novel reverse-bottleneck perspective. Moreover, we introduce the concept of Generalization Gain via Mutual Information (GGMI) and elucidate the relationship between generalization gain and information gain. This analysis serves as a theoretical foundation for synthetic data generation and further highlights its connection with the generalization capability of post-trained models, offering an understanding about the design of synthetic data generation techniques and the optimization of the post-training process. We open source our code at https://github.com/ZyGan1999/Towards-a-Theoretical-Understanding-of-Synthetic-Data-in-LLM-Post-Training.

We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with discrete-time reinforcement learning (RL) with function approximation. We establish high-order numerical accuracy as well as the approximation error guarantees for the proposed approach. In contrast to discrete-time RL problems where the approximation factor depends on the effective horizon, we obtain a bounded approximation factor using the underlying elliptic structures, even if the effective horizon diverges to infinity.

Generative artificial intelligence (AI) systems are trained on large data corpora to generate new pieces of text, images, videos, and other media. There is growing concern that such systems may infringe on the copyright interests of training data contributors. To address the copyright challenges of generative AI, we propose a framework that compensates copyright owners proportionally to their contributions to the creation of AI-generated content. The metric for contributions is quantitatively determined by leveraging the probabilistic nature of modern generative AI models and using techniques from cooperative game theory in economics. This framework enables a platform where AI developers benefit from access to high-quality training data, thus improving model performance. Meanwhile, copyright owners receive fair compensation, driving the continued provision of relevant data for generative model training. Experiments demonstrate that our framework successfully identifies the most relevant data sources used in artwork generation, ensuring a fair and interpretable distribution of revenues among copyright owners.