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.

Equivariant neural networks encode symmetry as an inductive bias and have achieved strong empirical performance in wide domains. However, their expressive power remains not well understood. Focusing on 2-layer ReLU networks, this paper investigates the impact of equiv-ariance constraints on the expressivity of equivariant and layer-wise equivariant networks. By examining the boundary hyperplanes and the channel vectors of ReLU networks, we construct an example showing that equivariance constraints could strictly limit expressive power. However, we demonstrate that this drawback can be compensated via enlarging the model size. Furthermore, we show that despite a larger model size, the resulting architecture could still correspond to a hypothesis space with lower complexity, implying superior generalizability for equivariant networks.

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

The new Gen. 2 QuietComfort Ultra earbuds reinforce everything Bose active noise cancellation does right. We may earn revenue from the products available on this page and participate in affiliate programs. Washington-Dulles airport, red-eye to Berlin, time to kill and batteries to fill. Time was that would force a hard choice, because time was that the Bose QuietComfort Ultra Bluetooth earbuds didn't charge wirelessly. Drop the new QC Ultra Gen. 2 case on the Qi pad, however, and it blinks to life, no awkward adapters or extra plugs required.

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.