It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters. Here, we analyze a continuous diffusion approximation of SGD, called homogenized stochastic gradient descent, and show in a regularized linear regression framework that it leads to an asymptotically heavy-tailed parameter distribution, even though local gradient noise is Gaussian. We give explicit upper and lower bounds on the tail-index of the resulting parameter distribution and validate these bounds in numerical experiments. Moreover, the explicit form of these bounds enables us to quantify the interplay between optimization hyperparameters and the tail-index. Doing so, we contribute to the ongoing discussion on links between heavy tails and the generalization performance of neural networks as well as the ability of SGD to avoid suboptimal local minima.

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks.

We study the fundamental problem of sequential probability assignment, also known as online learning with logarithmic loss, with respect to an arbitrary, possibly nonparametric hypothesis class. Our goal is to obtain a complexity measure for the hypothesis class that characterizes the minimax regret and to determine a general, minimax optimal algorithm.

In this paper, we analyze the sample and communication complexity of the federated linear stochastic approximation (FedLSA) algorithm. We explicitly quantify the effects of local training with agent heterogeneity. We show that the communication complexity of FedLSA scales polynomially with the inverse of the desired accuracy ϵ. To overcome this, we propose SCAFFLSA, a new variant of FedLSA that uses control variates to correct for client drift, and establish its sample and communication complexities. We show that for statistically heterogeneous agents, its communication complexity scales logarithmically with the desired accuracy, similar to Scaffnew [37]. An important finding is that, compared to the existing results for Scaffnew, the sample complexity scales with the inverse of the number of agents, a property referred to as linear speed-up. Achieving this linear speed-up requires completely new theoretical arguments. We apply the proposed method to federated temporal difference learning with linear function approximation and analyze the corresponding complexity improvements.

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of the weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinitedimensional function spaces, we recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant (as is the case in many scientific inference tasks). At the same time, it stays competitive for black-box supervised learning problems, where neural networks typically excel.

The alignment of large language models (LLMs) is critical for developing effective and safe language models. Traditional approaches focus on aligning models during the instruction tuning or reinforcement learning stages, referred to in this paper as'post alignment'. We argue that alignment during the pre-training phase, which we term'native alignment', warrants investigation. Native alignment aims to prevent unaligned content from the beginning, rather than relying on posthoc processing. This approach leverages extensively aligned pre-training data to enhance the effectiveness and usability of pre-trained models. Our study specifically explores the application of native alignment in the context of Arabic LLMs. We conduct comprehensive experiments and ablation studies to evaluate the impact of native alignment on model performance and alignment stability. Additionally, we release open-source Arabic LLMs that demonstrate state-of-the-art performance on various benchmarks, providing significant benefits to the Arabic LLM community.

As the scale of data and models for video understanding rapidly expand, handling long-form video input in transformer-based models presents a practical challenge. Rather than resorting to input sampling or token dropping, which may result in information loss, token merging shows promising results when used in collaboration with transformers. However, the application of token merging for long-form video processing is not trivial. We begin with the premise that token merging should not rely solely on the similarity of video tokens; the saliency of tokens should also be considered. To address this, we explore various video token merging strategies for long-form video classification, starting with a simple extension of image token merging, moving to region-concentrated merging, and finally proposing a learnable video token merging (VTM) algorithm that dynamically merges tokens based on their saliency. Extensive experimental results show that we achieve better or comparable performances on the LVU, COIN, and Breakfast datasets. Moreover, our approach significantly reduces memory costs by 84% and boosts throughput by approximately 6.89 times compared to baseline algorithms.

Hierarchical clustering has usually been addressed by discrete optimization using heuristics or continuous optimization of relaxed scores for hierarchies. In this work, we propose to optimize expected scores under a probabilistic model over hierarchies.

Real-world image denoising remains a challenge task. This paper studies selfsupervised image denoising, requiring only noisy images captured in a single shot. We revamping the blind-spot technique by leveraging the transformer's capability for long-range pixel interactions, which is crucial for effectively removing noise dependence in relating pixel-a requirement for achieving great performance for the blind-spot technique. The proposed method integrates these elements with two key innovations: a directional self-attention (DSA) module using a halfplane grid for self-attention, creating a sophisticated blind-spot structure, and a Siamese architecture with mutual learning to mitigate the performance impacts from the restricted attention grid in DSA. Experiments on benchmark datasets demonstrate that our method outperforms existing self-supervised and clean-imagefree methods. This combination of blind-spot and transformer techniques provides a natural synergy for tackling real-world image denoising challenges.

Existing high-resolution image harmonization methods typically rely on global color adjustments or the upsampling of parameter maps. However, these methods ignore local variations, leading to inharmonious appearances. To address this problem, we propose an Adaptive-Interval Color Transformation method (AICT), which predicts pixel-wise color transformations and adaptively adjusts the sampling interval to model local non-linearities of the color transformation at high resolution. Specifically, a parameter network is first designed to generate multiple position-dependent 3-dimensional lookup tables (3D LUTs), which use the color and position of each pixel to perform pixel-wise color transformations. Then, to enhance local variations adaptively, we separate a color transform into a cascade of sub-transformations using two 3D LUTs to achieve the non-uniform sampling intervals of the color transform. Finally, a global consistent weight learning method is proposed to predict an image-level weight for each color transform, utilizing global information to enhance the overall harmony. Extensive experiments demonstrate that our AICT achieves state-of-the-art performance with a lightweight architecture. The code is available at https://github.com/aipixel/AICT.