We consider online bandit learning in which at every time step, an algorithm has to make a decision and then observe only its reward. The goal is to design efficient (polynomial-time) algorithms that achieve a total reward approximately close to that of the best fixed decision in hindsight. In this paper, we introduce a new notion of (λ, µ)-concave functions and present a bandit learning algorithm that achieves a performance guarantee which is characterized as a function of the concavity parameters λ and µ. The algorithm is based on the mirror descent algorithm in which the update directions follow the gradient of the multilinear extensions of the reward functions. The regret bound induced by our algorithm is Õ( T) which is nearly optimal.

We released FineWeb to make large language model training more accessible to the machine learning community at large. The dataset was curated by Hugging Face. The dataset was funded by Hugging Face. The dataset is released under the Open Data Commons Attribution License (ODC-By) v1.0 license. The use of this dataset is also subject to Common-Crawl's Terms of Use.

We consider the dynamic price competition between two firms operating within an opaque marketplace, where each firm lacks information about its competitor. The demand follows the multinomial logit (MNL) choice model, which depends on the consumers'

Diffusion models have recently advanced Combinatorial Optimization (CO) as a powerful backbone for neural solvers.

Novel view acoustic synthesis (NVAS) aims to render binaural audio at any target viewpoint, given a mono audio emitted by a sound source at a 3D scene. Existing methods have proposed NeRF-based implicit models to exploit visual cues as a condition for synthesizing binaural audio. However, in addition to low efficiency originating from heavy NeRF rendering, these methods all have a limited ability of characterizing the entire scene environment such as room geometry, material properties, and the spatial relation between the listener and sound source. To address these issues, we propose a novel Audio-Visual Gaussian Splatting (AV-GS) model. To obtain an implicit material-aware and geometry-aware condition for audio synthesis, we learn an explicit point-based scene representation with an audio-guidance parameter on locally initialized Gaussian points, taking into account the space relation from the listener and sound source. To make the visual scene model audio adaptive, we propose a point densification and pruning strategy to optimally distribute the Gaussian points, with the per-point contribution in sound propagation (e.g., more points needed for texture-less wall surfaces as they affect sound path diversion).

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over the depth of neural networks. Di erent depths correspond to subnetworks which share weights and whose predictions are combined via marginalisation, yielding model uncertainty. By exploiting the sequential structure of feed-forward networks, we are able to both evaluate our training objective and make predictions with a single forward pass.

A toric fibration is a surjective flat map f: X Y with connected fibres where (a) X is a toric variety (b) Y is a normal algebraic variety (c) dim(Y) < dim(X).

High-quality, large-scale corpora are the cornerstone of building foundation models.