Transformer-based autoregressive sampling has been the major bottleneck for slowing down large language model inferences. One effective way to accelerate inference is Speculative Decoding, which employs a small model to sample a sequence of draft tokens and a large model to validate. Given its empirical effectiveness, the theoretical understanding of Speculative Decoding is falling behind. This paper tackles this gap by conceptualizing the decoding problem via markov chain abstraction and studying the key properties, output quality and inference acceleration, from a theoretical perspective. Our analysis covers the theoretical limits of speculative decoding, batch algorithms, and output quality-inference acceleration tradeoffs. Our results reveal the fundamental connections between different components of LLMs via total variation distances and show how they jointly affect the efficiency of decoding algorithms.

Recently, researchers have found that representations learned by large-scale pretrained language models are useful in various downstream tasks. However, there is little theoretical understanding of how pre-training performance is related to downstream task performance. In this paper, we analyze how this performance transfer depends on the properties of the downstream task and the structure of the representations. We consider a log-linear model where a word can be predicted from its context through a network having softmax as its last layer. We show that even if the downstream task is highly structured and depends on a simple function of the hidden representation, there are still cases when a low pre-training loss cannot guarantee good performance on the downstream task. On the other hand, we propose and empirically validate the existence of an "anchor vector" in the representation space, and show that this assumption, together with properties of the downstream task, guarantees performance transfer.

Recently, researchers have found that representations learned by large-scale pretrained language models are useful in various downstream tasks. However, there is little theoretical understanding of how pre-training performance is related to downstream task performance. In this paper, we analyze how this performance transfer depends on the properties of the downstream task and the structure of the representations. We consider a log-linear model where a word can be predicted from its context through a network having softmax as its last layer. We show that even if the downstream task is highly structured and depends on a simple function of the hidden representation, there are still cases when a low pre-training loss cannot guarantee good performance on the downstream task. On the other hand, we propose and empirically validate the existence of an "anchor vector" in the representation space, and show that this assumption, together with properties of the downstream task, guarantees performance transfer.

Seams, distortions, wasted UVspace, vertex-duplication, and varying resolution over the surface are the most prominent issues of the standard UV-based texturing of meshes. These issues are particularly acute when automatic UV-unwrapping techniques are used. For this reason, instead of generating textures in automatically generated UV-planes like most state-of-the-art methods, we propose to represent textures as coloured point-clouds whose colours are generated by a denoising diffusion probabilistic model constrained to operate on the surface of 3D objects. Our sampling and resolution agnostic generative model heavily relies on heat diffusion over the surface of the meshes for spatial communication between points. To enable processing of arbitrarily sampled point-cloud textures and ensure longdistance texture consistency we introduce a fast re-sampling of the mesh spectral properties used during the heat diffusion and introduce a novel heat-diffusionbased self-attention mechanism. Our code and pre-trained models are available at github.com/simofoti/UV3-TeD.

Machine learning for node classification on graphs is a prominent area driven by applications such as recommendation systems. State-of-the-art models often use multiple graph convolutions on the data, as empirical evidence suggests they can enhance performance. However, it has been shown empirically and theoretically, that too many graph convolutions can degrade performance significantly, a phenomenon known as oversmoothing. In this paper, we provide a rigorous theoretical analysis, based on the two-class contextual stochastic block model (CSBM), of the performance of vanilla graph convolution from which we remove the principal eigenvector to avoid oversmoothing. We perform a spectral analysis for k rounds of corrected graph convolutions, and we provide results for partial and exact classification. For partial classification, we show that each round of convolution can reduce the misclassification error exponentially up to a saturation level, after which performance does not worsen. We also extend this analysis to the multi-class setting with features distributed according to a Gaussian mixture model. For exact classification, we show that the separability threshold can be improved exponentially up to O(log n/log log n) corrected convolutions.

Temporal Domain Generalization (TDG) addresses the challenge of training predictive models under temporally varying data distributions. Traditional TDG approaches typically focus on domain data collected at fixed, discrete time intervals, which limits their capability to capture the inherent dynamics within continuous-evolving and irregularly-observed temporal domains. To overcome this, this work formalizes the concept of Continuous Temporal Domain Generalization (CTDG), where domain data are derived from continuous times and are collected at arbitrary times. CTDG tackles critical challenges including: 1) Characterizing the continuous dynamics of both data and models, 2) Learning complex high-dimensional nonlinear dynamics, and 3) Optimizing and controlling the generalization across continuous temporal domains. To address them, we propose a Koopman operator-driven continuous temporal domain generalization (Koodos) framework. We formulate the problem within a continuous dynamic system and leverage the Koopman theory to learn the underlying dynamics; the framework is further enhanced with a comprehensive optimization strategy equipped with analysis and control driven by prior knowledge of the dynamics patterns. Extensive experiments demonstrate the effectiveness and efficiency of our approach.

The objective of this paper is a model that is able to discover, track and segment multiple moving objects in a video. We make four contributions: First, we introduce an object-centric segmentation model with a depth-ordered layer representation. This is implemented using a variant of the transformer architecture that ingests optical flow, where each query vector specifies an object and its layer for the entire video. The model can effectively discover multiple moving objects and handle mutual occlusions; Second, we introduce a scalable pipeline for generating multi-object synthetic training data via layer compositions, that is used to train the proposed model, significantly reducing the requirements for labour-intensive annotations, and supporting Sim2Real generalisation; Third, we conduct thorough ablation studies, showing that the model is able to learn object permanence and temporal shape consistency, and is able to predict amodal segmentation masks; Fourth, we evaluate our model, trained only on synthetic data, on standard video segmentation benchmarks, DAVIS, MoCA, SegTrack, FBMS-59, and achieve stateof-the-art performance among existing methods that do not rely on any manual annotations. With test-time adaptation, we observe further performance boosts.