We study the convergence behavior of the celebrated temporal-difference (TD) learning algorithm. By looking at the algorithm through the lens of optimization, we first argue that TD can be viewed as an iterative optimization algorithm where the function to be minimized changes per iteration. By carefully investigating the divergence displayed by TD on a classical counter example, we identify two forces that determine the convergent or divergent behavior of the algorithm. We next formalize our discovery in the linear TD setting with quadratic loss and prove that convergence of TD hinges on the interplay between these two forces. We extend this optimization perspective to prove convergence of TD in a much broader setting than just linear approximation and squared loss. Our results provide a theoretical explanation for the successful application of TD in reinforcement learning.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (ϵ-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Emerging ethical approaches have attempted to filter pretraining material, but such approaches have been ad hoc and failed to take context into account. We offer an approach to filtering grounded in law, which has directly addressed the tradeoffs in filtering material. First, we gather and make available the Pile of Law, a 256GB (and growing) dataset of open-source English-language legal and administrative data, covering court opinions, contracts, administrative rules, and legislative records. Pretraining on the Pile of Law may help with legal tasks that have the promise to improve access to justice. Second, we distill the legal norms that governments have developed to constrain the inclusion of toxic or private content into actionable lessons for researchers and discuss how our dataset reflects these norms. Third, we show how the Pile of Law offers researchers the opportunity to learn such filtering rules directly from the data, providing an exciting new research direction in model-based processing. Warning: this paper contains quotations that may be offensive or upsetting.

Multimodal learning has developed very fast in recent years. However, during the multimodal training process, the model tends to rely on only one modality based on which it could learn faster, thus leading to inadequate use of other modalities. Existing methods to balance the training process always have some limitations on the loss functions, optimizers and the number of modalities and only consider modulating the magnitude of the gradients while ignoring the directions of the gradients. To solve these problems, in this paper, we present a novel method to balance multimodal learning with Classifier-Guided Gradient Modulation (CGGM), considering both the magnitude and directions of the gradients. We conduct extensive experiments on four multimodal datasets: UPMC-Food 101, CMU-MOSI, IEMOCAP and BraTS 2021, covering classification, regression and segmentation tasks. The results show that CGGM outperforms all the baselines and other stateof-the-art methods consistently, demonstrating its effectiveness and versatility. Our code is available at https://github.com/zrguo/CGGM.

Novel-view synthesis aims to generate novel views of a scene from multiple input images or videos, and recent advancements like 3D Gaussian splatting (3DGS) have achieved notable success in producing photorealistic renderings with efficient pipelines. However, generating high-quality novel views under challenging settings, such as sparse input views, remains difficult due to insufficient information in under-sampled areas, often resulting in noticeable artifacts. This paper presents 3DGS-Enhancer, a novel pipeline for enhancing the representation quality of 3DGS representations. We leverage 2D video diffusion priors to address the challenging 3D view consistency problem, reformulating it as achieving temporal consistency within a video generation process.

Quantizing the activation, weight, and gradient to 4-bit is promising to accelerate neural network training. However, existing 4-bit training methods require custom numerical formats which are not supported by contemporary hardware. In this work, we propose a training method for transformers with all matrix multiplications implemented with the INT4 arithmetic. Training with an ultra-low INT4 precision is challenging. To achieve this, we carefully analyze the specific structures of activation and gradients in transformers to propose dedicated quantizers for them. For forward propagation, we identify the challenge of outliers and propose a Hadamard quantizer to suppress the outliers.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

Diffusion Transformers have recently demonstrated unprecedented generative capabilities for various tasks. The encouraging results, however, come with the cost of slow inference, since each denoising step requires inference on a transformer model with a large scale of parameters. In this study, we make an interesting and somehow surprising observation: the computation of a large proportion of layers in the diffusion transformer, through introducing a caching mechanism, can be readily removed even without updating the model parameters. In the case of U-ViT-H/2, for example, we may remove up to 93.68% of the computation in the cache steps (46.84% for all steps), with less than 0.01 drop in FID. To achieve this, we introduce a novel scheme, named Learning-to-Cache (L2C), that learns to conduct caching in a dynamic manner for diffusion transformers. Specifically, by leveraging the identical structure of layers in transformers and the sequential nature of diffusion, we explore redundant computations between timesteps by treating each layer as the fundamental unit for caching. To address the challenge of the exponential search space in deep models for identifying layers to cache and remove, we propose a novel differentiable optimization objective. An input-invariant yet timestep-variant router is then optimized, which can finally produce a static computation graph. Experimental results show that L2C largely outperforms samplers such as DDIM and DPM-Solver, alongside prior cache-based methods at the same inference speed.