We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.
相關內容
Dataset distillation methods reduce large-scale datasets to smaller sets of synthetic data, which preserve sufficient information for quickly training a new model from scratch. However, prior work on dataset distillation has focused exclusively on image classification datasets, whereas modern large-scale datasets are primarily in the vision-language space. In this work, we design the first vision-language dataset distillation method, building on the idea of trajectory matching. A key challenge is that vision-language datasets do not have a set of discrete classes. To overcome this, our proposed method jointly distills the image-text pairs in a contrastive formulation. Further, we leverage Low-Rank Adaptation (LoRA) matching to enable more efficient and effective trajectory matching in complex modern vision-language models. Since there are no existing baselines, we compare our distillation approach to three adapted vision-language coreset selection methods. We demonstrate significant improvements on the challenging Flickr30K and COCO retrieval benchmarks: for example, on Flickr30K, the best coreset selection method selecting 1000 image-text pairs for training achieves only 5.6% image-to-text retrieval accuracy (i.e., recall@1); in contrast, our dataset distillation approach almost doubles that to 9.9% with just 100 (an order of magnitude fewer) training pairs.
Conformal prediction (CP) is a method for constructing a prediction interval around the output of a fitted model, whose validity does not rely on the model being correct--the CP interval offers a coverage guarantee that is distribution-free, but relies on the training data being drawn from the same distribution as the test data. A recent variant, weighted conformal prediction (WCP), reweights the method to allow for covariate shift between the training and test distributions. However, WCP requires knowledge of the nature of the covariate shift-specifically,the likelihood ratio between the test and training covariate distributions. In practice, since this likelihood ratio is estimated rather than known exactly, the coverage guarantee may degrade due to the estimation error. In this paper, we consider a special scenario where observations belong to a finite number of groups, and these groups determine the covariate shift between the training and test distributions-for instance, this may arise if the training set is collected via stratified sampling. Our results demonstrate that in this special case, the predictive coverage guarantees of WCP can be drastically improved beyond the bounds given by existing estimation error bounds.
The recent breakthrough successes in machine learning are mainly attributed to scale: namely large-scale attention-based architectures and datasets of unprecedented scale. This paper investigates the impact of training at scale for chess. Unlike traditional chess engines that rely on complex heuristics, explicit search, or a combination of both, we train a 270M parameter transformer model with supervised learning on a dataset of 10 million chess games. We annotate each board in the dataset with action-values provided by the powerful Stockfish 16 engine, leading to roughly 15 billion data points. Our largest model reaches a Lichess blitz Elo of 2895 against humans, and successfully solves a series of challenging chess puzzles, without any domain-specific tweaks or explicit search algorithms. We also show that our model outperforms AlphaZero's policy and value networks (without MCTS) and GPT-3.5-turbo-instruct. A systematic investigation of model and dataset size shows that strong chess performance only arises at sufficient scale. To validate our results, we perform an extensive series of ablations of design choices and hyperparameters.
Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless, frequently, the researcher is confronted with multiple sets of results obtained from experiments conducted with different setups. Traditional SR methods may fail to find the underlying expression since the parameters of each experiment can be different. In this work we present Multi-View Symbolic Regression (MvSR), which takes into account multiple datasets simultaneously, mimicking experimental environments, and outputs a general parametric solution. This approach fits the evaluated expression to each independent dataset and returns a parametric family of functions f(x; \theta) simultaneously capable of accurately fitting all datasets. We demonstrate the effectiveness of MvSR using data generated from known expressions, as well as real-world data from astronomy, chemistry and economy, for which an a priori analytical expression is not available. Results show that MvSR obtains the correct expression more frequently and is robust to hyperparameters change. In real-world data, it is able to grasp the group behaviour, recovering known expressions from the literature as well as promising alternatives, thus enabling the use SR to a large range of experimental scenarios.
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t. given OT discrepancies. We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT, which has recently gained the attention of the ML community. Beyond its novelty, our method enjoys several advantageous properties: (i) we establish quality bounds for the recovered solution; (ii) this approach seemlessly interconnects with the Energy-Based Models (EBMs) learning procedure enabling the use of well-tuned algorithms for the problem of interest; (iii) it provides an intuitive optimization scheme avoiding min-max, reinforce and other intricate technical tricks. For validation, we consider several low-dimensional scenarios and image-space setups, including non-Euclidean cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications.
The test-time optimization of scene flow - using a coordinate network as a neural prior - has gained popularity due to its simplicity, lack of dataset bias, and state-of-the-art performance. We observe, however, that although coordinate networks capture general motions by implicitly regularizing the scene flow predictions to be spatially smooth, the neural prior by itself is unable to identify the underlying multi-body rigid motions present in real-world data. To address this, we show that multi-body rigidity can be achieved without the cumbersome and brittle strategy of constraining the $SE(3)$ parameters of each rigid body as done in previous works. This is achieved by regularizing the scene flow optimization to encourage isometry in flow predictions for rigid bodies. This strategy enables multi-body rigidity in scene flow while maintaining a continuous flow field, hence allowing dense long-term scene flow integration across a sequence of point clouds. We conduct extensive experiments on real-world datasets and demonstrate that our approach outperforms the state-of-the-art in 3D scene flow and long-term point-wise 4D trajectory prediction. The code is available at: //github.com/kavisha725/MBNSF.
A confidence sequence (CS) is a sequence of confidence sets that contains a target parameter of an underlying stochastic process at any time step with high probability. This paper proposes a new approach to constructing CSs for means of bounded multivariate stochastic processes using a general gambling framework, extending the recently established coin toss framework for bounded random processes. The proposed gambling framework provides a general recipe for constructing CSs for categorical and probability-vector-valued observations, as well as for general bounded multidimensional observations through a simple reduction. This paper specifically explores the use of the mixture portfolio, akin to Cover's universal portfolio, in the proposed framework and investigates the properties of the resulting CSs. Simulations demonstrate the tightness of these confidence sequences compared to existing methods. When applied to the sampling without-replacement setting for finite categorical data, it is shown that the resulting CS based on a universal gambling strategy is provably tighter than that of the posterior-prior ratio martingale proposed by Waudby-Smith and Ramdas.
We introduce SELF-DISCOVER, a general framework for LLMs to self-discover the task-intrinsic reasoning structures to tackle complex reasoning problems that are challenging for typical prompting methods. Core to the framework is a self-discovery process where LLMs select multiple atomic reasoning modules such as critical thinking and step-by-step thinking, and compose them into an explicit reasoning structure for LLMs to follow during decoding. SELF-DISCOVER substantially improves GPT-4 and PaLM 2's performance on challenging reasoning benchmarks such as BigBench-Hard, grounded agent reasoning, and MATH, by as much as 32% compared to Chain of Thought (CoT). Furthermore, SELF-DISCOVER outperforms inference-intensive methods such as CoT-Self-Consistency by more than 20%, while requiring 10-40x fewer inference compute. Finally, we show that the self-discovered reasoning structures are universally applicable across model families: from PaLM 2-L to GPT-4, and from GPT-4 to Llama2, and share commonalities with human reasoning patterns.
We propose GAN-Supervised Learning, a framework for learning discriminative models and their GAN-generated training data jointly end-to-end. We apply our framework to the dense visual alignment problem. Inspired by the classic Congealing method, our GANgealing algorithm trains a Spatial Transformer to map random samples from a GAN trained on unaligned data to a common, jointly-learned target mode. We show results on eight datasets, all of which demonstrate our method successfully aligns complex data and discovers dense correspondences. GANgealing significantly outperforms past self-supervised correspondence algorithms and performs on-par with (and sometimes exceeds) state-of-the-art supervised correspondence algorithms on several datasets -- without making use of any correspondence supervision or data augmentation and despite being trained exclusively on GAN-generated data. For precise correspondence, we improve upon state-of-the-art supervised methods by as much as $3\times$. We show applications of our method for augmented reality, image editing and automated pre-processing of image datasets for downstream GAN training.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191