The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from 20.9% to 39.3% on a collection of mathematical competition problems.

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License.

最近已被证明大型语言模型在各种任务集中获得合理的零射普通化（Brown等，2020）。它已经假设这是语言模型的隐式多任务学习的结果，在语言模型中的预押（Radford等，2019）。可以通过明确的多任务学习直接引起零拍常规化？为了以缩放测试这个问题，我们开发一个系统，以便轻松地将任何自然语言任务映射到人类可读的提示表单中。我们转换一组大量的监督数据集，每个数据集都有多个提示，具有不同的措辞。这些提示的数据集允许基准测试模型执行完全看不见的任务的能力。我们介绍了一个普拉克尔编码器 - 解码器模型（Raffel等，2020; Lester等，2021），覆盖各种任务。该模型在多个标准数据集中达到强大的零点性能，通常优于其尺寸的型号超过16倍。此外，我们的方法对来自Big-替补基准测试的任务子集具有强烈性能，优于其尺寸的6倍。所有提示和培训的型号都可以在https://github.com/ bigscience-workshop / protectsource / httpsource / https：//huggingface.co/bigscience/t0pp。

This paper focuses on designing efficient models with low parameters and FLOPs for dense predictions. Even though CNN-based lightweight methods have achieved stunning results after years of research, trading-off model accuracy and constrained resources still need further improvements. This work rethinks the essential unity of efficient Inverted Residual Block in MobileNetv2 and effective Transformer in ViT, inductively abstracting a general concept of Meta-Mobile Block, and we argue that the specific instantiation is very important to model performance though sharing the same framework. Motivated by this phenomenon, we deduce a simple yet efficient modern \textbf{I}nverted \textbf{R}esidual \textbf{M}obile \textbf{B}lock (iRMB) for mobile applications, which absorbs CNN-like efficiency to model short-distance dependency and Transformer-like dynamic modeling capability to learn long-distance interactions. Furthermore, we design a ResNet-like 4-phase \textbf{E}fficient \textbf{MO}del (EMO) based only on a series of iRMBs for dense applications. Massive experiments on ImageNet-1K, COCO2017, and ADE20K benchmarks demonstrate the superiority of our EMO over state-of-the-art methods, \eg, our EMO-1M/2M/5M achieve 71.5, 75.1, and 78.4 Top-1 that surpass \textbf{SoTA} CNN-/Transformer-based models, while trading-off the model accuracy and efficiency well.

We aim to bridge the gap between our common-sense few-sample human learning and large-data machine learning. We derive a theory of human-like few-shot learning from von-Neuman-Landauer's principle. modelling human learning is difficult as how people learn varies from one to another. Under commonly accepted definitions, we prove that all human or animal few-shot learning, and major models including Free Energy Principle and Bayesian Program Learning that model such learning, approximate our theory, under Church-Turing thesis. We find that deep generative model like variational autoencoder (VAE) can be used to approximate our theory and perform significantly better than baseline models including deep neural networks, for image recognition, low resource language processing, and character recognition.

Despite significant progress in object categorization, in recent years, a number of important challenges remain; mainly, the ability to learn from limited labeled data and to recognize object classes within large, potentially open, set of labels. Zero-shot learning is one way of addressing these challenges, but it has only been shown to work with limited sized class vocabularies and typically requires separation between supervised and unsupervised classes, allowing former to inform the latter but not vice versa. We propose the notion of vocabulary-informed learning to alleviate the above mentioned challenges and address problems of supervised, zero-shot, generalized zero-shot and open set recognition using a unified framework. Specifically, we propose a weighted maximum margin framework for semantic manifold-based recognition that incorporates distance constraints from (both supervised and unsupervised) vocabulary atoms. Distance constraints ensure that labeled samples are projected closer to their correct prototypes, in the embedding space, than to others. We illustrate that resulting model shows improvements in supervised, zero-shot, generalized zero-shot, and large open set recognition, with up to 310K class vocabulary on Animal with Attributes and ImageNet datasets.

We consider infinite horizon Markov decision processes (MDPs) with fast-slow structure, meaning that certain parts of the state space move "fast" (and in a sense, are more influential) while other parts transition more "slowly." Such structure is common in real-world problems where sequential decisions need to be made at high frequencies, yet information that varies at a slower timescale also influences the optimal policy. Examples include: (1) service allocation for a multi-class queue with (slowly varying) stochastic costs, (2) a restless multi-armed bandit with an environmental state, and (3) energy demand response, where both day-ahead and real-time prices play a role in the firm's revenue. Models that fully capture these problems often result in MDPs with large state spaces and large effective time horizons (due to frequent decisions), rendering them computationally intractable. We propose an approximate dynamic programming algorithmic framework based on the idea of "freezing" the slow states, solving a set of simpler finite-horizon MDPs (the lower-level MDPs), and applying value iteration (VI) to an auxiliary MDP that transitions on a slower timescale (the upper-level MDP). We also extend the technique to a function approximation setting, where a feature-based linear architecture is used. On the theoretical side, we analyze the regret incurred by each variant of our frozen-state approach. Finally, we give empirical evidence that the frozen-state approach generates effective policies using just a fraction of the computational cost, while illustrating that simply omitting slow states from the decision modeling is often not a viable heuristic.

We present Muse, a text-to-image Transformer model that achieves state-of-the-art image generation performance while being significantly more efficient than diffusion or autoregressive models. Muse is trained on a masked modeling task in discrete token space: given the text embedding extracted from a pre-trained large language model (LLM), Muse is trained to predict randomly masked image tokens. Compared to pixel-space diffusion models, such as Imagen and DALL-E 2, Muse is significantly more efficient due to the use of discrete tokens and requiring fewer sampling iterations; compared to autoregressive models, such as Parti, Muse is more efficient due to the use of parallel decoding. The use of a pre-trained LLM enables fine-grained language understanding, translating to high-fidelity image generation and the understanding of visual concepts such as objects, their spatial relationships, pose, cardinality etc. Our 900M parameter model achieves a new SOTA on CC3M, with an FID score of 6.06. The Muse 3B parameter model achieves an FID of 7.88 on zero-shot COCO evaluation, along with a CLIP score of 0.32. Muse also directly enables a number of image editing applications without the need to fine-tune or invert the model: inpainting, outpainting, and mask-free editing. More results are available at https://muse-model.github.io

Reinforcement Learning (RL) is currently one of the most commonly used techniques for traffic signal control (TSC), which can adaptively adjusted traffic signal phase and duration according to real-time traffic data. However, a fully centralized RL approach is beset with difficulties in a multi-network scenario because of exponential growth in state-action space with increasing intersections. Multi-agent reinforcement learning (MARL) can overcome the high-dimension problem by employing the global control of each local RL agent, but it also brings new challenges, such as the failure of convergence caused by the non-stationary Markov Decision Process (MDP). In this paper, we introduce an off-policy nash deep Q-Network (OPNDQN) algorithm, which mitigates the weakness of both fully centralized and MARL approaches. The OPNDQN algorithm solves the problem that traditional algorithms cannot be used in large state-action space traffic models by utilizing a fictitious game approach at each iteration to find the nash equilibrium among neighboring intersections, from which no intersection has incentive to unilaterally deviate. One of main advantages of OPNDQN is to mitigate the non-stationarity of multi-agent Markov process because it considers the mutual influence among neighboring intersections by sharing their actions. On the other hand, for training a large traffic network, the convergence rate of OPNDQN is higher than that of existing MARL approaches because it does not incorporate all state information of each agent. We conduct an extensive experiments by using Simulation of Urban MObility simulator (SUMO), and show the dominant superiority of OPNDQN over several existing MARL approaches in terms of average queue length, episode training reward and average waiting time.

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic approximations of the objective function and its associated derivatives can be computed via inexact probabilistic zeroth- and first-order oracles. Under reasonable assumptions, a high-probability bound on the iteration complexity of the algorithm to approximate first-order stationarity is derived. Numerical results on standard nonlinear optimization test problems illustrate the advantages and limitations of our proposed method.