Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the theoretical understanding of how to train a Transformer to achieve the CoT ability remains less explored. This is primarily due to the technical challenges involved in analyzing the nonconvex optimization on nonlinear attention models. To the best of our knowledge, this work provides the first theoretical study of training Transformers with nonlinear attention to obtain the CoT generalization capability so that the resulting model can inference on unseen tasks when the input is augmented by examples of the new task. We first quantify the required training samples and iterations to train a Transformer model towards CoT ability. We then prove the success of its CoT generalization on unseen tasks with distribution-shifted testing data. Moreover, we theoretically characterize the conditions for an accurate reasoning output by CoT even when the provided reasoning examples contain noises and are not always accurate. In contrast, in-context learning (ICL), which can be viewed as one-step CoT without intermediate steps, may fail to provide an accurate output when CoT does. These theoretical findings are justified through experiments.

We study the problem of minimizing the expectation of smooth nonconvex functions with the help of several parallel workers whose role is to compute stochastic gradients. In particular, we focus on the challenging situation where the workers' compute times are arbitrarily heterogeneous and random. In the simpler regime characterized by arbitrarily heterogeneous but deterministic compute times, Tyurin and Richt\'arik (NeurIPS 2023) recently designed the first theoretically optimal asynchronous SGD method, called Rennala SGD, in terms of a novel complexity notion called time complexity. The starting point of our work is the observation that Rennala SGD can have arbitrarily bad performance in the presence of random compute times -- a setting it was not designed to handle. To advance our understanding of stochastic optimization in this challenging regime, we propose a new asynchronous SGD method, for which we coin the name MindFlayer SGD. Our theory and empirical results demonstrate the superiority of MindFlayer SGD over existing baselines, including Rennala SGD, in cases when the noise is heavy tailed.

Neural Information Processing Systems http://nips.cc/

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of features specific to that hypothesis. For example, in genetic association studies, each hypothesis tests the correlation between a variant and the trait. We have a rich set of features for each variant (e.g. its location, conservation, epigenetics etc.) which could inform how likely the variant is to have a true association. However popular empirically-validated testing approaches, such as Benjamini-Hochberg's procedure (BH) and independent hypothesis weighting (IHW), either ignore these features or assume that the features are categorical or uni-variate. We propose a new algorithm, NeuralFDR, which automatically learns a discovery threshold as a function of all the hypothesis features. We parametrize the discovery threshold as a neural network, which enables flexible handling of multi-dimensional discrete and continuous features as well as efficient end-to-end optimization. We prove that NeuralFDR has strong false discovery rate (FDR) guarantees, and show that it makes substantially more discoveries in synthetic and real datasets. Moreover, we demonstrate that the learned discovery threshold is directly interpretable.

We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.

Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here, we study extrapolation methods in a stochastic setting, where the iterates are produced by either a simple or an accelerated stochastic gradient algorithm. We first derive convergence bounds for arbitrary, potentially biased perturbations, then produce asymptotic bounds using the ratio between the variance of the noise and the accuracy of the current point. Finally, we apply this acceleration technique to stochastic algorithms such as SGD, SAGA, SVRG and Katyusha in different settings, and show significant performance gains.

We introduce an online active exploration algorithm for data-efficiently learning an abstract symbolic model of an environment. Our algorithm is divided into two parts: the first part quickly generates an intermediate Bayesian symbolic model from the data that the agent has collected so far, which the agent can then use along with the second part to guide its future exploration towards regions of the state space that the model is uncertain about. We show that our algorithm outperforms random and greedy exploration policies on two different computer game domains. The first domain is an Asteroids-inspired game with complex dynamics but basic logical structure. The second is the Treasure Game, with simpler dynamics but more complex logical structure.

Neural networks have a smooth initial inductive bias, such that small changes in input do not lead to large changes in output. However, in reinforcement learning domains with sparse rewards, value functions have non-smooth structure with a characteristic asymmetric discontinuity whenever rewards arrive. We propose a mechanism that learns an interpolation between a direct value estimate and a projected value estimate computed from the encountered reward and the previous estimate. This reduces the need to learn about discontinuities, and thus improves the value function approximation. Furthermore, as the interpolation is learned and state-dependent, our method can deal with heterogeneous observability. We demonstrate that this one change leads to significant improvements on multiple Atari games, when applied to the state-of-the-art A3C algorithm.

Neural Information Processing Systems http://nips.cc/

Asynchronous-parallel algorithms have the potential to vastly speed up algorithms by eliminating costly synchronization. However, our understanding of these algorithms is limited because the current convergence theory of asynchronous block coordinate descent algorithms is based on somewhat unrealistic assumptions. In particular, the age of the shared optimization variables being used to update blocks is assumed to be independent of the block being updated. Additionally, it is assumed that the updates are applied to randomly chosen blocks. In this paper, we argue that these assumptions either fail to hold or will imply less efficient implementations.