The emergence of differentiable simulators enabling analytic gradient computation has motivated a new wave of learning algorithms that hold the potential to significantly increase sample efficiency over traditional Reinforcement Learning (RL) methods. While recent research has demonstrated performance gains in scenarios with comparatively smooth dynamics and, thus, smooth optimization landscapes, research on leveraging differentiable simulators for contact-rich scenarios, such as legged locomotion, is scarce. This may be attributed to the discontinuous nature of contact, which introduces several challenges to optimizing with analytic gradients. The purpose of this paper is to determine if analytic gradients can be beneficial even in the face of contact. Our investigation focuses on the effects of different soft and hard contact models on the learning process, examining optimization challenges through the lens of contact simulation. We demonstrate the viability of employing analytic gradients to learn physically plausible locomotion skills with a quadrupedal robot using Short-Horizon Actor-Critic (SHAC), a learning algorithm leveraging analytic gradients, and draw a comparison to a state-of-the-art RL algorithm, Proximal Policy Optimization (PPO), to understand the benefits of analytic gradients.
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In statistical mechanics, computing the partition function is generally difficult. An approximation method using a variational autoregressive network (VAN) has been proposed recently. This approach offers the advantage of directly calculating the generation probabilities while obtaining a significantly large number of samples. The present study introduces a novel approximation method that employs samples derived from quantum annealing machines in conjunction with VAN, which are empirically assumed to adhere to the Gibbs-Boltzmann distribution. When applied to the finite-size Sherrington-Kirkpatrick model, the proposed method demonstrates enhanced accuracy compared to the traditional VAN approach and other approximate methods, such as the widely utilized naive mean field.
We are interested in the problem of learning the directed acyclic graph (DAG) when data are generated from a linear structural equation model (SEM) and the causal structure can be characterized by a polytree. Under the Gaussian polytree models, we study sufficient conditions on the sample sizes for the well-known Chow-Liu algorithm to exactly recover both the skeleton and the equivalence class of the polytree, which is uniquely represented by a CPDAG. On the other hand, necessary conditions on the required sample sizes for both skeleton and CPDAG recovery are also derived in terms of information-theoretic lower bounds, which match the respective sufficient conditions and thereby give a sharp characterization of the difficulty of these tasks. We also consider the problem of inverse correlation matrix estimation under the linear polytree models, and establish the estimation error bound in terms of the dimension and the total number of v-structures. We also consider an extension of group linear polytree models, in which each node represents a group of variables. Our theoretical findings are illustrated by comprehensive numerical simulations, and experiments on benchmark data also demonstrate the robustness of polytree learning when the true graphical structures can only be approximated by polytrees.
Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based methods, such as physics-informed neural networks (PINNs) and neural operators, exhibit deficiencies in robustness and generalization. To address these issues, numerous studies have integrated classical numerical frameworks with machine learning techniques, incorporating neural networks into parts of traditional numerical methods. In this study, we focus on hyperbolic conservation laws by replacing traditional numerical fluxes with neural operators. To this end, we developed loss functions inspired by established numerical schemes related to conservation laws and approximated numerical fluxes using Fourier neural operators (FNOs). Our experiments demonstrated that our approach combines the strengths of both traditional numerical schemes and FNOs, outperforming standard FNO methods in several respects. For instance, we demonstrate that our method is robust, has resolution invariance, and is feasible as a data-driven method. In particular, our method can make continuous predictions over time and exhibits superior generalization capabilities with out-of-distribution (OOD) samples, which are challenges that existing neural operator methods encounter.
Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a \emph{quadratic} behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency.
The conventional probabilistic rounding error analysis in numerical linear algebra provides worst-case bounds with an associated failure probability, which can still be pessimistic. In this paper, we develop a new probabilistic rounding error analysis from a statistical perspective. By assuming both the data and the relative error are independent random variables, we derive the approximate closed-form expressions for the expectation and variance of the rounding errors in various key computational kernels. Our analytical expressions have three notable characteristics: they are statistical and do not involve a failure probability; they are sharper than other deterministic and probabilistic bounds, using mean square error as the metric; they are correct to all orders of unit roundoff and valid for any dimension. Furthermore, numerical experiments validate the accuracy of our derivations and demonstrate that our analytical expressions are generally at least two orders of magnitude tighter than alternative worst-case bounds, exemplified through the inner products. We also discuss a scenario involving inner products where the underlying assumptions are invalid, i.e., input data are dependent, rendering the analytical expressions inapplicable.
We consider estimation and inference using data collected from reinforcement learning algorithms. These algorithms, characterized by their adaptive experimentation, interact with individual units over multiple stages, dynamically adjusting their strategies based on previous interactions. Our goal is to evaluate a counterfactual policy post-data collection and estimate structural parameters, like dynamic treatment effects, which can be used for credit assignment and determining the effect of earlier actions on final outcomes. Such parameters of interest can be framed as solutions to moment equations, but not minimizers of a population loss function, leading to Z-estimation approaches for static data. However, in the adaptive data collection environment of reinforcement learning, where algorithms deploy nonstationary behavior policies, standard estimators do not achieve asymptotic normality due to the fluctuating variance. We propose a weighted Z-estimation approach with carefully designed adaptive weights to stabilize the time-varying estimation variance. We identify proper weighting schemes to restore the consistency and asymptotic normality of the weighted Z-estimators for target parameters, which allows for hypothesis testing and constructing uniform confidence regions. Primary applications include dynamic treatment effect estimation and dynamic off-policy evaluation.
Contrastive learning models have achieved great success in unsupervised visual representation learning, which maximize the similarities between feature representations of different views of the same image, while minimize the similarities between feature representations of views of different images. In text summarization, the output summary is a shorter form of the input document and they have similar meanings. In this paper, we propose a contrastive learning model for supervised abstractive text summarization, where we view a document, its gold summary and its model generated summaries as different views of the same mean representation and maximize the similarities between them during training. We improve over a strong sequence-to-sequence text generation model (i.e., BART) on three different summarization datasets. Human evaluation also shows that our model achieves better faithfulness ratings compared to its counterpart without contrastive objectives.
Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.
Deep learning has yielded state-of-the-art performance on many natural language processing tasks including named entity recognition (NER). However, this typically requires large amounts of labeled data. In this work, we demonstrate that the amount of labeled training data can be drastically reduced when deep learning is combined with active learning. While active learning is sample-efficient, it can be computationally expensive since it requires iterative retraining. To speed this up, we introduce a lightweight architecture for NER, viz., the CNN-CNN-LSTM model consisting of convolutional character and word encoders and a long short term memory (LSTM) tag decoder. The model achieves nearly state-of-the-art performance on standard datasets for the task while being computationally much more efficient than best performing models. We carry out incremental active learning, during the training process, and are able to nearly match state-of-the-art performance with just 25\% of the original training data.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
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