CORE: Common Random Reconstruction for Distributed Optimization with Provable Low Communication Complexity

With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose a new technique named Common randOm REconstruction(CORE), which can be used to compress the information transmitted between machines in order to reduce communication complexity without other strict conditions. Especially, our technique CORE projects the vector-valued information to a low-dimensional one through common random vectors and reconstructs the information with the same random noises after communication. We apply CORE to two distributed tasks, respectively convex optimization on linear models and generic non-convex optimization, and design new distributed algorithms, which achieve provably lower communication complexities. For example, we show for linear models CORE-based algorithm can encode the gradient vector to $\mathcal{O}(1)$-bits (against $\mathcal{O}(d)$), with the convergence rate not worse, preceding the existing results.

Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.

Towards Revealing the Mystery behind Chain of Thought: a Theoretical Perspective

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the capacity of LLMs with CoT in solving fundamental mathematical and decision-making problems. We start by giving an impossibility result showing that any bounded-depth Transformer cannot directly output correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of a constant size suffice to solve both tasks by generating CoT derivations using a commonly-used math language format. Moreover, we show LLMs with CoT are capable of solving a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, extensive experiments on four tasks show that, while Transformers always fail to predict the answers directly, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

Personalized Predictive ASR for Latency Reduction in Voice Assistants

Streaming Automatic Speech Recognition (ASR) in voice assistants can utilize prefetching to partially hide the latency of response generation. Prefetching involves passing a preliminary ASR hypothesis to downstream systems in order to prefetch and cache a response. If the final ASR hypothesis after endpoint detection matches the preliminary one, the cached response can be delivered to the user, thus saving latency. In this paper, we extend this idea by introducing predictive automatic speech recognition, where we predict the full utterance from a partially observed utterance, and prefetch the response based on the predicted utterance. We introduce two personalization approaches and investigate the tradeoff between potential latency gains from successful predictions and the cost increase from failed predictions. We evaluate our methods on an internal voice assistant dataset as well as the public SLURP dataset.

Adaptive Endpointing with Deep Contextual Multi-armed Bandits

Current endpointing (EP) solutions learn in a supervised framework, which does not allow the model to incorporate feedback and improve in an online setting. Also, it is a common practice to utilize costly grid-search to find the best configuration for an endpointing model. In this paper, we aim to provide a solution for adaptive endpointing by proposing an efficient method for choosing an optimal endpointing configuration given utterance-level audio features in an online setting, while avoiding hyperparameter grid-search. Our method does not require ground truth labels, and only uses online learning from reward signals without requiring annotated labels. Specifically, we propose a deep contextual multi-armed bandit-based approach, which combines the representational power of neural networks with the action exploration behavior of Thompson modeling algorithms. We compare our approach to several baselines, and show that our deep bandit models also succeed in reducing early cutoff errors while maintaining low latency.

Highly Accurate Quantum Chemical Property Prediction with Uni-Mol+

Recent developments in deep learning have made remarkable progress in speeding up the prediction of quantum chemical (QC) properties by removing the need for expensive electronic structure calculations like density functional theory. However, previous methods that relied on 1D SMILES sequences or 2D molecular graphs failed to achieve high accuracy as QC properties are primarily dependent on the 3D equilibrium conformations optimized by electronic structure methods. In this paper, we propose a novel approach called Uni-Mol+ to tackle this challenge. Firstly, given a 2D molecular graph, Uni-Mol+ generates an initial 3D conformation from inexpensive methods such as RDKit. Then, the initial conformation is iteratively optimized to its equilibrium conformation, and the optimized conformation is further used to predict the QC properties. All these steps are automatically learned using Transformer models. We observed the quality of the optimized conformation is crucial for QC property prediction performance. To effectively optimize conformation, we introduce a two-track Transformer model backbone in Uni-Mol+ and train it together with the QC property prediction task. We also design a novel training approach called linear trajectory injection to ensure proper supervision for the Uni-Mol+ learning process. Our extensive benchmarking results demonstrate that the proposed Uni-Mol+ significantly improves the accuracy of QC property prediction. We have made the code and model publicly available at \url{https://github.com/dptech-corp/Uni-Mol}.

A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. Targeting these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which $\mathsf{SSWL}$ achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. In addition, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of Folklore WL tests (FWL). Overall, our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments on the ZINC benchmark demonstrate that $\mathsf{SSWL}$-inspired subgraph GNNs can significantly outperform prior architectures despite great simplicity.

3D Molecular Generation via Virtual Dynamics

Structure-based drug design, i.e., finding molecules with high affinities to the target protein pocket, is one of the most critical tasks in drug discovery. Traditional solutions, like virtual screening, require exhaustively searching on a large molecular database, which are inefficient and cannot return novel molecules beyond the database. The pocket-based 3D molecular generation model, i.e., directly generating a molecule with a 3D structure and binding position in the pocket, is a new promising way to address this issue. Herein, we propose VD-Gen, a novel pocket-based 3D molecular generation pipeline. VD-Gen consists of several carefully designed stages to generate fine-grained 3D molecules with binding positions in the pocket cavity end-to-end. Rather than directly generating or sampling atoms with 3D positions in the pocket like in early attempts, in VD-Gen, we first randomly initialize many virtual particles in the pocket; then iteratively move these virtual particles, making the distribution of virtual particles approximate the distribution of molecular atoms. After virtual particles are stabilized in 3D space, we extract a 3D molecule from them. Finally, we further refine atoms in the extracted molecule by iterative movement again, to get a high-quality 3D molecule, and predict a confidence score for it. Extensive experiment results on pocket-based molecular generation demonstrate that VD-Gen can generate novel 3D molecules to fill the target pocket cavity with high binding affinities, significantly outperforming previous baselines.

Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers

We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for nongeometric data, as well as novel RPEs operating on the sequences of tokens embedded in higher-dimensional Euclidean spaces (e.g. point clouds). FLTs construct the optimal RPE mechanism implicitly by learning its spectral representation. As opposed to other architectures combining efficient low-rank linear attention with RPEs, FLTs remain practical in terms of their memory usage and do not require additional assumptions about the structure of the RPE-mask. FLTs allow also for applying certain structural inductive bias techniques to specify masking strategies, e.g. they provide a way to learn the so-called local RPEs introduced in this paper and providing accuracy gains as compared with several other linear Transformers for language modeling. We also thoroughly tested FLTs on other data modalities and tasks, such as: image classification and 3D molecular modeling. For 3D-data FLTs are, to the best of our knowledge, the first Transformers architectures providing RPE-enhanced linear attention.

Rethinking the Expressive Power of GNNs via Graph Biconnectivity

Designing expressive Graph Neural Networks (GNNs) is a central topic in learning graph-structured data. While numerous approaches have been proposed to improve GNNs in terms of the Weisfeiler-Lehman (WL) test, generally there is still a lack of deep understanding of what additional power they can systematically and provably gain. In this paper, we take a fundamentally different perspective to study the expressive power of GNNs beyond the WL test. Specifically, we introduce a novel class of expressivity metrics via graph biconnectivity and highlight their importance in both theory and practice. As biconnectivity can be easily calculated using simple algorithms that have linear computational costs, it is natural to expect that popular GNNs can learn it easily as well. However, after a thorough review of prior GNN architectures, we surprisingly find that most of them are not expressive for any of these metrics. The only exception is the ESAN framework (Bevilacqua et al., 2022), for which we give a theoretical justification of its power. We proceed to introduce a principled and more efficient approach, called the Generalized Distance Weisfeiler-Lehman (GD-WL), which is provably expressive for all biconnectivity metrics. Practically, we show GD-WL can be implemented by a Transformer-like architecture that preserves expressiveness and enjoys full parallelizability. A set of experiments on both synthetic and real datasets demonstrates that our approach can consistently outperform prior GNN architectures.