NeurIPS 2023 Papers

Building trees to represent or to fit distances is a critical component of phylogenetic analysis, metric embeddings, approximation algorithms, geometric graph neural nets, and the analysis of hierarchical data. Much of the previous algorithmic work, however, has focused on generic metric spaces (i.e., those with no \emph{a priori} constraints). Leveraging several ideas from the mathematical analysis of hyperbolic geometry and geometric group theory, we study the tree fitting problem as finding the relation between the hyperbolicity (ultrametricity) vector and the error of tree (ultrametric) embedding. That is, we define a vector of hyperbolicity (ultrametric) values over all triples of points and compare the $\ell_p$ norms of this vector with the $\ell_q$ norm of the distortion of the best tree fit to the distances. This formulation allows us to define the average hyperbolicity (ultrametricity) in terms of a normalized $\ell_1$ norm of the hyperbolicity vector. Furthermore, we can interpret the classical tree fitting result of Gromov as a $p = q = \infty$ result. We present an algorithm \textsc{HCCRootedTreeFit} such that the $\ell_1$ error of the output embedding is analytically bounded in terms of the $\ell_1$-norm of the hyperbolicity vector (i.e., $p = q = 1$) and that this result is tight. Furthermore, this algorithm has significantly different theoretical and empirical performance as compared to Gromov's result and related algorithms. Finally, we show using \textsc{HCCRootedTreeFit} and related tree fitting algorithms, that supposedly standard data sets for hierarchical data analysis and geometric graph neural networks have radically different tree fits than those of synthetic, truly tree-like data sets, suggesting that a much more refined analysis of these standard data sets is called for.

Pruning at initialization (PaI) aims to remove weights of neural networks before training in pursuit of training efficiency besides the inference. While off-the-shelf PaI methods manage to find trainable subnetworks that outperform random pruning, their performance in terms of both accuracy and computational reduction is far from satisfactory compared to post-training pruning and the understanding of PaI is missing. For instance, recent studies show that existing PaI methods only able to find good layerwise sparsities not weights, as the discovered subnetworks are surprisingly resilient against layerwise random mask shuffling and weight re-initialization. In this paper, we study PaI from a brand-new perspective -- the topology of subnetworks. In particular, we propose a principled framework for analyzing the performance of Pruning and Initialization (PaI) methods with two quantities, namely, the number of effective paths and effective nodes. These quantities allow for a more comprehensive understanding of PaI methods, giving us an accurate assessment of different subnetworks at initialization. We systematically analyze the behavior of various PaI methods through our framework and observe a guiding principle for constructing effective subnetworks: *at a specific sparsity, the top-performing subnetwork always presents a good balance between the number of effective nodes and the number of effective paths.* Inspired by this observation, we present a novel data-agnostic pruning method by solving a multi-objective optimization problem. By conducting extensive experiments across different architectures and datasets, our results demonstrate that our approach outperforms state-of-the-art PaI methods while it is able to discover subnetworks that have much lower inference FLOPs (up to 3.4$\times$). Code will be fully released.

This paper proposes a novel strategy for estimating the heterogeneous treatment effect called the Fused and Accurate Shrinkage Tree ($\mathrm{FAST}$). Our approach utilizes both trial and observational data to improve the accuracy and robustness of the estimator. Inspired by the concept of shrinkage estimation in statistics, we develop an optimal weighting scheme and a corresponding estimator that balances the unbiased estimator based on the trial data with the potentially biased estimator based on the observational data. Specifically, combined with tree-based techniques, we introduce a new split criterion that utilizes both trial data and observational data to more accurately estimate the treatment effect. Furthermore, we confirm the consistency of our proposed tree-based estimator and demonstrate the effectiveness of our criterion in reducing prediction error through theoretical analysis. The advantageous finite sample performance of the $\mathrm{FAST}$ and its ensemble version over existing methods is demonstrated via simulations and real data analysis.

This paper introduces an efficient and robust framework for hybrid query (HQ) processing, which combines approximate nearest neighbor search (ANNS) with attribute constraint. HQ aims to find objects that are similar to a feature vector and match some structured attributes. Existing methods handle ANNS and attribute filtering separately, leading to inefficiency and inaccuracy. Our framework, called native hybrid query (NHQ), builds a composite index based on proximity graph (PG) and applies joint pruning for HQ. We can easily adapt existing PGs to this framework for efficient HQ processing. We also propose two new navigable PGs (NPGs) with optimized edge selection and routing, which improve the overall ANNS performance. We implement five HQ methods based on the proposed NPGs and existing PGs in NHQ, and show that they outperform the state-of-the-art methods on 10 real-world datasets (up to 315$\times$ faster with the same accuracy).

Reinforcement learning with the help of neural-guided search consumes huge computational resources to achieve remarkable performance. Path consistency (PC), i.e., $f$ values on one optimal path should be identical, was previously imposed on MCTS by PCZero to improve the learning efficiency of AlphaZero. Not only PCZero still lacks a theoretical support but also considers merely board games. In this paper, PCZero is generalized into GW-PCZero for real applications with non-zero immediate reward. A weighting mechanism is introduced to reduce the variance caused by scouting's uncertainty on the $f$ value estimation. For the first time, it is theoretically proved that neural-guided MCTS is guaranteed to find the optimal solution under the constraint of PC. Experiments are conducted on the Atari $100$k benchmark with $26$ games and GW-PCZero achieves $198\%$ mean human performance, higher than the state-of-the-art EfficientZero's $194\\%$, while consuming only $25\\%$ of the computational resources consumed by EfficientZero.

The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution. There are two existing approaches for choosing this distribution. The first approach is using a fixed prior distribution. The second approach is optimizing for the best distribution which belongs to a parametric family of distributions and can maximize the expected distance. However, both approaches have their limitations. A fixed prior distribution is non-informative in terms of highlighting projecting directions that can discriminate two general probability measures. Doing optimization for the best distribution is often expensive and unstable. Moreover, designing the parametric family of the candidate distribution could be easily misspecified. To address the issues, we propose to design the slicing distribution as an energy-based distribution that is parameter-free and has the density proportional to an energy function of the projected one-dimensional Wasserstein distance. We then derive a novel sliced Wasserstein variant, energy-based sliced Waserstein (EBSW) distance, and investigate its topological, statistical, and computational properties via importance sampling, sampling importance resampling, and Markov Chain methods. Finally, we conduct experiments on point-cloud gradient flow, color transfer, and point-cloud reconstruction to show the favorable performance of the EBSW.

In many search applications related to passage retrieval, text entailment, and subgraph search, the query and each 'document' is a set of elements, with a document being relevant if it contains the query. These elements are not represented by atomic IDs, but by embedded representations, thereby extending set containment to *soft* set containment. Recent applications address soft set containment by encoding sets into fixed-size vectors and checking for elementwise *vector* *dominance*. This 0/1 property can be relaxed to an asymmetric *hinge* *distance* for scoring and ranking candidate documents. Here we focus on data-sensitive, trainable indices for fast retrieval of relevant documents. Existing LSH methods are designed for mostly symmetric or few simple asymmetric distance functions, which are not suitable for hinge distance. Instead, we transform hinge distance into a proposed *dominance* *similarity* measure, to which we then apply a Fourier transform, thereby expressing dominance similarity as an expectation of inner products of functions in the frequency domain. Next, we approximate the expectation with an importance-sampled estimate. The overall consequence is that now we can use a traditional LSH, but in the frequency domain. To ensure that the LSH uses hash bits efficiently, we learn hash functions that are sensitive to both corpus and query distributions, mapped to the frequency domain. Our experiments show that the proposed asymmetric dominance similarity is critical to the targeted applications, and that our LSH, which we call FourierHashNet, provides a better query time vs. retrieval quality trade-off, compared to several baselines. Both the Fourier transform and the trainable hash codes contribute to performance gains.

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.

Search is an important technique in program synthesis that allows for adaptive strategies such as focusing on particular search directions based on execution results. Several prior works have demonstrated that neural models are effective at guiding program synthesis searches. However, a common drawback of those approaches is the inability to handle iterative loops, higher-order functions, or lambda functions, thus limiting prior neural searches from synthesizing longer and more general programs. We address this gap by designing a search algorithm called LambdaBeam that can construct arbitrary lambda functions that compose operations within a given DSL. We create semantic vector representations of the execution behavior of the lambda functions and train a neural policy network to choose which lambdas to construct during search, and pass them as arguments to higher-order functions to perform looping computations. Our experiments show that LambdaBeam outperforms neural, symbolic, and LLM-based techniques in an integer list manipulation domain.

Recent works have shown that line search methods can speed up Stochastic Gradient Descent (SGD) and Adam in modern over-parameterized settings. However, existing line searches may take steps that are smaller than necessary since they require a monotone decrease of the (mini-)batch objective function. We explore nonmonotone line search methods to relax this condition and possibly accept larger step sizes. Despite the lack of a monotonic decrease, we prove the same fast rates of convergence as in the monotone case. Our experiments show that nonmonotone methods improve the speed of convergence and generalization properties of SGD/Adam even beyond the previous monotone line searches. We propose a POlyak NOnmonotone Stochastic (PoNoS) method, obtained by combining a nonmonotone line search with a Polyak initial step size. Furthermore, we develop a new resetting technique that in the majority of the iterations reduces the amount of backtracks to zero while still maintaining a large initial step size. To the best of our knowledge, a first runtime comparison shows that the epoch-wise advantage of line-search-based methods gets reflected in the overall computational time.

In this paper, we present Neural k-Opt (NeuOpt), a novel learning-to-search (L2S) solver for routing problems. It learns to perform flexible k-opt exchanges based on a tailored action factorization method and a customized recurrent dual-stream decoder. As a pioneering work to circumvent the pure feasibility masking scheme and enable the autonomous exploration of both feasible and infeasible regions, we then propose the Guided Infeasible Region Exploration (GIRE) scheme, which supplements the NeuOpt policy network with feasibility-related features and leverages reward shaping to steer reinforcement learning more effectively. Additionally, we equip NeuOpt with Dynamic Data Augmentation (D2A) for more diverse searches during inference. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that our NeuOpt not only significantly outstrips existing (masking-based) L2S solvers, but also showcases superiority over the learning-to-construct (L2C) and learning-to-predict (L2P) solvers. Notably, we offer fresh perspectives on how neural solvers can handle VRP constraints. Our code is available: https://github.com/yining043/NeuOpt.

Solving the quantum many-body Schrödinger equation is a fundamental and challenging problem in the fields of quantum physics, quantum chemistry, and material sciences. One of the common computational approaches to this problem is Quantum Variational Monte Carlo (QVMC), in which ground-state solutions are obtained by minimizing the energy of the system within a restricted family of parameterized wave functions. Deep learning methods partially address the limitations of traditional QVMC by representing a rich family of wave functions in terms of neural networks. However, the optimization objective in QVMC remains notoriously hard to minimize and requires second-order optimization methods such as natural gradient. In this paper, we first reformulate energy functional minimization in the space of Born distributions corresponding to particle-permutation (anti-)symmetric wave functions, rather than the space of wave functions. We then interpret QVMC as the Fisher--Rao gradient flow in this distributional space, followed by a projection step onto the variational manifold. This perspective provides us with a principled framework to derive new QMC algorithms, by endowing the distributional space with better metrics, and following the projected gradient flow induced by those metrics. More specifically, we propose "Wasserstein Quantum Monte Carlo" (WQMC), which uses the gradient flow induced by the Wasserstein metric, rather than the Fisher--Rao metric, and corresponds to *transporting* the probability mass, rather than *teleporting* it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.

The local search methods have been widely used to solve the clustering problems. In practice, local search algorithms for clustering problems mainly adapt the single-swap strategy, which enables them to handle large-scale datasets and achieve linear running time in the data size. However, compared with multi-swap local search algorithms, there is a considerable gap on the approximation ratios of the single-swap local search algorithms. Although the current multi-swap local search algorithms provide small constant approximation, the proposed algorithms tend to have large polynomial running time, which cannot be used to handle large-scale datasets. In this paper, we propose a multi-swap local search algorithm for the $k$-means problem with linear running time in the data size. Given a swap size $t$, our proposed algorithm can achieve a $(50(1+\frac{1}{t})+\epsilon)$-approximation, which improves the current best result 509 (ICML 2019) with linear running time in the data size. Our proposed method, compared with previous multi-swap local search algorithms, is the first one to achieve linear running time in the data size. To obtain a more practical algorithm for the problem with better clustering quality and running time, we propose a sampling-based method which accelerates the process of clustering cost update during swaps. Besides, a recombination mechanism is proposed to find potentially better solutions. Empirical experiments show that our proposed algorithms achieve better performances compared with branch and bound solver (NeurIPS 2022) and other existing state-of-the-art local search algorithms on both small and large datasets.

In this paper, we propose Barrier Hamiltonian Monte Carlo (BHMC), a version of the HMC algorithm which aims at sampling from a Gibbs distribution $\pi$ on a manifold $\mathsf{M}$, endowed with a Hessian metric $\mathfrak{g}$ derived from a self-concordant barrier. Our method relies on Hamiltonian dynamics which comprises $\mathfrak{g}$. Therefore, it incorporates the constraints defining $\mathsf{M}$ and is able to exploit its underlying geometry. However, the corresponding Hamiltonian dynamics is defined via non separable Ordinary Differential Equations (ODEs) in contrast to the Euclidean case. It implies unavoidable bias in existing generalization of HMC to Riemannian manifolds. In this paper, we propose a new filter step, called ``involution checking step'', to address this problem. This step is implemented in two versions of BHMC, coined continuous BHMC (c-bHMC) and numerical BHMC (n-BHMC) respectively. Our main results establish that these two new algorithms generate reversible Markov chains with respect to $\pi$ and do not suffer from any bias in comparison to previous implementations. Our conclusions are supported by numerical experiments where we consider target distributions defined on polytopes.

Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its "slow preprocessing'' version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded "intrinsic'' dimension. For the other data structure variants studied, including DiskANN with "fast preprocessing'', HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a "reasonable'' accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least $0.1 n$ steps on instances of size $n$ before it encounters any of the $5$ nearest neighbors of the query.

Building agents based on tree-search planning capabilities with learned models has achieved remarkable success in classic decision-making problems, such as Go and Atari. However, it has been deemed challenging or even infeasible to extend Monte Carlo Tree Search (MCTS) based algorithms to diverse real-world applications, especially when these environments involve complex action spaces and significant simulation costs, or inherent stochasticity. In this work, we introduce LightZero, the first unified benchmark for deploying MCTS/MuZero in general sequential decision scenarios. Specificially, we summarize the most critical challenges in designing a general MCTS-style decision-making solver, then decompose the tightly-coupled algorithm and system design of tree-search RL methods into distinct sub-modules. By incorporating more appropriate exploration and optimization strategies, we can significantly enhance these sub-modules and construct powerful LightZero agents to tackle tasks across a wide range of domains, such as board games, Atari, MuJoCo, MiniGrid and GoBigger. Detailed benchmark results reveal the significant potential of such methods in building scalable and efficient decision intelligence. The code is available as part of OpenDILab at https://github.com/opendilab/LightZero.

We propose the Thinker algorithm, a novel approach that enables reinforcement learning agents to autonomously interact with and utilize a learned world model. The Thinker algorithm wraps the environment with a world model and introduces new actions designed for interacting with the world model. These model-interaction actions enable agents to perform planning by proposing alternative plans to the world model before selecting a final action to execute in the environment. This approach eliminates the need for handcrafted planning algorithms by enabling the agent to learn how to plan autonomously and allows for easy interpretation of the agent's plan with visualization. We demonstrate the algorithm's effectiveness through experimental results in the game of Sokoban and the Atari 2600 benchmark, where the Thinker algorithm achieves state-of-the-art performance and competitive results, respectively. Visualizations of agents trained with the Thinker algorithm demonstrate that they have learned to plan effectively with the world model to select better actions. Thinker is the first work showing that an RL agent can learn to plan with a learned world model in complex environments.

We study the problem of $\text{\emph{vector set search}}$ with $\text{\emph{vector set queries}}$. This task is analogous to traditional near-neighbor search, with the exception that both the query and each element in the collection are $\text{\textit{sets}}$ of vectors. We identify this problem as a core subroutine for semantic search applications and find that existing solutions are unacceptably slow. Towards this end, we present a new approximate search algorithm, DESSERT ($\text{\bf D}$ESSERT $\text{\bf E}$ffeciently $\text{\bf S}$earches $\text{\bf S}$ets of $\text{\bf E}$mbeddings via $\text{\bf R}$etrieval $\text{\bf T}$ables). DESSERT is a general tool with strong theoretical guarantees and excellent empirical performance. When we integrate DESSERT into ColBERT, a state-of-the-art semantic search model, we find a 2-5x speedup on the MS MARCO and LoTTE retrieval benchmarks with minimal loss in recall, underscoring the effectiveness and practical applicability of our proposal.

Multi-hop Knowledge Graph Question Answering (KGQA) is a task that involves retrieving nodes from a knowledge graph (KG) to answer natural language questions. Recent GNN-based approaches formulate this task as a KG path searching problem, where messages are sequentially propagated from the seed node towards the answer nodes. However, these messages are past-oriented, and they do not consider the full KG context. To make matters worse, KG nodes often represent pronoun entities and are sometimes encrypted, being uninformative in selecting between paths. To address these problems, we propose Neural Tree Search (NuTrea), a tree search-based GNN model that incorporates the broader KG context. Our model adopts a message-passing scheme that probes the unreached subtree regions to boost the past-oriented embeddings. In addition, we introduce the Relation Frequency-Inverse Entity Frequency (RF-IEF) node embedding that considers the global KG context to better characterize ambiguous KG nodes. The general effectiveness of our approach is demonstrated through experiments on three major multi-hop KGQA benchmark datasets, and our extensive analyses further validate its expressiveness and robustness. Overall, NuTrea provides a powerful means to query the KG with complex natural language questions. Code is available at https://github.com/mlvlab/NuTrea.