Chain-of-thought (CoT) reasoning applies to complex tasks with multiple intermediate steps, a key feature of large language models. Recent studies have revealed CoT as a composition of in-context filtering and learning. This paper proposes a unified framework for CoT optimization that exploits the nested problem structure to formulate training as multilevel optimization. Each intermediate reasoning step is a distinct optimization level. We develop an epigraph-based multilevel optimization (EMO) method to iteratively find the optimal solution for this class of problems. Experiments using GPT-2 show that the proposed EMO achieves the lowest generalization errors across all intermediate steps compared to state-of-the-art, highlighting the importance of nested optimization approaches for CoT reasoning.

Randomized trace estimation is a popular technique to approximate the trace of an implicitly-defined matrix $A$ by averaging the quadratic form $x’Ax$ across several samples of a random vector $x$. This paper focuses on the application of randomized trace estimators on asynchronous computing environments where the quadratic form $x’Ax$ is computed partially by observing only a random row subset of $A$ for each sample of the random vector $x$. Our asynchronous framework treats the number of rows, as well as the row subset observed for each sample, as random variables, and our theoretical analysis establishes the variance of the randomized estimator for Rademacher and Gaussian samples. We also present error analysis and sampling complexity bounds for the proposed asynchronous randomized trace estimator. Our numerical experiments illustrate that the asynchronous variant can be competitive even when a small number of rows is updated per each sample.

Automated Planning and Scheduling is among the growing areas in Artificial Intelligence (AI) where mention of LLMs has gained popularity. Based on a comprehensive review of 126 papers, this paper investigates eight categories based on the unique applications of LLMs in addressing various aspects of planning problems: language translation, plan generation, model construction, multi-agent planning, interactive planning, heuristics optimization, tool integration, and brain-inspired planning. For each category, we articulate the issues considered and existing gaps. A critical insight resulting from our review is that the true potential of LLMs unfolds when they are integrated with traditional symbolic planners, pointing towards a promising neuro-symbolic approach. This approach effectively combines the generative aspects of LLMs with the precision of classical planning methods. By synthesizing insights from existing literature, we underline the potential of this integration to address complex planning challenges. Our goal is to encourage the ICAPS community to recognize the complementary strengths of LLMs and symbolic planners, advocating for a direction in automated planning that leverages these synergistic capabilities to develop more advanced and intelligent planning systems. We aim to keep the categorization of papers updated on https://ai4society.github.io/LLM-Planning-Viz/, a collaborative resource that allows researchers to contribute and add new literature to the categorization.

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.

Plansformer is a novel tool that utilizes a fine-tuned language model based on transformer architecture to generate symbolic plans. Transformers are a type of neural network architecture that have been shown to be highly effective in a range of natural language processing tasks. Unlike traditional planning systems that use heuristic-based search strategies, Plansformer is fine-tuned on specific classical planning domains to generate high-quality plans that are both fluent and feasible. Plansformer takes the domain and problem files as input (in PDDL) and outputs a sequence of actions that can be executed to solve the problem. We demonstrate the effectiveness of Plansformer on a variety of benchmark problems and provide both qualitative and quantitative results obtained during our evaluation, including its limitations. Plansformer has the potential to significantly improve the efficiency and effectiveness of planning in various domains, from logistics and scheduling to natural language processing and human-computer interaction. In addition, we provide public access to Plansformer via a website as well as an API endpoint; this enables other researchers to utilize our tool for planning and execution. The demo video is available at https://youtu.be/_1rlctCGsrk

Decentralized optimization with multiple networked clients/learners has advanced machine learning significantly over the past few years. When data distributions at different nodes/locations are heterogeneous, consensus-based decentralized algorithms ignore distinctive features of local data samples. In this paper, we propose a decentralized client adaptation strategy for personalized learning by taking local client data structures into account. It turns out that optimizing the model parameters can be formulated as a decentralized bilevel programming problem. Motivated by this application, we propose a stochastic primal-dual framework for solving decentralized bilevel nonconvex problems and show that the devised algorithm achieves the Karush–Kuhn–Tucker (KKT) points for this class of problems at a rate of $\mathcal{O}(1/\sqrt {nT} )$, where n denotes the number of total learners and T the total number of iterations. Multiple experiments show the superiority of our proposed method compared to state-of-the-art methods in terms of both training speed and testing accuracy for decentralized learning problems on real datasets.

We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of attention in recent years; we obtain sharper bounds for these problems. More significantly, we achieve these improvements by arguing that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise; these are powerful and standard techniques in randomized numerical linear algebra. With this recognition, we are able to employ the large body of work in numerical linear algebra to obtain algorithms for these problems that are simpler or faster (or both) than existing approaches. Our experiments demonstrate that the proposed data structures also work well on real-world datasets.

Bilevel optimization has been shown to be a powerful framework for formulating multi-task machine learning problems, e.g., reinforcement learning (RL) and meta-learning, where the decision variables are coupled in both levels of the minimization problems. In practice, the learning tasks would be located at different computing resource environments, and thus there is a need for deploying a decentralized training framework to implement multi-agent and multi-task learning. We develop a stochastic linearized augmented Lagrangian method (SLAM) for solving general nonconvex bilevel optimization problems over a graph, where both upper and lower optimization variables are able to achieve a consensus. We also establish that the theoretical convergence rate of the proposed SLAM to the Karush-Kuhn-Tucker (KKT) points of this class of problems is on the same order as the one achieved by the classical distributed stochastic gradient descent for only single-level nonconvex minimization problems. Numerical results tested on multi-agent RL problems showcase the superiority of SLAM compared with the benchmarks.

Current deep neural networks (DNNs) are vulnerable to adversarial attacks, where adversarial perturbations to the inputs can change or manipulate classification. To defend against such attacks, an effective and popular approach, known as adversarial training (AT), has been shown to mitigate the negative impact of adversarial attacks by virtue of a min-max robust training method. While effective, it remains unclear whether it can successfully be adapted to the distributed learning context. The power of distributed optimization over multiple machines enables us to scale up robust training over large models and datasets. Spurred by that, we propose distributed adversarial training (DAT), a large-batch adversarial training framework implemented over multiple machines. We show that DAT is general, which supports training over labeled and unlabeled data, multiple types of attack generation methods, and gradient compression operations favored for distributed optimization. Theoretically, we provide, under standard conditions in the optimization theory, the convergence rate of DAT to the first-order stationary points in general non-convex settings. Empirically, we demonstrate that DAT either matches or outperforms state-of-the-art robust accuracies and achieves a graceful training speedup (e.g., on ResNet-50 under ImageNet). Codes are available at https://github.com/dat-2022/dat.

This paper proposes a research direction to advance AI which draws inspiration from cognitive theories of human decision making. The premise is that if we gain insights about the causes of some human capabilities that are still lacking in AI (for instance, adaptability, generalizability, common sense, and causal reasoning), we may obtain similar capabilities in an AI system by embedding these causal components. We hope that the high-level description of our vision included in this paper, as well as the several research questions that we propose to consider, can stimulate the AI research community to define, try and evaluate new methodologies, frameworks, and evaluation metrics, in the spirit of achieving a better understanding of both human and machine intelligence.

This paper deals with distributed reinforcement learning problems with safety constraints. In particular, we consider that a team of agents cooperate in a shared environment, where each agent has its individual reward function and safety constraints that involve all agents' joint actions. As such, the agents aim to maximize the team-average long-term return, subject to all the safety constraints. More intriguingly, no central controller is assumed to coordinate the agents, and both the rewards and constraints are only known to each agent locally/privately. Instead, the agents are connected by a peer-to-peer communication network to share information with their neighbors. In this work, we first formulate this problem as a distributed constrained Markov decision process (D-CMDP) with networked agents. Then, we propose a decentralized policy gradient (PG) method, Safe Dec-PG, to perform policy optimization based on this D-CMDP model over a network. Convergence guarantees, together with numerical results, showcase the superiority of the proposed algorithm. To the best of our knowledge, this is the first decentralized PG algorithm that accounts for the coupled safety constraints with a quantifiable convergence rate in multi-agent reinforcement learning. Finally, we emphasize that our algorithm is also novel in solving a class of decentralized stochastic nonconvex-concave minimax optimization problems, where both the algorithm design and corresponding theoretical analysis are of independent interest.

In recent years, a variety of randomized constructions of sketching matrices have been devised, that have been used in fast algorithms for numerical linear algebra problems, such as least squares regression, low-rank approximation, and the approximation of leverage scores. A key property of sketching matrices is that of subspace embedding. In this paper, we study sketching matrices that are obtained from bipartite graphs that are sparse, i.e., have left degree s that is small. In particular, we explore two popular classes of sparse graphs, namely, expander graphs and magical graphs. For a given subspace ${\mathcal{U}} \subseteq {{\mathbb{R}}^n}$ of dimension k, we show that the magical graph with left degree s = 2 yields a (1 ± ϵ) ℓ2-subspace embedding for ${\mathcal{U}}$, if the number of right vertices (the sketch size) $m = {\mathcal{O}}\left( {{k^2}/{\varepsilon ^2}} \right)$. The expander graph with $s = {\mathcal{O}}(\log k/\varepsilon )$ yields a subspace embedding for $m = {\mathcal{O}}\left( {k\log k/{\varepsilon ^2}} \right)$. We also discuss the construction of sparse sketching matrices with reduced randomness using expanders based on error-correcting codes. Empirical results on various synthetic and real datasets show that these sparse graph sketching matrices work very well in practice.

Parametrized machine learning models for inference often include non-linear and nonconvex constraints over the parameters and meta-parameters. Training these models to convergence is in general difficult, and naive methods such as projected gradient descent or grid search are not easily able to enforce the functional constraints. This work explores the optimization of a constrained neural network (familiar from machine learning but with parameter constraints), in the service of neuro-symbolic logical reasoning. Logical neural networks (LNNs) provide a well-justified, interpretable example of training under non-trivial constraints. In this paper, we propose a unified framework for solving this nonlinear programming problem by leveraging primal-dual optimization methods, and quantify the corresponding convergence rate to the Karush-Kuhn-Tucker (KKT) points of this problem. Extensive numerical results on both a toy example and training an LNN over real datasets validate the efficacy of the method.

This submission considers the problem of updating the rank-$k$ truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel in applications such as Latent Semantic Indexing and Recommender Systems. Nonetheless, the proposed framework is purely algebraic and targets general updating problems. The algorithm presented in this paper undertakes a projection viewpoint and focuses on building a pair of subspaces which approximate the linear span of the sought singular vectors of the updated matrix. We discuss and analyze two different choices to form the projection subspaces. Results on matrices from real applications suggest that the proposed algorithm can lead to higher accuracy, especially for the singular triplets associated with the largest modulus singular values. Several practical details and key differences with other approaches are also discussed.

Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. In many of the real-world applications, the underlying graph changes over time, however, most of the existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs using a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results presented establish a connection between the proposed tensor approach and spectral convolution of tensors. The proposed method TM-GCN is consistent with the Message Passing Neural Network (MPNN) framework, accounting for both spatial and temporal message passing. Numerical experiments on real-world datasets demonstrate the performance of the proposed method for edge classification and link prediction tasks on dynamic graphs. We also consider an application related to the COVID-19 pandemic, and show how our method can be used for early detection of infected individuals from contact tracing data.

Local graph diffusions have proven to be valuable tools for solving various graph clustering problems. As such, there has been much interest recently in efficient local algorithms for computing them. We present an efficient local algorithm for approximating a graph diffusion that generalizes both the celebrated personalized PageRank and its recent competitor/companion - the heat kernel. Our algorithm is based on writing the diffusion vector as the solution of an initial value problem, and then using a waveform relaxation approach to approximate the solution. Our experimental results suggest that it produces rankings that are distinct and competitive with the ones produced by high quality implementations of personalized PageRank and localized heat kernel, and that our algorithm is a useful addition to the toolset of localized graph diffusions.

Hessian-free training has become a popular parallel second order optimization technique for Deep Neural Network training. This study aims at speeding up Hessian-free training, both by means of decreasing the amount of data used for training, as well as through reduction of the number of Krylov subspace solver iterations used for implicit estimation of the Hessian. In this paper, we develop an L-BFGS based preconditioning scheme that avoids the need to access the Hessian explicitly. Since L-BFGS cannot be regarded as a fixed-point iteration, we further propose the employment of flexible Krylov subspace solvers that retain the desired theoretical convergence guarantees of their conventional counterparts. Second, we propose a new sampling algorithm, which geometrically increases the amount of data utilized for gradient and Krylov subspace iteration calculations. On a 50-hr English Broadcast News task, we find that these methodologies provide roughly a 1.5× speed-up, whereas, on a 300-hr Switchboard task, these techniques provide over a 2.3× speedup, with no loss in WER. These results suggest that even further speed-up is expected, as problems scale and complexity grows.