United States

Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are challenging to learn due to the presence of nonlinear potentials and a number of interactions that scales quadratically with the number of particles N, as in the case of the N-body problem. In this work we introduce an approach that transforms a fully-connected interaction graph into a hierarchical one which reduces the number of edges to O(N). This results in a linear time and space complexity while the pre-computation of the hierarchical graph requires O(N log (N)) time and O(N) space. Using our approach, we are able to train models on much larger particle counts, even on a single GPU. We evaluate how the phase space position accuracy and energy conservation depend on the number of simulated particles. Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations which are impossible to run on a single machine if a fully-connected graph is used. Similar results are also observed when simulating Coulomb interactions. Furthermore, we make several important observations regarding the performance of this new hierarchical model, including: i) its accuracy tends to improve with the number of particles in the simulation and ii) its generalisation to unseen particle counts is also much better than for models that use all O(N^2) interactions.

AAAI 2021

Scalable Graph Networks for Particle Simulations

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

AAAI 2022

technical paper

Optical neural networks (ONNs) have demonstrated record-breaking potential in high-performance neuromorphic computing due to their ultra-high execution speed and low energy consumption. However, current learning protocols fail to provide scalable and efficient solutions to photonic circuit optimization in practical applications. In this work, we propose a novel on-chip learning framework to release the full potential of ONNs for power-efficient in situ training. Instead of deploying implementation-costly back-propagation, we directly optimize the device configurations with computation budgets and power constraints. We are the first to model the ONN on-chip learning as a resource-constrained stochastic noisy zeroth-order optimization problem, and propose a novel mixed-training strategy with two-level sparsity and power-aware dynamic pruning to offer a scalable on-chip training solution in practical ONN deployment. Compared with previous methods, we are the first to optimize over 2,500 optical components on chip. We can achieve much better optimization stability, 3.7x-7.6x higher efficiency, and save >90% power under practical device variations and thermal crosstalk.

Efficient On-Chip Learning for Optical Neural Networks through Power-Aware Sparse Zeroth-Order Optimization

This paper studies the unsupervised cross-domain translation problem by proposing a generative framework, in which the probability distribution of each domain is represented by a generative cooperative network that consists of an energy-based model and a latent variable model. The use of generative cooperative network enables maximum likelihood learning of the domain model by MCMC teaching, where the energy-based model seeks to fit the data distribution of domain and distills its knowledge to the latent variable model via MCMC. Specifically, in the MCMC teaching process, the latent variable model parameterized by an encoder-decoder maps examples from the source domain to the target domain, while the energy-based model further refines the mapped results by Langevin revision such that the revised results match to the examples in the target domain in terms of the statistical properties, which are defined by the learned energy function. For the purpose of building up a correspondence between two unpaired domains, the proposed framework simultaneously learns a pair of cooperative networks with cycle consistency, accounting for a two-way translation between two domains, by alternating MCMC teaching. Experiments show that the proposed framework is useful for unsupervised image-to-image translation and unpaired image sequence translation.

Learning Cycle-Consistent Cooperative Networks via Alternating MCMC Teaching for Unsupervised Cross-Domain Translation

Description logics (DLs) are knowledge representation languages that are used in the field of artificial intelligence (AI).
A common technique is to query DL knowledge bases, e.g., by Boolean Datalog queries, and ask for entailment. 
But real world knowledge-bases are often obtained by combining data from various sources. 
This, inherently, might result in certain inconsistencies (with respect to a given query) and requires to estimate a degree of inconsistency before using a knowledge-base.
In this paper, we provide a complexity analysis of fixed-domain non-entailment (NE) on Datalog programs for well-established families of knowledge bases (KBs).
We exhibit a detailed complexity map for the decision cases, counting and projected counting, which may serve as a quantitative measure for inconsistency of a KB with respect to a query.
Our results show that NE is natural for the second, third, and fourth level of the polynomial (counting) hierarchy depending on the type of the studied query (stratified, normal, disjunctive) and one level higher for the projected versions.
Further, we show fixed-parameter tractability by bounding the treewidth, provide a constructive algorithm, and show its theoretical limitation in terms of conditional lower bounds.

Knowledge-Base Degrees of Inconsistency: Complexity and Counting

We study approval-based committee elections for the case where the voters' preferences come from a 2D-Euclidean model. We consider two main issues: First, we ask for the complexity of computing election results. Second, we evaluate election outcomes experimentally, following the visualization technique of Elkind et al., (AAAI-2017).  Regarding the first issue, we find that many NP-hard rules remain intractable for 2D-Euclidean elections. For the second one, we observe that the behavior and nature of many rules strongly depends on the exact protocol for choosing the approved candidates.

An Analysis of Approval-Based Committee Rules for 2D-Euclidean Elections

Bayesian optimization (BO) is an efficient framework for solving black-box optimization problems with expensive function evaluations. This paper addresses the BO problem setting for combinatorial spaces (e.g., sequences and graphs) that occurs naturally in science and engineering applications. A prototypical example is molecular optimization guided by expensive experiments. The key challenge is to balance the complexity of statistical models and tractability of search to select combinatorial structures for evaluation. In this paper, we propose an efficient approach referred as Mercer Features for Combinatorial Bayesian Optimization (MerCBO). The key idea behind MerCBO is to provide explicit feature maps for diffusion kernels over discrete objects by exploiting the structure of their combinatorial graph representation. These Mercer features combined with Thompson sampling as the acquisition function allows us to employ efficient solvers for finding the next structure for evaluation. Experimental evaluation on diverse real-world benchmarks demonstrates that MerCBO performs similarly or better than prior methods.

Mercer Features for Efficient Combinatorial Bayesian Optimization

We propose a market-inspired bidding scheme for the assignment of paper reviews in large academic conferences. We provide an analysis of the incentives of reviewers during the bidding phase, when reviewers have both private costs and some information about the demand for each paper; and their  goal is to obtain the best possible k papers for a predetermined k. 

We show that by assigning `budgets' to reviewers and a `price' for every paper that is (roughly) proportional to its  demand, the best response of a reviewer is to bid sincerely, i.e., on her most favorite papers, and match the budget even when it is not enforced.  This game-theoretic analysis is based on a simple, prototypical assignment algorithm.
We show via extensive simulations on bidding data from real conferences, that our  bidding scheme would substantially improve both the bid distribution and the resulting assignment.

A Market-Inspired Bidding Scheme for Peer Review Paper Assignment

Interpretable machine learning has gained much attention recently. Briefness and comprehensiveness are necessary in order to provide a large amount of information concisely when explaining a black-box decision system. However, existing interpretable machine learning methods fail to consider briefness and comprehensiveness simultaneously, leading to redundant explanations. We propose the variational information bottleneck for interpretation, VIBI, a system-agnostic interpretable method that provides a brief but comprehensive explanation. VIBI adopts an information theoretic principle, information bottleneck principle, as a criterion for finding such explanations. For each instance, VIBI selects key features that are maximally compressed about an input (briefness), and informative about a decision made by a black-box system on that input (comprehensive). We evaluate VIBI on three datasets and compare with state-of-the-art interpretable machine learning methods in terms of both interpretability and fidelity evaluated by human and quantitative metrics.

Explaining a Black-Box by Using a Deep Variational information Bottleneck Approach

Out-of-town recommendation is designed for those users who leave their home-town areas and visit the areas they have never been to before. It is challenging to recommend Point-of-Interests (POIs) for out-of-town users since the out-of-town check-in behavior is determined by not only the userâ€™s home-town preference but also the userâ€™s travel intention. Besides, the userâ€™s travel intentions are complex and dynamic, which leads to big difficulties in understanding such intentions precisely. In this paper, we propose a TRAvel-INtention-aware Out-of-town Recommendation framework, named TRAINOR. The proposed TRAINOR framework distinguishes itself from existing out-of-town recommenders in three aspects. First, graph neural networks are explored to represent usersâ€™ home-town check-in preference and geographical constraints in out-of-town check-in behaviors. Second, a user-specific travel intention is formulated as an aggregation combining home-town preference and generic travel intention together, where the generic travel intention is regarded as a mixture of inherent intentions that can be learned by Neural Topic Model (NTM). Third, a non-linear mapping function, as well as a matrix factorization method, are employed to transfer usersâ€™ home-town preference and estimate out-of-town POIâ€™s representation, respectively. Extensive experiments on real-world data sets validate the effectiveness of the TRAINOR framework. Moreover, the learned travel intention can deliver meaningful explanations for understanding a userâ€™s travel purposes.

Out-of-Town Recommendation with Travel Intention Modeling

Constrained Markov decision processes (CMDPs) formalize sequential decision-making problems whose objective is to minimize a cost function while satisfying constraints on various cost functions. In this paper, we consider the setting of episodic fixed-horizon CMDPs. We propose an online algorithm which leverages the linear programming formulation of repeated optimistic planning for finite-horizon CMDP to provide a probably approximately correctness (PAC) guarantee on the number of episodes needed to ensure a near optimal policy,  i.e., with resulting objective value close to that of the optimal value and satisfying the constraints within low tolerance, with high probability. The number of episodes needed is shown to have linear dependence on the sizes of the state and action spaces and quadratic dependence on the time horizon and an upper bound on the number of possible successor states for a state-action pair. Therefore, if the upper bound on the number of possible successor states is much smaller than the size of the state space, the number of needed episodes becomes linear in the sizes of the state and action spaces and quadratic in the time horizon.

A Sample-Efficient Algorithm for Episodic Finite-Horizon MDP with Constraints

Due to the intractable partition function, training energy-based models (EBMs) by maximum likelihood requires Markov chain Monte Carlo (MCMC) sampling to approximate the gradient of the Kullback-Leibler divergence between data and model distributions. However, it is non-trivial to sample from an EBM because of the difficulty of mixing between modes. In this paper, we propose to learn a variational auto-encoder (VAE) to initialize the finite-step MCMC, such as Langevin dynamics that is derived from the energy function, for efficient amortized sampling of the EBM. With these amortized MCMC samples, the EBM can be trained by maximum likelihood, which follows an "analysis by synthesis" scheme; while the VAE learns from these MCMC samples via variational Bayes. We call this joint training algorithm the variational MCMC teaching, in which the VAE chases the EBM toward data distribution. We interpret the learning algorithm as a dynamic alternating projection in the context of information geometry. Our proposed models can generate samples comparable to GANs and EBMs. Additionally, we demonstrate that our model can learn effective probabilistic distribution toward supervised conditional learning tasks.

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Efficient On-Chip Learning for Optical Neural Networks through Power-Aware Sparse Zeroth-Order Optimization

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Sharp Analysis of Random Fourier Features in Classification

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