United States

This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system state using deep convolutional autoencoders. This defines a low-dimensional nonlinear manifold on which the state is subsequently enforced to evolve. Second, the method defines a latent-dynamics model that associates with the solution to a constrained optimization problem. Here, the objective function is defined as the sum of squares of conservation-law violations over control volumes within a finite-volume discretization of the problem; nonlinear equality constraints explicitly enforce conservation over prescribed subdomains of the problem. Under modest conditions, the resulting dynamics model guarantees that the time-evolution of the latent state exactly satisfies conservation laws over the prescribed subdomains.

AAAI 2021

Deep Conservation: A Latent-Dynamics Model for Exact Satisfaction of Physical Conservation Laws

Join AAPT and Physics Educators worldwide in developing and strengthening your professional connections by attending the 2021 AAPT Virtual Summer Meeting. AAPT meetings are a great way to reflect on your teaching, recommit to best practices and re-energize your career with new research, products, and techniques.

Listen to internationally known plenary speakers, attend sessions, workshops, and special activities. Attending the virtual summer meeting is an excellent opportunity to share your expertise and learn from and network with leaders in the field.

Please log in with your AAPT account or register for the event if you haven't already.

If you are registered please note that you need to be logged in with your AAPT email / credentials in order to get access.

AAPT SM 21

technical paper

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. 

Recently, deep reinforcement learning (RL) has achieved remarkable empirical success by integrating deep neural networks into RL frameworks. However, these algorithms often require a large number of training samples and admit little theoretical understanding. To mitigate these issues, we propose a theoretically principled nearest neighbor (NN) function approximator that can replace the value networks in deep RL methods. Inspired by human similarity judgments, the NN approximator estimates the action values using rollouts on past observations and can provably obtain a small regret bound that depends only on the intrinsic complexity of the environment. We present (1) Nearest Neighbor Actor-Critic (NNAC), an online policy gradient algorithm that demonstrates the practicality of combining function approximation with deep RL, and (2) a plug-and-play NN update module that aids the training of existing deep RL methods. Experiments on classical control and MuJoCo locomotion tasks show that the NN-accelerated agents achieve higher sample efficiency and stability than the baseline agents. Based on its theoretical benefits, we believe that the NN approximator can be further applied to other complex domains to speed-up learning.

Theoretically Principled Deep Rl Acceleration via Nearest Neighbor Function Approximation

Consider a set of voters V, represented by a multiset in a metric space (X,d). The voters have to reach a decision - a point in X. A choice pâˆˆ X is called a Î²-plurality point for V, if for any other choice qâˆˆ X it holds that |{vâˆˆ V âˆ£Â  Î²â‹… d(p,v)â‰¤ d(q,v)}|Â â‰¥|V|/2 . In other words, at least half of the voters ``prefer'' over q, when an extra factor of Î² is taken in favor of p.

For Î²=1, this is equivalent to Condorcet winner, which rarely exists. The concept of Î²-plurality was suggested by Aronov, de Berg, Gudmundsson, and Horton [SoCG 2020] as a relaxation of the Condorcet criterion. 

Denote by Î²*(X,d) the value sup{ Î² âˆ£Â  every finite multiset V in X admits a Î²-plurality point}}.
The parameter Î²* determines the amount of relaxation required in order to reach a stable decision.
Aronov et al. showed that for the Euclidean plane Î²*(â„2,\|â‹…\|2)=âˆš3/2 , and more generally, for d-dimensional Euclidean space, 1/âˆšd â‰¤ Î²*(â„d,\|â‹…\|2)â‰¤âˆš3/2 .

In this paper, we show that 0.557â‰¤ Î²*(â„d,\|â‹…\|2) for any dimension d (notice that 1/âˆšd <0.557 for any dâ‰¥ 4). In addition, we prove that for every metric space (X,d) it holds that âˆš2-1â‰¤Î²*(X,d), and show that there exists a metric space for which Î²*(X,d)â‰¤ 1/2 .

Condorcet Relaxation in Spatial Voting

We study an important and challenging task of attacking natural language processing models in a hard label black box setting. We propose a decision-based attack strategy that crafts high quality adversarial examples on text classification and entailment tasks. Our proposed attack strategy leverages population-based optimization algorithm to craft plausible and semantically similar adversarial examples by observing only the top label predicted by the target model. At each iteration, the optimization procedure allow word replacements that maximizes the overall semantic similarity between the original and the adversarial text. Further, our approach does not rely on using substitute models or any kind of training data. We demonstrate the efficacy of our proposed approach through extensive experimentation and ablation studies on five state-of-the-art target models across seven benchmark datasets. In comparison to attacks proposed in prior literature, we are able to achieve a higher success rate with lower word perturbation percentage that too in a highly restricted setting.

Generating Natural Language Attacks in a Hard Label Black Box Setting

Training an agent to solve control tasks directly from high-dimensional images with model-free reinforcement learning (RL) has proven difficult. A promising approach is to learn a latent representation together with the control policy. However, fitting a high-capacity encoder using a scarce reward signal is sample inefficient and leads to poor performance.
Prior work has shown that auxiliary losses, such as image reconstruction, can aid efficient representation learning.  
However, incorporating reconstruction loss into an off-policy learning algorithm often leads to training instability. We explore the underlying reasons and 
identify variational autoencoders, used by previous investigations, as the cause of the divergence.   
Following these findings, we propose effective techniques to improve training stability. 
This results in a simple approach capable of
matching state-of-the-art model-free and model-based algorithms on MuJoCo control tasks. Furthermore, our approach demonstrates robustness to observational noise, surpassing existing approaches in this setting. Code, results, and videos are anonymously available at https://sites.google.com/view/sac-ae/home.

Improving Sample Efficiency in Model-Free Reinforcement Learning from Images

This paper aims at enlarging the problem of Neural Architecture Search (NAS) from Single-Path and Multi-Path Search to automated Mixed-Path Search. In particular, we model the NAS problem as a sparse supernet using a new continuous architecture representation with a mixture of sparsity constraints. The sparse supernet enables us to automatically achieve sparsely-mixed paths upon a compact set of nodes. To optimize the proposed sparse supernet, we exploit a hierarchical accelerated proximal gradient algorithm within a bi-level optimization framework. Extensive experiments on Convolutional Neural Network and Recurrent Neural Network search demonstrate that the proposed method is capable of searching for compact, general and powerful neural architectures.

Neural Architecture Search as Sparse Supernet

Existing image segmentation networks mainly leverage large-scale labeled datasets to attain high accuracy. However, labeling medical images is very expensive since it requires sophisticated expert knowledge. Thus, it is more desirable to employ only a few labeled data in pursuing high segmentation performance. In this paper, we develop a data augmentation method for one-shot brain magnetic resonance imaging (MRI) image segmentation which exploits only one labeled MRI image (named atlas) and a few unlabeled images. In particular, we propose to learn the probability distributions of deformations (including shapes and intensities) of different unlabeled MRI images with respect to the atlas via 3D variational autoencoders (VAEs). In this manner, our method is able to exploit the learned distributions of image deformations to generate new authentic brain MRI images, and the number of generated samples will be sufficient to train a deep segmentation network. Furthermore, we introduce a new standard segmentation benchmark to evaluate the generalization performance of a segmentation network through a cross-dataset setting (collected from different sources). Extensive experiments demonstrate that our method outperforms the state-of-the-art one-shot medical segmentation methods. Our code has been released at https://github.com/dyh127/Modeling-the-Probabilistic-Distribution-of-Unlabeled-Data.

Modeling the Probabilistic Distribution of Unlabeled Data for One-Shot Medical Image Segmentation

Motivated by the increasing concern about privacy in nowadays data-intensive online learning systems, we consider a black-box optimization in the nonparametric Gaussian process setting with local differential privacy (LDP) guarantee. Specifically, the rewards from each user are further corrupted to protect privacy and the learner only has access to the corrupted rewards to minimize the regret. We first derive the regret lower bounds for any LDP mechanism and any learning algorithm. Then, we present three almost optimal algorithms based on the GP-UCB framework and Laplace DP mechanism. In this process, we also propose a new Bayesian optimization (BO) method (called MoMA-GP-UCB) based on median-of-means techniques and kernel approximations, which complements previous BO algorithms under heavy-tailed payoffs with reduced complexity. Further, empirical comparisons of different algorithms on both synthetic and real-world datasets highlight the superior performance of MoMA-GP-UCB in both private and non-private scenarios.

Local Differential Privacy for Bayesian Optimization

Recently decentralized optimization attracts much attention in machine learning because it is more communication-efficient than the centralized fashion. Quantization is a promising method to reduce the communication cost via cutting down the budget of each single communication using the gradient compression. To further improve the communication efficiency, more recently, some quantized decentralized algorithms have been studied. However, the quantized decentralized algorithm for nonconvex constrained machine learning problems is still limited. Frank-Wolfe (a.k.a., conditional gradient or projection-free) method is very efficient to solve many constrained optimization tasks, such as low-rank or sparsity-constrained models training. In this paper, to fill the gap of decentralized quantized constrained optimization, we propose a novel communication-efficient Decentralized Quantized Stochastic Frank-Wolfe (DQSFW) algorithm for non-convex constrained learning models. We first design a new counterexample to show that the vanilla decentralized quantized stochastic Frank-Wolfe algorithm usually diverges. Thus, we propose DQSFW algorithm with the gradient tracking technique to guarantee the method will converge to the stationary point of non-convex optimization safely. In our theoretical analysis, we prove that to achieve the stationary point our DQSFW algorithm achieves the same gradient complexity as the standard stochastic Frank-Wolfe and centralized Frank-Wolfe algorithms, but has much less communication cost. Experiments on matrix completion and model compression applications demonstrate the efficiency of our new algorithm.

Communication-Efficient Projection-Free Algorithm for Nonconvex Constrained Learning Models

Core-guided techniques have revolutionized Boolean satisfiability
approaches to optimization problems (MaxSAT), but the process at
the heart of these methods, strengthening bounds on solutions by
repeatedly adding cardinality constraints, remains a bottleneck.
Cardinality constraints require significant work to be re-encoded to
SAT, and SAT solvers are notoriously weak at cardinality reasoning.

In this work, we lift core-guided search to pseudo-Boolean (PB)
solvers, which deal with more general PB optimization problems
and operate natively with cardinality constraints. The cutting planes
method used in such solvers allows us to derive stronger cardinality
constraints, which yield better updates to solution bounds, and the
increased efficiency of objective function reformulation also makes it
feasible to switch repeatedly between lower-bounding and upper-
bounding search. A thorough evaluation on applied and crafted
benchmarks shows that our core-guided PB solver significantly
improves on the state of the art in pseudo-Boolean optimization.

Cutting to the Core of Pseudo-Boolean Optimization: Combining Core-Guided Search with Cutting Planes Reasoning

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.

Downloads

Next from AAAI 2021

Theoretically Principled Deep Rl Acceleration via Nearest Neighbor Function Approximation

Similar lecture

Spiraling Conservation of Energy/Mass in Introductory Physics: Kirchhoff to Bernoulli

.css-70qvj9{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}Downloads

Next from AAAI 2021

Theoretically Principled Deep Rl Acceleration via Nearest Neighbor Function Approximation

Similar lecture

Spiraling Conservation of Energy/Mass in Introductory Physics: Kirchhoff to Bernoulli

Downloads