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Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches often rely on the eigenvalue spectrum of the sample covariance matrix derived from finite measurement matrices; however, these spectra are sensitive to the size of the measurement matrix, leading to biased insights. In this paper, we introduce a novel algorithm that provides unbiased estimates of the spectral moments of the kernel integral operator in the limit of infinite inputs and features from finitely sampled measurement matrices. Our method, based on dynamic programming, is efficient and capable of estimating the moments of the operator spectrum. We demonstrate the accuracy of our estimator on radial basis function (RBF) kernels, highlighting its consistency with the theoretical spectra. Furthermore, we showcase the practical utility and robustness of our method in understanding the geometry of learned representations in neural networks.

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that emulate the physics of quantum systems. Similar to how physics problems are usually solved, parametric matrix models learn the governing equations that lead to the desired outputs. Parametric matrix models can be efficiently trained from empirical data, and the equations may use algebraic, differential, or integral relations. While originally designed for scientific computing, we prove that parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within an efficient and interpretable computational framework that allows for input feature extrapolation., Comment: Exact same content as previous version (v4); corrected author email

Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of those trajectories challenging. For many problems, such as for dexterous manipulation, the exact timings of the trajectories should be factored from their spatial path characteristics. In this work, we propose TimewarpVAE, a fully differentiable manifold-learning algorithm that incorporates Dynamic Time Warping (DTW) to simultaneously learn both timing variations and latent factors of spatial variation. We show how the TimewarpVAE algorithm learns appropriate time alignments and meaningful representations of spatial variations in handwriting and fork manipulation datasets. Our results have lower spatial reconstruction test error than baseline approaches and the learned low-dimensional representations can be used to efficiently generate semantically meaningful novel trajectories. We demonstrate the utility of our algorithm to generate novel high-speed trajectories for a robotic arm., Comment: Artificial Intelligence for Time Series Analysis (AI4TS): Theory, Algorithms, and Applications Workshop at IJCAI '24

We investigate how sparse neural activity affects the generalization performance of a deep Bayesian neural network at the large width limit. To this end, we derive a neural network Gaussian Process (NNGP) kernel with rectified linear unit (ReLU) activation and a predetermined fraction of active neurons. Using the NNGP kernel, we observe that the sparser networks outperform the non-sparse networks at shallow depths on a variety of datasets. We validate this observation by extending the existing theory on the generalization error of kernel-ridge regression.

Event-based sensors have recently drawn increasing interest in robotic perception due to their lower latency, higher dynamic range, and lower bandwidth requirements compared to standard CMOS-based imagers. These properties make them ideal tools for real-time perception tasks in highly dynamic environments. In this work, we demonstrate an application where event cameras excel: accurately estimating the impact location of fast-moving objects. We introduce a lightweight event representation called Binary Event History Image (BEHI) to encode event data at low latency, as well as a learning-based approach that allows real-time inference of a confidence-enabled control signal to the robot. To validate our approach, we present an experimental catching system in which we catch fast-flying ping-pong balls. We show that the system is capable of achieving a success rate of 81% in catching balls targeted at different locations, with a velocity of up to 13 m/s even on compute-constrained embedded platforms such as the Nvidia Jetson NX., Comment: 8 pages, 6 figures, IEEE Robotics and Automation Letters ( Volume: 7, Issue: 4, October 2022)

Large-scale AI systems that combine search and learning have reached super-human levels of performance in game-playing, but have also been shown to fail in surprising ways. The brittleness of such models limits their efficacy and trustworthiness in real-world deployments. In this work, we systematically study one such algorithm, AlphaZero, and identify two phenomena related to the nature of exploration. First, we find evidence of policy-value misalignment -- for many states, AlphaZero's policy and value predictions contradict each other, revealing a tension between accurate move-selection and value estimation in AlphaZero's objective. Further, we find inconsistency within AlphaZero's value function, which causes it to generalize poorly, despite its policy playing an optimal strategy. From these insights we derive VISA-VIS: a novel method that improves policy-value alignment and value robustness in AlphaZero. Experimentally, we show that our method reduces policy-value misalignment by up to 76%, reduces value generalization error by up to 50%, and reduces average value error by up to 55%., Comment: 9 pages, 5 figures

A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned from structural information such as the distribution of excitatory/inhibitory synapse types and the distribution of synaptic weights. Motivated by this question, we developed a statistical mechanical theory of learning in neural networks that incorporates structural information as constraints. We derived an analytical solution for the memory capacity of the perceptron, a basic feedforward model of supervised learning, with constraint on the distribution of its weights. Our theory predicts that the reduction in capacity due to the constrained weight-distribution is related to the Wasserstein distance between the imposed distribution and that of the standard normal distribution. To test the theoretical predictions, we use optimal transport theory and information geometry to develop an SGD-based algorithm to find weights that simultaneously learn the input-output task and satisfy the distribution constraint. We show that training in our algorithm can be interpreted as geodesic flows in the Wasserstein space of probability distributions. We further developed a statistical mechanical theory for teacher-student perceptron rule learning and ask for the best way for the student to incorporate prior knowledge of the rule. Our theory shows that it is beneficial for the learner to adopt different prior weight distributions during learning, and shows that distribution-constrained learning outperforms unconstrained and sign-constrained learning. Our theory and algorithm provide novel strategies for incorporating prior knowledge about weights into learning, and reveal a powerful connection between structure and function in neural networks., Comment: 38 pages, 13 figures. Updated introduction part and fixed several typos

Being able to grasp objects is a fundamental component of most robotic manipulation systems. In this paper, we present a new approach to simultaneously reconstruct a mesh and a dense grasp quality map of an object from a depth image. At the core of our approach is a novel camera-centric object representation called the "object shell" which is composed of an observed "entry image" and a predicted "exit image". We present an image-to-image residual ConvNet architecture in which the object shell and a grasp-quality map are predicted as separate output channels. The main advantage of the shell representation and the corresponding neural network architecture, ShellGrasp-Net, is that the input-output pixel correspondences in the shell representation are explicitly represented in the architecture. We show that this coupling yields superior generalization capabilities for object reconstruction and accurate grasp quality estimation implicitly considering the object geometry. Our approach yields an efficient dense grasp quality map and an object geometry estimate in a single forward pass. Both of these outputs can be used in a wide range of robotic manipulation applications. With rigorous experimental validation, both in simulation and on a real setup, we show that our shell-based method can be used to generate precise grasps and the associated grasp quality with over 90% accuracy. Diverse grasps computed on shell reconstructions allow the robot to select and execute grasps in cluttered scenes with more than 93% success rate., Comment: 18 pages, 12 figures, 8 tables

Emergent communication has made strides towards learning communication from scratch, but has focused primarily on protocols that resemble human language. In nature, multi-agent cooperation gives rise to a wide range of communication that varies in structure and complexity. In this work, we recognize the full spectrum of communication that exists in nature and propose studying lower-level communication. Specifically, we study emergent implicit signaling in the context of decentralized multi-agent learning in difficult, sparse reward environments. However, learning to coordinate in such environments is challenging. We propose a curriculum-driven strategy that combines: (i) velocity-based environment shaping, tailored to the skill level of the multi-agent team; and (ii) a behavioral curriculum that helps agents learn successful single-agent behaviors as a precursor to learning multi-agent behaviors. Pursuit-evasion experiments show that our approach learns effective coordination, significantly outperforming sophisticated analytical and learned policies. Our method completes the pursuit-evasion task even when pursuers move at half of the evader's speed, whereas the highest-performing baseline fails at 80% of the evader's speed. Moreover, we examine the use of implicit signals in coordination through position-based social influence. We show that pursuers trained with our strategy exchange more than twice as much information (in bits) than baseline methods, indicating that our method has learned, and relies heavily on, the exchange of implicit signals., Comment: 12 pages, 11 figures

We study fairness through the lens of cooperative multi-agent learning. Our work is motivated by empirical evidence that naive maximization of team reward yields unfair outcomes for individual team members. To address fairness in multi-agent contexts, we introduce team fairness, a group-based fairness measure for multi-agent learning. We then prove that it is possible to enforce team fairness during policy optimization by transforming the team's joint policy into an equivariant map. We refer to our multi-agent learning strategy as Fairness through Equivariance (Fair-E) and demonstrate its effectiveness empirically. We then introduce Fairness through Equivariance Regularization (Fair-ER) as a soft-constraint version of Fair-E and show that it reaches higher levels of utility than Fair-E and fairer outcomes than non-equivariant policies. Finally, we present novel findings regarding the fairness-utility trade-off in multi-agent settings; showing that the magnitude of the trade-off is dependent on agent skill., Comment: 12 pages, 5 figures

There have been many recent advances in representation learning; however, unsupervised representation learning can still struggle with model identification issues related to rotations of the latent space. Variational Auto-Encoders (VAEs) and their extensions such as $\beta$-VAEs have been shown to improve local alignment of latent variables with PCA directions, which can help to improve model disentanglement under some conditions. Borrowing inspiration from Independent Component Analysis (ICA) and sparse coding, we propose applying an $L_1$ loss to the VAE's generative Jacobian during training to encourage local latent variable alignment with independent factors of variation in images of multiple objects or images with multiple parts. We demonstrate our results on a variety of datasets, giving qualitative and quantitative results using information theoretic and modularity measures that show our added $L_1$ cost encourages local axis alignment of the latent representation with individual factors of variation., Comment: 17 pages, 10 figures, NeurIPS 2021 camera ready

This paper presents a supervised learning method to generate continuous cost-to-go functions of non-holonomic systems directly from the workspace description. Supervision from informative examples reduces training time and improves network performance. The manifold representing the optimal trajectories of a non-holonomic system has high-curvature regions which can not be efficiently captured with uniform sampling. To address this challenge, we present an adaptive sampling method which makes use of sampling-based planners along with local, closed-form solutions to generate training samples. The cost-to-go function over a specific workspace is represented as a neural network whose weights are generated by a second, higher order network. The networks are trained in an end-to-end fashion. In our previous work, this architecture was shown to successfully learn to generate the cost-to-go functions of holonomic systems using uniform sampling. In this work, we show that uniform sampling fails for non-holonomic systems. However, with the proposed adaptive sampling methodology, our network can generate near-optimal trajectories for non-holonomic systems while avoiding obstacles. Experiments show that our method is two orders of magnitude faster compared to traditional approaches in cluttered environments.

This paper presents c2g-HOF networks which learn to generate cost-to-go functions for manipulator motion planning. The c2g-HOF architecture consists of a cost-to-go function over the configuration space represented as a neural network (c2g-network) as well as a Higher Order Function (HOF) network which outputs the weights of the c2g-network for a given input workspace. Both networks are trained end-to-end in a supervised fashion using costs computed from traditional motion planners. Once trained, c2g-HOF can generate a smooth and continuous cost-to-go function directly from workspace sensor inputs (represented as a point cloud in 3D or an image in 2D). At inference time, the weights of the c2g-network are computed very efficiently and near-optimal trajectories are generated by simply following the gradient of the cost-to-go function. We compare c2g-HOF with traditional planning algorithms for various robots and planning scenarios. The experimental results indicate that planning with c2g-HOF is significantly faster than other motion planning algorithms, resulting in orders of magnitude improvement when including collision checking. Furthermore, despite being trained from sparsely sampled trajectories in configuration space, c2g-HOF generalizes to generate smoother, and often lower cost, trajectories. We demonstrate cost-to-go based planning on a 7 DoF manipulator arm where motion planning in a complex workspace requires only 0.13 seconds for the entire trajectory.

In this work, we study emergent communication through the lens of cooperative multi-agent behavior in nature. Using insights from animal communication, we propose a spectrum from low-bandwidth (e.g. pheromone trails) to high-bandwidth (e.g. compositional language) communication that is based on the cognitive, perceptual, and behavioral capabilities of social agents. Through a series of experiments with pursuit-evasion games, we identify multi-agent reinforcement learning algorithms as a computational model for the low-bandwidth end of the communication spectrum., Comment: 10 pages, 6 figures, Appearing in Talking to Strangers: Zero-Shot Emergent Communication Workshop NeurIPS 2020. Fixed part (a) of Figure 2 to include correct baseline reported in quantitative results section

This paper presents a Dynamic Vision Sensor (DVS) based system for reasoning about high speed motion. As a representative scenario, we consider the case of a robot at rest reacting to a small, fast approaching object at speeds higher than 15m/s. Since conventional image sensors at typical frame rates observe such an object for only a few frames, estimating the underlying motion presents a considerable challenge for standard computer vision systems and algorithms. In this paper we present a method motivated by how animals such as insects solve this problem with their relatively simple vision systems. Our solution takes the event stream from a DVS and first encodes the temporal events with a set of causal exponential filters across multiple time scales. We couple these filters with a Convolutional Neural Network (CNN) to efficiently extract relevant spatiotemporal features. The combined network learns to output both the expected time to collision of the object, as well as the predicted collision point on a discretized polar grid. These critical estimates are computed with minimal delay by the network in order to react appropriately to the incoming object. We highlight the results of our system to a toy dart moving at 23.4m/s with a 24.73{\deg} error in ${\theta}$, 18.4mm average discretized radius prediction error, and 25.03% median time to collision prediction error.

Traditional motion planning is computationally burdensome for practical robots, involving extensive collision checking and considerable iterative propagation of cost values. We present a novel neural network architecture which can directly generate the cost-to-go (c2g) function for a given configuration space and a goal configuration. The output of the network is a continuous function whose gradient in configuration space can be directly used to generate trajectories in motion planning without the need for protracted iterations or extensive collision checking. This higher order function (i.e. a function generating another function) representation lies at the core of our motion planning architecture, c2g-HOF, which can take a workspace as input, and generate the cost-to-go function over the configuration space map (C-map). Simulation results for 2D and 3D environments show that c2g-HOF can be orders of magnitude faster at execution time than methods which explore the configuration space during execution. We also present an implementation of c2g-HOF which generates trajectories for robot manipulators directly from an overhead image of the workspace.

We solve active target tracking, one of the essential tasks in autonomous systems, using a deep reinforcement learning (RL) approach. In this problem, an autonomous agent is tasked with acquiring information about targets of interests using its onboard sensors. The classical challenges in this problem are system model dependence and the difficulty of computing information-theoretic cost functions for a long planning horizon. RL provides solutions for these challenges as the length of its effective planning horizon does not affect the computational complexity, and it drops the strong dependency of an algorithm on system models. In particular, we introduce Active Tracking Target Network (ATTN), a unified RL policy that is capable of solving major sub-tasks of active target tracking -- in-sight tracking, navigation, and exploration. The policy shows robust behavior for tracking agile and anomalous targets with a partially known target model. Additionally, the same policy is able to navigate in obstacle environments to reach distant targets as well as explore the environment when targets are positioned in unexpected locations., Comment: IEEE Transaction on Robotics (under review); Demo video: https://youtu.be/0ZFyOWJ2ulo ; Source code: https://github.com/coco66/ttenv

Single-view 3D object reconstruction is a challenging fundamental problem in computer vision, largely due to the morphological diversity of objects in the natural world. In particular, high curvature regions are not always captured effectively by methods trained using only set-based loss functions, resulting in reconstructions short-circuiting the surface or cutting corners. In particular, high curvature regions are not always captured effectively by methods trained using only set-based loss functions, resulting in reconstructions short-circuiting the surface or cutting corners. To address this issue, we propose learning an image-conditioned mapping function from a canonical sampling domain to a high dimensional space where the Euclidean distance is equal to the geodesic distance on the object. The first three dimensions of a mapped sample correspond to its 3D coordinates. The additional lifted components contain information about the underlying geodesic structure. Our results show that taking advantage of these learned lifted coordinates yields better performance for estimating surface normals and generating surfaces than using point cloud reconstructions alone. Further, we find that this learned geodesic embedding space provides useful information for applications such as unsupervised object decomposition.

This paper presents a novel end-to-end system for pedestrian detection using Dynamic Vision Sensors (DVSs). We target applications where multiple sensors transmit data to a local processing unit, which executes a detection algorithm. Our system is composed of (i) a near-chip event filter that compresses and denoises the event stream from the DVS, and (ii) a Binary Neural Network (BNN) detection module that runs on a low-computation edge computing device (in our case a STM32F4 microcontroller). We present the system architecture and provide an end-to-end implementation for pedestrian detection in an office environment. Our implementation reduces transmission size by up to 99.6% compared to transmitting the raw event stream. The average packet size in our system is only 1397 bits, while 307.2 kb are required to send an uncompressed DVS time window. Our detector is able to perform a detection every 450 ms, with an overall testing F1 score of 83%. The low bandwidth and energy properties of our system make it ideal for IoT applications., Comment: 6 pages, 5 figures

We address the problem of generating a high-resolution surface reconstruction from a single image. Our approach is to learn a Higher Order Function (HOF) which takes an image of an object as input and generates a mapping function. The mapping function takes samples from a canonical domain (e.g. the unit sphere) and maps each sample to a local tangent plane on the 3D reconstruction of the object. Each tangent plane is represented as an origin point and a normal vector at that point. By efficiently learning a continuous mapping function, the surface can be generated at arbitrary resolution in contrast to other methods which generate fixed resolution outputs. We present the Surface HOF in which both the higher order function and the mapping function are represented as neural networks, and train the networks to generate reconstructions of PointNet objects. Experiments show that Surface HOF is more accurate and uses more efficient representations than other state of the art methods for surface reconstruction. Surface HOF is also easier to train: it requires minimal input pre-processing and output post-processing and generates surface representations that are more parameter efficient. Its accuracy and convenience make Surface HOF an appealing method for single image reconstruction.

In this paper, we propose a novel Reinforcement Learning approach for solving the Active Information Acquisition problem, which requires an agent to choose a sequence of actions in order to acquire information about a process of interest using on-board sensors. The classic challenges in the information acquisition problem are the dependence of a planning algorithm on known models and the difficulty of computing information-theoretic cost functions over arbitrary distributions. In contrast, the proposed framework of reinforcement learning does not require any knowledge on models and alleviates the problems during an extended training stage. It results in policies that are efficient to execute online and applicable for real-time control of robotic systems. Furthermore, the state-of-the-art planning methods are typically restricted to short horizons, which may become problematic with local minima. Reinforcement learning naturally handles the issue of planning horizon in information problems as it maximizes a discounted sum of rewards over a long finite or infinite time horizon. We discuss the potential benefits of the proposed framework and compare the performance of the novel algorithm to an existing information acquisition method for multi-target tracking scenarios., Comment: IROS 2019, Video https://youtu.be/0ZFyOWJ2ulo

We consider the problem of planning views for a robot to acquire images of an object for visual inspection and reconstruction. In contrast to offline methods which require a 3D model of the object as input or online methods which rely on only local measurements, our method uses a neural network which encodes shape information for a large number of objects. We build on recent deep learning methods capable of generating a complete 3D reconstruction of an object from a single image. Specifically, in this work, we extend a recent method which uses Higher Order Functions (HOF) to represent the shape of the object. We present a new generalization of this method to incorporate multiple images as input and establish a connection between visibility and reconstruction quality. This relationship forms the foundation of our view planning method where we compute viewpoints to visually cover the output of the multi-view HOF network with as few images as possible. Experiments indicate that our method provides a good compromise between online and offline methods: Similar to online methods, our method does not require the true object model as input. In terms of number of views, it is much more efficient. In most cases, its performance is comparable to the optimal offline case even on object classes the network has not been trained on., Comment: 7 pages, 6 figures

We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by applying its encoded transformation to points randomly sampled from a simple geometric space, such as the unit sphere. We study the effectiveness of our method through various experiments on subsets of the ShapeNet dataset. We find that the proposed approach can reconstruct encoded objects with accuracy equal to or exceeding state-of-the-art methods with orders of magnitude fewer parameters. Our smallest mapping network has only about 7000 parameters and shows reconstruction quality on par with state-of-the-art object decoder architectures with millions of parameters. Further experiments on feature mixing through the composition of learned functions show that the encoding captures a meaningful subspace of objects., Comment: To be published in International Conference on Learning Representations (ICLR 2020) [https://openreview.net/forum?id=HJgfDREKDB]; 19 pages

In this paper, we introduce a new probabilistically safe local steering primitive for sampling-based motion planning in complex high-dimensional configuration spaces. Our local steering procedure is based on a new notion of a convex probabilistically safe corridor that is constructed around a configuration using tangent hyperplanes of confidence ellipsoids of Gaussian mixture models learned from prior collision history. Accordingly, we propose to expand a random motion planning graph towards a sample goal using its projection onto probabilistically safe corridors, which efficiently exploits the local geometry of configuration spaces for selecting proper steering direction and adapting steering stepsize. We observe that the proposed local steering procedure generates effective steering motion around difficult regions of configuration spaces, such as narrow passages, while minimizing collision likelihood. We evaluate the proposed steering method with randomized motion planners in a number of planning scenarios, both in simulation and on a physical 7DoF robot arm, demonstrating the effectiveness of our safety guided local planner over the standard straight-line planner., Comment: 10 pages

Periodical inspection and maintenance of critical infrastructure such as dams, penstocks, and locks are of significant importance to prevent catastrophic failures. Conventional manual inspection methods require inspectors to climb along a penstock to spot corrosion, rust and crack formation which is unsafe, labor-intensive, and requires intensive training. This work presents an alternative approach using a Micro Aerial Vehicle (MAV) that autonomously flies to collect imagery which is then fed into a pretrained deep-learning model to identify corrosion. Our simplified U-Net trained with less than 40 image samples can do inference at 12 fps on a single GPU. We analyze different loss functions to solve the class imbalance problem, followed by a discussion on choosing proper metrics and weights for object classes. Results obtained with the dataset collected from Center Hill Dam, TN show that focal loss function, combined with a proper set of class weights yield better segmentation results than the base loss, Softmax cross entropy. Our method can be used in combination with planning algorithm to offer a complete, safe and cost-efficient solution to autonomous infrastructure inspection., Comment: 8 Pages, 4 figures

This paper considers the design of optimal resource allocation policies in wireless communication systems which are generically modeled as a functional optimization problem with stochastic constraints. These optimization problems have the structure of a learning problem in which the statistical loss appears as a constraint, motivating the development of learning methodologies to attempt their solution. To handle stochastic constraints, training is undertaken in the dual domain. It is shown that this can be done with small loss of optimality when using near-universal learning parameterizations. In particular, since deep neural networks (DNN) are near-universal their use is advocated and explored. DNNs are trained here with a model-free primal-dual method that simultaneously learns a DNN parametrization of the resource allocation policy and optimizes the primal and dual variables. Numerical simulations demonstrate the strong performance of the proposed approach on a number of common wireless resource allocation problems.

Sampling-based motion planners have experienced much success due to their ability to efficiently and evenly explore the state space. However, for many tasks, it may be more efficient to not uniformly explore the state space, especially when there is prior information about its structure. Previous methods have attempted to modify the sampling distribution using hand selected heuristics that can work well for specific environments but not universally. In this paper, a policy- search based method is presented as an adaptive way to learn implicit sampling distributions for different environments. It utilizes information from past searches in similar environments to generate better distributions in novel environments, thus reducing overall computational cost. Our method can be incor- porated with a variety of sampling-based planners to improve performance. Our approach is validated on a number of tasks, including a 7DOF robot arm, showing marked improvement in number of collision checks as well as number of nodes expanded compared with baseline methods., Comment: Currently under review for IROS 2018 and RAL

In this paper, we explore using deep reinforcement learning for problems with multiple agents. Most existing methods for deep multi-agent reinforcement learning consider only a small number of agents. When the number of agents increases, the dimensionality of the input and control spaces increase as well, and these methods do not scale well. To address this, we propose casting the multi-agent reinforcement learning problem as a distributed optimization problem. Our algorithm assumes that for multi-agent settings, policies of individual agents in a given population live close to each other in parameter space and can be approximated by a single policy. With this simple assumption, we show our algorithm to be extremely effective for reinforcement learning in multi-agent settings. We demonstrate its effectiveness against existing comparable approaches on co-operative and competitive tasks.

A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a $k$-nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function $f.$ Some instantiations of the proposed estimator recover existing $k$-nearest neighbor based estimators of Shannon and R\'enyi entropies and Kullback--Leibler and R\'enyi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The $L_2$-consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities., Comment: 43 pages, 4 figures. IEEE Transactions on Information Theory (to appear)

Human populations exhibit complex behaviors---characterized by long-range correlations and surges in activity---across a range of social, political, and technological contexts. Yet it remains unclear where these collective behaviors come from, or if there even exists a set of unifying principles. Indeed, existing explanations typically rely on context-specific mechanisms, such as traffic jams driven by work schedules or spikes in online traffic induced by significant events. However, analogies with statistical mechanics suggest a more general mechanism: that collective patterns can emerge organically from fine-scale interactions within a population. Here, across four different modes of human activity, we show that the simplest correlations in a population---those between pairs of individuals---can yield accurate quantitative predictions for the large-scale behavior of the entire population. To quantify the minimal consequences of pairwise correlations, we employ the principle of maximum entropy, making our description equivalent to an Ising model whose interactions and external fields are notably calculated from past observations of population activity. In addition to providing accurate quantitative predictions, we show that the topology of learned Ising interactions resembles the network of inter-human communication within a population. Together, these results demonstrate that fine-scale correlations can be used to predict large-scale social behaviors, a perspective that has critical implications for modeling and resource allocation in human populations.

A wide array of complex biological, social, and physical systems have recently been shown to be quantitatively described by Ising models, which lie at the intersection of statistical physics and machine learning. Here, we study the fundamental question of how to optimize the state of a networked Ising system given a budget of external influence. In the continuous setting where one can tune the influence applied to each node, we propose a series of approximate gradient ascent algorithms based on the Plefka expansion, which generalizes the na\"{i}ve mean field and TAP approximations. In the discrete setting where one chooses a small set of influential nodes, the problem is equivalent to the famous influence maximization problem in social networks with an additional stochastic noise term. In this case, we provide sufficient conditions for when the objective is submodular, allowing a greedy algorithm to achieve an approximation ratio of $1-1/e$. Additionally, we compare the Ising-based algorithms with traditional influence maximization algorithms, demonstrating the practical importance of accurately modeling stochastic fluctuations in the system.

While off-policy temporal difference (TD) methods have widely been used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have not been utilized as frequently. One reason is that the non-linear max operation in the Bellman optimality equation makes it difficult to define conjugate distributions over the value functions. In this paper, we introduce a novel Bayesian approach to off-policy TD methods, called as ADFQ, which updates beliefs on state-action values, Q, through an online Bayesian inference method known as Assumed Density Filtering. We formulate an efficient closed-form solution for the value update by approximately estimating analytic parameters of the posterior of the Q-beliefs. Uncertainty measures in the beliefs not only are used in exploration but also provide a natural regularization for the value update considering all next available actions. ADFQ converges to Q-learning as the uncertainty measures of the Q-beliefs decrease and improves common drawbacks of other Bayesian RL algorithms such as computational complexity. We extend ADFQ with a neural network. Our empirical results demonstrate that ADFQ outperforms comparable algorithms on various Atari 2600 games, with drastic improvements in highly stochastic domains or domains with a large action space., Comment: source code: https://github.com/coco66/ADFQ.git ; IJCAI-19

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination requires classifying the manifolds in a manner that is insensitive to variability within a manifold. How neuronal systems give rise to invariant object classification and recognition is a fundamental problem in brain theory as well as in machine learning. Here we study the ability of a readout network to classify objects from their perceptual manifold representations. We develop a statistical mechanical theory for the linear classification of manifolds with arbitrary geometry revealing a remarkable relation to the mathematics of conic decomposition. Novel geometrical measures of manifold radius and manifold dimension are introduced which can explain the classification capacity for manifolds of various geometries. The general theory is demonstrated on a number of representative manifolds, including L2 ellipsoids prototypical of strictly convex manifolds, L1 balls representing polytopes consisting of finite sample points, and orientation manifolds which arise from neurons tuned to respond to a continuous angle variable, such as object orientation. The effects of label sparsity on the classification capacity of manifolds are elucidated, revealing a scaling relation between label sparsity and manifold radius. Theoretical predictions are corroborated by numerical simulations using recently developed algorithms to compute maximum margin solutions for manifold dichotomies. Our theory and its extensions provide a powerful and rich framework for applying statistical mechanics of linear classification to data arising from neuronal responses to object stimuli, as well as to artificial deep networks trained for object recognition tasks., Comment: 24 pages, 12 figures, Supplementary Materials

Planning problems in partially observable environments cannot be solved directly with convolutional networks and require some form of memory. But, even memory networks with sophisticated addressing schemes are unable to learn intelligent reasoning satisfactorily due to the complexity of simultaneously learning to access memory and plan. To mitigate these challenges we introduce the Memory Augmented Control Network (MACN). The proposed network architecture consists of three main parts. The first part uses convolutions to extract features and the second part uses a neural network-based planning module to pre-plan in the environment. The third part uses a network controller that learns to store those specific instances of past information that are necessary for planning. The performance of the network is evaluated in discrete grid world environments for path planning in the presence of simple and complex obstacles. We show that our network learns to plan and can generalize to new environments.