arXiv subjects

Daniel D. Lee

Publications and source records attributed to Daniel D. Lee.

45 records · Page 3Linked to original sources

arXiv2017

Neural Network Memory Architectures for Autonomous Robot Navigation

This paper highlights the significance of including memory structures in neural networks when the latter are used to learn perception-action loops for autonomous robot navigation. Traditional navigation approaches rely on global maps of the environment to overcome cul-de-sacs and plan feasible motions. Yet, maintaining an accurate global map may be challenging in real-world settings. A possible way to mitigate this limitation is to use learning techniques that forgo hand-engineered map representations and infer appropriate control responses directly from sensed information. An important but unexplored aspect of such approaches is the effect of memory on their performance. This work is a first thorough study of memory structures for deep-neural-network-based robot navigation, and offers novel tools to train such networks from supervision and quantify their ability to generalize to unseen scenarios. We analyze the separation and generalization abilities of feedforward, long short-term memory, and differentiable neural computer networks. We introduce a new method to evaluate the generalization ability by estimating the VC-dimension of networks with a final linear readout layer. We validate that the VC estimates are good predictors of actual test performance. The reported method can be applied to deep learning problems beyond robotics.

cs.RO↗

arXiv2017

Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution

Influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising system at dynamic equilibrium. We formalize the \textit{Ising influence maximization} problem, which has a natural physical interpretation as maximizing the magnetization given a budget of external magnetic field. Under the mean-field (MF) approximation, we present a gradient ascent algorithm that uses the susceptibility to efficiently calculate local maxima of the magnetization, and we develop a number of sufficient conditions for when the MF magnetization is concave and our algorithm converges to a global optimum. We apply our algorithm on random and real-world networks, demonstrating, remarkably, that the MF optimal external fields (i.e., the external fields which maximize the MF magnetization) shift from focusing on high-degree individuals at high temperatures to focusing on low-degree individuals at low temperatures. We also establish a number of novel results about the structure of steady-states in the ferromagnetic MF Ising model on general graph topologies, which are of independent interest.

cond-mat.dis-nn↗

arXiv2016

Optimally Influencing Complex Ising Systems

In the study of social networks, a fundamental problem is that of influence maximization (IM): How can we maximize the collective opinion of individuals in a network given constrained marketing resources? Traditionally, the IM problem has been studied in the context of contagion models, which treat opinions as irreversible viruses that propagate through the network. To study reverberant opinion dynamics, which yield complex macroscopic behavior, the IM problem has recently been proposed in the context of the Ising model of opinion dynamics, in which individual opinions are treated as spins in an Ising system. In this paper, we are among the first to explore the \textit{Ising influence maximization (IIM)} problem, which has a natural physical interpretation as the maximization of the magnetization given a budget of external magnetic field, and we are the first to consider the IIM problem in general Ising systems with negative couplings and negative external fields. For a general Ising system, we show analytically that the optimal external field (i.e., that which maximizes the magnetization) exhibits a phase shift from intuitively focusing on high-degree nodes at high temperatures to counterintuitively focusing on "loosely-connected" nodes, which are weakly energetically bound to the ground state, at low temperatures. We also present a novel and efficient algorithm for solving IIM with provable performance guarantees for ferromagnetic systems in nonnegative external fields. We apply our algorithm on large random and real-world networks, verifying the existence of phase shifts in the optimal external fields and comparing the performance of our algorithm with the state-of-the-art mean-field-based algorithm.

cond-mat.dis-nn↗

arXiv2016

Linear Readout of Object Manifolds

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory that characterizes the ability of a linear readout network, the perceptron, to classify objects from variable neural responses. We show how the readout perceptron capacity depends on the dimensionality, size, and shape of the object manifolds in its input neural representation.

cond-mat.dis-nn↗

arXiv2015

Belief Flows of Robust Online Learning

This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian belief over the optimal weight parameters. Unlike traditional Bayesian updates, the model incorporates a small number of gradient evaluations at locations chosen using Thompson sampling, making it computationally tractable. The belief is then transformed via a linear flow field which optimally updates the belief distribution using rules derived from information theoretic principles. Several versions of the algorithm are shown using different constraints on the flow field and compared with conventional online learning algorithms. Results are given for several classification tasks including logistic regression and multilayer neural networks.

stat.ML↗

arXiv2014

An Adversarial Interpretation of Information-Theoretic Bounded Rationality

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory.

cs.AI↗

arXiv2011

Learning Discriminative Metrics via Generative Models and Kernel Learning

Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework. Specifically, we learn local metrics optimized from parametric generative models. These are then used as base kernels to construct a global kernel that minimizes a discriminative training criterion. We consider both linear and nonlinear combinations of local metric kernels. Our empirical results show that these combinations significantly improve performance on classification tasks. The proposed learning algorithm is also very efficient, achieving order of magnitude speedup in training time compared to previous discriminative baseline methods.

cs.LG↗

arXiv2004

Short-Term Memory in Orthogonal Neural Networks

We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.

cond-mat.dis-nn↗

arXiv2000

Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity

A theory of temporally asymmetric Hebb (TAH) rules which depress or potentiate synapses depending upon whether the postsynaptic cell fires before or after the presynaptic one is presented. Using the Fokker-Planck formalism, we show that the equilibrium synaptic distribution induced by such rules is highly sensitive to the manner in which bounds on the allowed range of synaptic values are imposed. In a biologically plausible multiplicative model, we find that the synapses in asynchronous networks reach a distribution that is invariant to the firing rates of either the pre- or post-synaptic cells. When these cells are temporally correlated, the synaptic strength varies smoothly with the degree and phase of synchrony between the cells.

cond-mat.dis-nn↗