Jing Pei

Enabling an Integrated Rate-temporal Learning Scheme on Memristor

Learning scheme is the key to the utilization of spike-based computation and the emulation of neural/synaptic behaviors toward realization of cognition. The biological observations reveal an integrated spike time- and spike rate-dependent plasticity as a function of presynaptic firing frequency. However, this integrated rate-temporal learning scheme has not been realized on any nano devices. In this paper, such scheme is successfully demonstrated on a memristor. Great robustness against the spiking rate fluctuation is achieved by waveform engineering with the aid of good analog properties exhibited by the iron oxide-based memristor. The spike-time-dependence plasticity (STDP) occurs at moderate presynaptic firing frequencies and spike-rate-dependence plasticity (SRDP) dominates other regions. This demonstration provides a novel approach in neural coding implementation, which facilitates the development of bio-inspired computing systems.

Minimum-cost control of complex networks

Finding the solution for driving a complex network at the minimum energy cost with a given number of controllers, known as the minimum-cost control problem, is critically important but remains largely open. We propose a projected gradient method to tackle this problem, which works efficiently in both synthetic and real-life networks. The study is then extended to the case where each controller can only be connected to a single network node to have the lowest connection complexity. We obtain the interesting insight that such connections basically avoid high-degree nodes of the network, which is in resonance with recent observations on controllability of complex networks. Our results provide the first technical path to enabling minimum-cost control of complex networks, and contribute new insights to locating the key nodes from a minimum-cost control perspective.

Complex Learning in Bio-plausible Memristive Networks

The emerging memristor-based neuromorphic engineering promises an efficient computing paradigm. However, the lack of both internal dynamics in the previous feedforward memristive networks and efficient learning algorithms in recurrent networks, fundamentally limits the learning ability of existing systems. In this work, we propose a framework to support complex learning functions by introducing dedicated learning algorithms to a bio-plausible recurrent memristive network with internal dynamics. We fabricate iron oxide memristor-based synapses, with well controllable plasticity and a wide dynamic range of excitatory/inhibitory connection weights, to build the network. To adaptively modify the synaptic weights, the comprehensive recursive least-squares (RLS) learning algorithm is introduced. Based on the proposed framework, the learning of various timing patterns and a complex spatiotemporal pattern of human motor is demonstrated. This work paves a new way to explore the brain-inspired complex learning in neuromorphic systems.

Temperature based Restricted Boltzmann Machines

Restricted Boltzmann machines (RBMs), which apply graphical models to learning probability distribution over a set of inputs, have attracted much attention recently since being proposed as building blocks of multi-layer learning systems called deep belief networks (DBNs). Note that temperature is a key factor of the Boltzmann distribution that RBMs originate from. However, none of existing schemes have considered the impact of temperature in the graphical model of DBNs. In this work, we propose temperature based restricted Boltzmann machines (TRBMs) which reveals that temperature is an essential parameter controlling the selectivity of the firing neurons in the hidden layers. We theoretically prove that the effect of temperature can be adjusted by setting the parameter of the sharpness of the logistic function in the proposed TRBMs. The performance of RBMs can be improved by adjusting the temperature parameter of TRBMs. This work provides a comprehensive insights into the deep belief networks and deep learning architectures from a physical point of view.

Hierarchical Chunking of Sequential Memory on Neuromorphic Architecture with Reduced Synaptic Plasticity

Chunking refers to a phenomenon whereby individuals group items together when performing a memory task to improve the performance of sequential memory. In this work, we build a bio-plausible hierarchical chunking of sequential memory (HCSM) model to explain why such improvement happens. We address this issue by linking hierarchical chunking with synaptic plasticity and neuromorphic engineering. We uncover that a chunking mechanism reduces the requirements of synaptic plasticity since it allows applying synapses with narrow dynamic range and low precision to perform a memory task. We validate a hardware version of the model through simulation, based on measured memristor behavior with narrow dynamic range in neuromorphic circuits, which reveals how chunking works and what role it plays in encoding sequential memory. Our work deepens the understanding of sequential memory and enables incorporating it for the investigation of the brain-inspired computing on neuromorphic architecture.

Optimal control of complex networks based on matrix differentiation

Finding the key node set to be connected to external control sources so as to minimize the energy for controlling a complex network, known as the minimum-energy control problem, is of critical importance but remains open. We address this critical problem where matrix differentiation is involved. To this end, the differentiation of energy/cost function with respect to the input matrix is obtained based on tensor analysis, and the Hessian matrix is compressed from a fourth-order tensor. Normalized projected gradient method (NPGM) normalized projected trust-region method (NPTM) are proposed with established convergence property. We show that NPGM is more computationally efficient than NPTM. Simulation results demonstrate satisfactory performance of the algorithms, and reveal important insights as well. Two interesting phenomena are observed. One is that the key node set tends to divide elementary paths equally. The other is that the low-degree nodes may be more important than hubs from a control point of view, indicating that controlling hub nodes does not help to lower the control energy. These results suggest a way of achieving optimal control of complex networks, and provide meaningful insights for future researches.

Enabling Controlling Complex Networks with Local Topological Information

Complex networks characterize the nature of internal/external interactions in real-world systems including social, economic, biological, ecological, and technological networks. Two issues keep as obstacles to fulfilling control of large-scale networks: structural controllability which describes the ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost for driving the network to a predefined state with a given number of control inputs. For large complex networks without global information of network topology, both problems remain essentially open. Here we combine graph theory and control theory for tackling the two problems in one go, using only local network topology information. For the structural controllability problem, a distributed local-game matching method is proposed, where every node plays a simple Bayesian game with local information and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity. Starring from any structural controllability solution, a minimizing longest control path method can efficiently reach a good solution for the optimal control in large networks. Our results provide solutions for distributed complex network control and demonstrate a way to link the structural controllability and optimal control together.

Training deep neural networks with discrete state transition

Abstract Deep neural networks have been achieving booming breakthroughs in various artificial intelligence tasks, however they are notorious for consuming unbearable hardware resources, training time and power. The emerging pruning/binarization methods, which aim at both decreasing overheads and retaining high performance, seem to promise applications on portable devices. However, even with these most advanced algorithms, we have to save the full-precision weights during the gradient descent process which remains size and power bottlenecks of memory access and the resulting computation. To address this challenge, we propose a unified discrete state transition (DST) framework by introducing a probabilistic projection operator that constrains the weight matrices in a discrete weight space (DWS) with configurable number of states, throughout the whole training process. The experimental results over various data sets including MNIST, CIFAR10 and SVHN show the effectiveness of this framework. The direct transition between discrete states significantly saves memory for storing weights in full precision, as well as simplifies the computation of weight updating. The proposed DST framework is hardware friendly as it can be easily implemented by a wide range of emerging portable devices, including binary, ternary and multiple-level memory devices. This work paves the way for on-chip learning on various portable devices in the near future.

GXNOR-Net: Training deep neural networks with ternary weights and activations without full-precision memory under a unified discretization framework

Although deep neural networks (DNNs) are being a revolutionary power to open up the AI era, the notoriously huge hardware overhead has challenged their applications. Recently, several binary and ternary networks, in which the costly multiply-accumulate operations can be replaced by accumulations or even binary logic operations, make the on-chip training of DNNs quite promising. Therefore there is a pressing need to build an architecture that could subsume these networks under a unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discrete. The second one is how to remove the full-precision hidden weights in the training phase to break the bottlenecks of memory/computation consumption. To address the first issue, we present a multi-step neuronal activation discretization method and a derivative approximation technique that enable the implementing the back propagation algorithm on discrete DNNs. While for the second issue, we propose a discrete state transition (DST) methodology to constrain the weights in a discrete space without saving the hidden weights. Through this way, we build a unified framework that subsumes the binary or ternary networks as its special cases, and under which a heuristic algorithm is provided at the website https://github.com/AcrossV/Gated-XNOR. More particularly, we find that when both the weights and activations become ternary values, the DNNs can be reduced to sparse binary networks, termed as gated XNOR networks (GXNOR-Nets) since only the event of non-zero weight and non-zero activation enables the control gate to start the XNOR logic operations in the original binary networks. This promises the event-driven hardware design for efficient mobile intelligence. We achieve advanced performance compared with state-of-the-art algorithms. Furthermore, the computational sparsity and the number of states in the discrete space can be flexibly modified to make it suitable for various hardware platforms.

Electronic Structure and Spin Configuration Trends of Single Transition Metal Impurity in Phase Change Material

Fe doped phase change material GexSbyTez has shown experimentally the ability to alter its magnetic properties by phase change. This engineered spin degree of freedom into the phase change material offers the possibility of logic devices or spintronic devices where they may enable fast manipulation of ferromagnetism by a phase change mechanism. The electronic structures and spin configurations of isolated transition metal dopant in phase change material (iTM-PCM) is important to understand the interaction between localized metal d states and the unique delocalized host states of phase change material. Identifying an impurity center that has, in isolation, a nonvanishing magnetic moment is the first step to study the collective magnetic ordering, which originates from the interaction among close enough individual impurities. Theoretical description of iTM-PCM is challenging. In this work, we use a screened exchange hybrid functional to study the single 3d transition metal impurity in crystalline GeTe and GeSb2Te4. By curing the problem of local density functional (LDA) such as over-delocalization of the 3d states, we find that Fe on the Ge/Sb site has its majority d states fully occupied while its minority d states are empty, which is different from the previously predicted electronic configuration by LDA. From early transition metal Cr to heavier Ni, the majority 3d states are gradually populated until fully occupied and then the minority 3d states begin to be filled. Interpretive orbital interaction pictures are presented for understanding the local and total magnetic moments.Fe doped GST has shown experimentally the ability to alter its magnetic properties by phase change. In this work, we use screened exchange hybrid functional to study the single neutral substitutional 3d transition metal (TM) in crystalline GeTe and GeSb2Te4. By curing the problem of local density functional (LDA) such as over delocalization of the 3d states, we find that Fe on Ge/Sb site has its majority d states fully occupied while its minority d states are empty, which is different than previous predicted electronic configuration by LDA. From early transition metal Cr to heavier Ni, the majority 3d states are gradually populated until fully occupied and then the minority 3d states begin to be filled. In order to study the magnetic contrast, we use lower symmetry crystalline GeTe and GeSb2Te4 as the amorphous phases, respectively, which has been proposed to model the medium range disordering. We find that only Co substitution in r-GeSb2Te4 and s-GeSb2Te4 shows magnetic contrast. The experimental magnetic contrast for Fe doped GST may be due to additional TM-TM interaction, which is not included in our model. It can also be possible that these lower symmetry crystalline models are not sufficient to characterize the magnetic properties of real 3d TM doped amorphous GST.