Quantization Policy Research Articles

Dynamic periodic event-triggered control for nonlinear systems with output dynamic quantization

This paper is concerned with the design of stabilizing event-triggered controllers for nonlinear systems subject to dynamic quantization. The plant state is assumed to be partially known, and the feedback signal is transmitted to the controller at discrete-time instants via a digital channel. To that end, an event-triggered controller is synthesized based solely on the available plant measurement. In addition, to better adapt it to practical implementation, the event-triggering law we construct is only verified at periodic time instants, i.e., periodic event-triggering mechanism. Since the network is digital, the transmitted output signal must be quantized to be encoded using a finite number of bits. Furthermore, the initial output value is assumed to be unknown, and the plant is affected by external disturbance, which can result in quantizer saturation. To overcome these challenges, a dynamic quantization policy is developed for the output measurement such that the quantization regions are dynamically updated according to the value of the quantized signal. The combined approach of periodic event-triggering mechanism and dynamic quantization ensures the stability of the networked control system under mild conditions. The stability is studied using appropriate Lyapunov functions. Numerical simulations have been conducted to justify the proposed technique.

A novel one-bit dynamic quantizer for event-triggered control systems

We investigate the problem of feedback stabilization of networked control linear systems with unknown initial state. In particular, the sampling and the quantization effects of network are considered and we propose a quantized event-triggered control technique to handle this case. To cope with unknown initial state, a novel exponential dynamic quantizer is synthesized, which enables to capture the state in a finite time. Moreover, the dynamic quantization policy only depends on the sign of the quantization error and allows for one-bit transmission rather than packet-based transmission, which is desirable in practice. Then, the quantized state measurements are transmitted to the controller using an event-triggering mechanism to reduce the amount of transmissions over the network. The approach ensures global asymptotic stability property for the closed-loop system and prevents the occurrence of Zeno behavior. The entire closed-loop system is represented as a hybrid dynamical system and the closed-loop stability is assessed using suitable Lyapunov functions. The effectiveness of the proposed approach is demonstrated through numerical simulations.

Event-triggered sliding mode control for networked linear systems

This paper investigates the control-based event-triggered sliding mode control for a networked linear system whose feedback information is transmitted over a digital communication network. In this paper, a novel event-triggered mechanism based on control value is proposed. Different from traditional event-triggered mechanisms that are normally based on states, our mechanism pays more attention to the desired control input value of the system. When the deviation between the current control input and the control input being calculated on the basis of the previous system state exceeds a given threshold, an event is triggered. For the sake of reducing the information to be transmitted, a quantization policy is executed and only a few bits are needed to transmit the feedback symbol of each sample. The combination of the control-based event-triggered mechanism and the quantization policy can significantly reduce both the transmission frequency and the number of bits of each feedback packet. For the concerned system, sliding mode control is implemented. The reachability of the sliding mode surface and the robust stability of the system are analyzed by fully taking quantization effects into account. Moreover, the effects of transmission delay of feedback packets on the event-triggering mechanism are considered. Under the proposed mechanism, the lower bound of event intervals is proven to be non-zero, i.e., the Zeno behavior is excluded. Simulations of a mechanical system are done to further verify the superiority of the proposed mechanism.

Decentralized Sensor Scheduling, Bandwidth Allocation, and Dynamic Quantization for FL Under Hybrid Data Partitioning

Considering the wide application of multiple types of sensors with diversified data sensing and collection capabilities, we focus on the resulting hybrid data partitioning among the local data set distributed at the edge sensors, especially the practical training implementation of federated learning (FL) under such a setting, where the neural network (NN) is trained collaboratively without requiring the sensors to share their data. Different from the conventional FL schemes, since each local sensor now only has partial data samples with type-specific features, the traditional stochastic gradient descent (SGD)-based training method cannot be directly utilized due to the intertype and intratype data coupling. To address this issue, we first transform the training problem into the primal–dual domain utilizing the corresponding Lagrangian and propose a stochastic primal-descent dual-ascent training method with a two-side residual feedback mechanism. Such a method can be implemented in a scalable way and compensate for the data distortion and loss caused by the practical transmission noise. Furthermore, a decentralized joint scheduling, bandwidth allocation, and dynamic quantization policy is proposed by analyzing the performance at each training iteration and the consumed transmission resources. The proposed method is adaptive to not only the channel state information (CSI) but also the instantaneous gradient importance and dynamic gradient statistics. The closed-form convergence analysis is provided, and the simulation experiments illustrate the superior performance of the proposed scheme.

Stabilizing bit rate conditions for a scalar linear event-triggered system with Markov dropouts

This paper investigates the stabilization problem of a scalar linear event-triggered system via a bit-rate-limited network, which suffers from bounded transmission delay and Markov feedback dropouts. Necessary and sufficient bit rate conditions for the asymptotic stability of the concerned system are derived in the mean square sense. Due to the influence of transmission delay and Markov dropouts, a higher bit rate is required for stabilization, which is quantitatively characterized. To overcome the difficulties induced by the temporal correlation of Markov dropouts, a variable bit rate quantization policy is proposed to achieve the minimum-bit-rate stability by appropriately determining the number of quantization bits for each feedback packet. The obtained sufficient bit rate condition is shown to be also necessary in some special cases. Simulations are done to verify the effectiveness of our results.

Device quantization policy in variation-aware in-memory computing design

Device quantization of in-memory computing (IMC) that considers the non-negligible variation and finite dynamic range of practical memory technology is investigated, aiming for quantitatively co-optimizing system performance on accuracy, power, and area. Architecture- and algorithm-level solutions are taken into consideration. Weight-separate mapping, VGG-like algorithm, multiple cells per weight, and fine-tuning of the classifier layer are effective for suppressing inference accuracy loss due to variation and allow for the lowest possible weight precision to improve area and energy efficiency. Higher priority should be given to developing low-conductance and low-variability memory devices that are essential for energy and area-efficiency IMC whereas low bit precision (< 3b) and memory window (< 10) are less concerned.

Target-Aware Neural Architecture Search and Deployment for Keyword Spotting

Keyword spotting (KWS) utilities have become increasingly popular on a wide range of mobile and home devices, representing a prolific application field for Convolutional Neural Networks (CNNs), which are commonly exploited to perform keyword classification. Addressing the challenges of targeting such resource-constrained platforms, requires a careful definition of the CNN architecture and the overall system implementation. These reasons have led to a growing need for design and optimization flows, able to intrinsically take into account the system’s performance when ported on the target platform. In this work, we present a design methodology based on Neural Architecture Search, exploited to combine the exploration of the optimal network topology, the audio pre-processing scheme, and the data quantization policy. The proposed design flow includes target-awareness in the exploration loop, comparing the different design alternatives according to a model-based pre-evaluation of metrics like execution latency, memory footprint, and energy consumption, evaluated considering the application’s execution on the target processing platform. We have tested our design flow to obtain target-specific CNNs for a resource-constrained commercial platform, the ST SensorTile. Considering two different application scenarios, enabling the comparison with the state-of-the-art of efficient CNN-based models for KWS, we have obtained up to a 1.8% accuracy improvement and a 40% footprint reduction in the most favorable case.

Event-Triggered Sliding Mode Control of Uncertain Switched Systems via Hybrid Quantized Feedback

This article is concerned with the sliding mode control (SMC) for stabilizing a switched linear system with external disturbances and uncertain nonlinearities. The state sampling is implemented by an event-triggered mechanism (ETM) and the sampled data are transmitted through a limited-bandwidth digital channel. The main challenge of such a work comes from the quantizer saturation and quantization error in the SMC design with finite-level quantization and the mismatched control caused by the switch and event-triggered sampling. To solve the above problem, we at first present an ETM and a limited-information-based SMC law. Then, a new discrete-time level-sets method is proposed to develop the dynamic quantization policy (DQP). If the disturbance bound is known, the DQP can avoid the quantizer saturation without the need of online detection. A switching law and quantization parameter conditions are provided to ensure the convergence of the state trajectory. At last, the result is generalized to the unknown bound of disturbance. The limited-information control problem of a single-link manipulator is taken as a potential application of the proposed method.

Hardware-Centric AutoML for Mixed-Precision Quantization

Model quantization is a widely used technique to compress and accelerate deep neural network (DNN) inference. Emergent DNN hardware accelerators begin to support mixed precision (1-8 bits) to further improve the computation efficiency, which raises a great challenge to find the optimal bitwidth for each layer: it requires domain experts to explore the vast design space trading off among accuracy, latency, energy, and model size, which is both time-consuming and sub-optimal. Conventional quantization algorithm ignores the different hardware architectures and quantizes all the layers in a uniform way. In this paper, we introduce the Hardware-Aware Automated Quantization (HAQ) framework which leverages the reinforcement learning to automatically determine the quantization policy, and we take the hardware accelerator's feedback in the design loop. Rather than relying on proxy signals such as FLOPs and model size, we employ a hardware simulator to generate direct feedback signals (latency and energy) to the RL agent. Compared with conventional methods, our framework is fully automated and can specialize the quantization policy for different neural network architectures and hardware architectures. Our framework effectively reduced the latency by 1.4-1.95x and the energy consumption by 1.9x with negligible loss of accuracy compared with the fixed bitwidth (8 bits) quantization. Our framework reveals that the optimal policies on different hardware architectures (i.e., edge and cloud architectures) under different resource constraints (i.e., latency, energy, and model size) are drastically different. We interpreted the implication of different quantization policies, which offer insights for both neural network architecture design and hardware architecture design.

Bayesian Automatic Model Compression

Model compression has drawn great attention in deep learning community. A core problem in model compression is to determine the layer-wise optimal compression policy, e.g., the layer-wise bit-width in network quantization. Conventional hand-crafted heuristics rely on human experts and are usually sub-optimal, while recent reinforcement learning based approaches can be inefficient during the exploration of the policy space. In this article, we propose Bayesian automatic model compression (BAMC), which leverages non-parametric Bayesian methods to learn the optimal quantization bit-width for each layer of the network. BAMC is trained in a one-shot manner, avoiding the back and forth (re)-training in reinforcement learning based approaches. Experimental results on various datasets validate that our proposed methods can find reasonable quantization policies efficiently with little accuracy drop for the quantized network.

On Optimal Quantized Non-Bayesian Quickest Change Detection With Energy Harvesting

In this paper, we consider a problem of decentralized non-Bayesian quickest change detection using a wireless sensor network where the sensor nodes are powered by harvested energy from the environment. The underlying random process being monitored by the sensors is subject to change in its distribution at an unknown but deterministic time point, and the sensors take samples (sensing) periodically, compute the likelihood ratio based on the distributions before and after the change, quantize it and send it to a remote fusion centre (FC) over fading channels for performing a sequential test to detect the change. Due to the unpredictable and intermittent nature of harvested energy arrivals, the sensors need to decide whether they want to sense, and at what rate they want to quantize their information before sending them to the FC, since higher quantization rates result in higher accuracy and better detection performance, at the cost of higher energy consumption. We formulate an optimal sensing and quantization rate allocation problem (in order to minimize the expected detection delay subject to false alarm rate constraint) based on the availability (at the FC) of non-causal and causal information of sensors’ energy state information, and channel state information between the sensors and the FC. Motivated by the asymptotically inverse relationship between the expected detection delay (under a vanishingly small probability of false alarm) and the Kullback-Leibler (KL) divergence measure at the FC, we maximize an expected sum of the KL divergence measure over a finite horizon to obtain the optimal sensing and quantization rate allocation policy, subject to energy causality constraints at each sensor. The optimal solution is obtained using a typical dynamic programming based technique, and based on the optimal quantization rate, the optimal quantization thresholds are found by maximizing the KL information measure per slot. We also provide suboptimal threshold design policies using uniform quantization and an asymptotically optimal quantization policy for higher number of quantization bits. We provide an asymptotic approximation for the loss due to quantization of the KL measure, and also consider an alternative optimization problem with minimizing the expected sum of the inverse the KL divergence measure as the cost per time slot. Numerical results are provided comparing the various optimal and suboptimal quantization strategies for both optimization problem formulations, illustrating the comparative performance of these strategies at different regimes of quantization rates.

Periodic Event-Triggered Quantization Policy Design for a Scalar LTI System With i.i.d. Feedback Dropouts

This technical note proposes an event-triggered quantization policy design method to stabilize a scalar continuous-time linear time-invariant (LTI) system, whose feedback loop is closed over an unreliable digital communication network. The feedback packets suffer from network delay and may be dropped in an independent and identically distributed (i.i.d.) way. In order to save quantization bit rate, we implement a periodic event-triggering strategy which periodically samples the state and only quantizes and transmits the sampled state when a predefined event is triggered. By making good use of both the information bits and the sampling time instants of the feedback packets, our policy can obtain the desired mean-square stability at a lower bit rate than the conventional time-triggered quantization policies which utilize only the information bits inside the feedback packets. Under our quantization policy, the stabilizing bit rate condition is up to the dropout rate, the processing and network delays and the unstable eigenvalue of the system, and is independent of the bounded process noise.

Incremental parsing in a continuous dynamical system: sentence processing in Gradient Symbolic Computation

Abstract Any incremental parser must solve two computational problems: (1) maintaining all interpretations consistent with the words that have been processed so far and (2) excluding all globally-incoherent interpretations. While these problems are well understood, it is not clear how the dynamic, continuous mechanisms that underlie human language processing solve them. We introduce a Gradient Symbolic Computation (GSC) parser, a continuous-state, continuous-time stochastic dynamical-system model of symbolic processing, which builds up a discrete symbolic structure gradually by dynamically strengthening a discreteness constraint. Online, interactive tutorials with open-source software are presented in a companion website. Our results reveal that the GSC parser can solve the two computational problems by moving to a non-discrete blend state that evolves exclusively to discrete states representing contextually-appropriate globally-coherent interpretations. In a simulation study using a simple formal grammar, we show that successful parsing requires appropriate control of the discreteness constraint strength (a quantization policy). With inappropriate quantization policies, the GSC parser makes mistakes that mirror those made in natural language comprehension (garden-path or local-coherence errors). These findings suggest that the GSC model offers a neurally plausible solution to these two core problems.

Interactive Scalar Quantization for Distributed Resource Allocation

In many resource allocation problems, a centralized controller needs to award some resource to a user selected from a collection of distributed users with the goal of maximizing the utility the user would receive from the resource. This can be modeled as the controller computing an extremum of the distributed users' utilities. The overhead rate necessary to enable the controller to reproduce the users' local state can be prohibitively high. An approach to reduce this overhead is interactive communication wherein rate savings are achieved by tolerating an increase in delay. In this paper, we consider the design of a simple achievable scheme based on successive refinements of scalar quantization at each user. The optimal quantization policy is computed via a dynamic program and we demonstrate that tolerating a small increase in delay can yield significant rate savings. We then consider two simpler quantization policies to investigate the scaling properties of the rate-delay trade-offs. Using a combination of these simpler policies, the performance of the optimal policy can be closely approximated with lower computational costs.

On Optimal Zero-Delay Coding of Vector Markov Sources

Optimal zero-delay coding (quantization) of a vector-valued Markov source driven by a noise process is considered. Using a stochastic control problem formulation, the existence and structure of optimal quantization policies are studied. For a finite-horizon problem with bounded per-stage distortion measure, the existence of an optimal zero-delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells. The bounded distortion assumption is relaxed to cover cases that include the linear quadratic Gaussian problem. For the infinite horizon problem and a stationary Markov source the optimality of deterministic Markov coding policies is shown. The existence of optimal stationary Markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed.

Jointly Optimal LQG Quantization and Control Policies for Multi-Dimensional Systems

For controlled R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -valued linear systems driven by Gaussian noise under quadratic cost criteria, we investigate the existence and the structure of optimal quantization and control policies. For fully observed and partially observed systems, we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists, provided that the quantizers allowed are ones which have convex codecells. Furthermore, optimal control policies are linear in the conditional estimate of the state, and a form of separation of estimation and control holds.

On optimal policies for control and estimation over a Gaussian relay channel

The problem of causal transmission of a memoryless Gaussian source over a two-hop memoryless Gaussian relay channel is considered. The source and the relay encoders have average transmit power constraints, and the performance criterion is mean-squared distortion. The main contribution of this paper is to show that unlike the case of a point-to-point scalar Gaussian channel, linear encoding schemes are not optimal over a two-hop relay channel in general, extending the sub-optimality results which are known for more than three hops. In some cases, simple three-level quantization policies employed at the source and at the relay can outperform the best linear policies. Further a lower bound on the distortion is derived and it is shown that the distortion bounds derived using cut-set arguments are not tight in general for sensor networks.

Quantized Feedback Control under Dynamic Logarithmic Quantization Schemes

This paper addresses the quantized feedback stabilization problem for networked control systems with unbounded process disturbance, where sensors, controllers and plants are connected by digital communication channels. A dynamic logarithmic quantization policy is proposed to stabilize the unstable plant. It is derived that the quantization policy can maintain stabilization in the presence of unbounded and possibly non-Gaussian process disturbance. Simulation results show the validity of the proposed scheme.

Observer-Based Quantized Feedback Control via Noisy Communication Channels

This paper investigates the input and output quantized control problem for stochastic linear systems with unbounded and possibly non-Gaussian process disturbance, where sensors, controllers and plants are connected by a noisy digital communication channel. Due to the unbounded process disturbance, a dynamic, logarithmic quantization scheme is proposed. An observer-based control policy is presented to stabilize the unstable plant in the mean square sense. Simulation results show the validity of the proposed quantization and control policy.

Stabilization for Quantized Feedback Control Systems: An LMI Approach

This paper addresses the feedback stabilization problem for quantized feedback control systems, where sensors and controllers are connected by a digital communication channel. A dynamic, logarithmic quantization scheme is proposed. It is shown that quantized feedback control problems can be converted to robust control problems. The proof techniques rely on the LMI approach. Simulation results show the validity of the proposed quantization policy.