Diffusion local time storage

In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic rate. For this storage process we find its stationary distribution and compute the joint distribution of the starting and ending times of the busy and idle periods. This work completes and extends to a more general setting the results in Mannersalo, Norros, and Salminen (2003).Comment: 24 pages; to appear in Stoch. Proc. App

Structured modeling for VHDL synthesis

This report will describe a proposed modeling style for the use of the VHSIC Hardware Description Language (VHDL) in design synthesis. We will describe the operations and underlying assumptions of four design models currently understood and used in practice by designers: combinational logic, functional descriptions (involving clocked components such as counters), register transfer (data path) descriptions, and behavioral (instruction set or processor) designs. We will illustrate the various uses of the VHDL description styles (structural, dataflow and behavioral) to represent characteristics of each of these design models. Emphasis is placed on how VHDL constructs should be used in order to synthesize optimal designs

Characterizing Deep-Learning I/O Workloads in TensorFlow

The performance of Deep-Learning (DL) computing frameworks rely on the performance of data ingestion and checkpointing. In fact, during the training, a considerable high number of relatively small files are first loaded and pre-processed on CPUs and then moved to accelerator for computation. In addition, checkpointing and restart operations are carried out to allow DL computing frameworks to restart quickly from a checkpoint. Because of this, I/O affects the performance of DL applications. In this work, we characterize the I/O performance and scaling of TensorFlow, an open-source programming framework developed by Google and specifically designed for solving DL problems. To measure TensorFlow I/O performance, we first design a micro-benchmark to measure TensorFlow reads, and then use a TensorFlow mini-application based on AlexNet to measure the performance cost of I/O and checkpointing in TensorFlow. To improve the checkpointing performance, we design and implement a burst buffer. We find that increasing the number of threads increases TensorFlow bandwidth by a maximum of 2.3x and 7.8x on our benchmark environments. The use of the tensorFlow prefetcher results in a complete overlap of computation on accelerator and input pipeline on CPU eliminating the effective cost of I/O on the overall performance. The use of a burst buffer to checkpoint to a fast small capacity storage and copy asynchronously the checkpoints to a slower large capacity storage resulted in a performance improvement of 2.6x with respect to checkpointing directly to slower storage on our benchmark environment.Comment: Accepted for publication at pdsw-DISCS 201

A three-threshold learning rule approaches the maximal capacity of recurrent neural networks

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network scenario, whose prototype is the Hopfield model. The model has a poor storage capacity, compared with the capacity achieved with perceptron learning algorithms. Here, by transforming the perceptron learning rule, we present an online learning rule for a recurrent neural network that achieves near-maximal storage capacity without an explicit supervisory error signal, relying only upon locally accessible information. The fully-connected network consists of excitatory binary neurons with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the memory patterns are presented online as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs. Synapses corresponding to active inputs are modified as a function of the value of the local fields with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. We simulated and analyzed a network of binary neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction. The storage capacity obtained through numerical simulations is shown to be close to the value predicted by analytical calculations. We also measured the dependence of capacity on the strength of external inputs. Finally, we quantified the statistics of the resulting synaptic connectivity matrix, and found that both the fraction of zero weight synapses and the degree of symmetry of the weight matrix increase with the number of stored patterns.Comment: 24 pages, 10 figures, to be published in PLOS Computational Biolog