Locality of temperature in spin chains

In traditional thermodynamics, temperature is a local quantity: a subsystem of a large thermal system is in a thermal state at the same temperature as the original system. For strongly interacting systems, however, the locality of temperature breaks down. We study the possibility of associating an effective thermal state to subsystems of infinite chains of interacting spin particles of arbitrary finite dimension. We study the effect of correlations and criticality in the definition of this effective thermal state and discuss the possible implications for the classical simulation of thermal quantum systems.Comment: 18+9 pages, 12 figure

DNA-TEQ: An Adaptive Exponential Quantization of Tensors for DNN Inference

Quantization is commonly used in Deep Neural Networks (DNNs) to reduce the storage and computational complexity by decreasing the arithmetical precision of activations and weights, a.k.a. tensors. Efficient hardware architectures employ linear quantization to enable the deployment of recent DNNs onto embedded systems and mobile devices. However, linear uniform quantization cannot usually reduce the numerical precision to less than 8 bits without sacrificing high performance in terms of model accuracy. The performance loss is due to the fact that tensors do not follow uniform distributions. In this paper, we show that a significant amount of tensors fit into an exponential distribution. Then, we propose DNA-TEQ to exponentially quantize DNN tensors with an adaptive scheme that achieves the best trade-off between numerical precision and accuracy loss. The experimental results show that DNA-TEQ provides a much lower quantization bit-width compared to previous proposals, resulting in an average compression ratio of 40% over the linear INT8 baseline, with negligible accuracy loss and without retraining the DNNs. Besides, DNA-TEQ leads the way in performing dot-product operations in the exponential domain, which saves 66% of energy consumption on average for a set of widely used DNNs.Comment: 8 pages, 8 figures, 5 table

An Energy-Efficient Near-Data Processing Accelerator for DNNs that Optimizes Data Accesses

The constant growth of DNNs makes them challenging to implement and run efficiently on traditional compute-centric architectures. Some accelerators have attempted to add more compute units and on-chip buffers to solve the memory wall problem without much success, and sometimes even worsening the issue since more compute units also require higher memory bandwidth. Prior works have proposed the design of memory-centric architectures based on the Near-Data Processing (NDP) paradigm. NDP seeks to break the memory wall by moving the computations closer to the memory hierarchy, reducing the data movements and their cost as much as possible. The 3D-stacked memory is especially appealing for DNN accelerators due to its high-density/low-energy storage and near-memory computation capabilities to perform the DNN operations massively in parallel. However, memory accesses remain as the main bottleneck for running modern DNNs efficiently. To improve the efficiency of DNN inference we present QeiHaN, a hardware accelerator that implements a 3D-stacked memory-centric weight storage scheme to take advantage of a logarithmic quantization of activations. In particular, since activations of FC and CONV layers of modern DNNs are commonly represented as powers of two with negative exponents, QeiHaN performs an implicit in-memory bit-shifting of the DNN weights to reduce memory activity. Only the meaningful bits of the weights required for the bit-shift operation are accessed. Overall, QeiHaN reduces memory accesses by 25\% compared to a standard memory organization. We evaluate QeiHaN on a popular set of DNNs. On average, QeiHaN provides $4.3x$ speedup and $3.5x$ energy savings over a Neurocube-like accelerator

ReDy: A Novel ReRAM-centric Dynamic Quantization Approach for Energy-efficient CNN Inference

The primary operation in DNNs is the dot product of quantized input activations and weights. Prior works have proposed the design of memory-centric architectures based on the Processing-In-Memory (PIM) paradigm. Resistive RAM (ReRAM) technology is especially appealing for PIM-based DNN accelerators due to its high density to store weights, low leakage energy, low read latency, and high performance capabilities to perform the DNN dot-products massively in parallel within the ReRAM crossbars. However, the main bottleneck of these architectures is the energy-hungry analog-to-digital conversions (ADCs) required to perform analog computations in-ReRAM, which penalizes the efficiency and performance benefits of PIM. To improve energy-efficiency of in-ReRAM analog dot-product computations we present ReDy, a hardware accelerator that implements a ReRAM-centric Dynamic quantization scheme to take advantage of the bit serial streaming and processing of activations. The energy consumption of ReRAM-based DNN accelerators is directly proportional to the numerical precision of the input activations of each DNN layer. In particular, ReDy exploits that activations of CONV layers from Convolutional Neural Networks (CNNs), a subset of DNNs, are commonly grouped according to the size of their filters and the size of the ReRAM crossbars. Then, ReDy quantizes on-the-fly each group of activations with a different numerical precision based on a novel heuristic that takes into account the statistical distribution of each group. Overall, ReDy greatly reduces the activity of the ReRAM crossbars and the number of A/D conversions compared to an static 8-bit uniform quantization. We evaluate ReDy on a popular set of modern CNNs. On average, ReDy provides 13\% energy savings over an ISAAC-like accelerator with negligible accuracy loss and area overhead.Comment: 13 pages, 16 figures, 4 Table