Showing papers on "Binary number published in 2017"

Towards Accurate Binary Convolutional Neural Network

Abstract: We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory size and accesses, and can replace arithmetic operations with more efficient bitwise operations, leading to much faster test-time inference and lower power consumption. However, previous works on binarizing CNNs usually result in severe prediction accuracy degradation. In this paper, we address this issue with two major innovations: (1) approximating full-precision weights with the linear combination of multiple binary weight bases; (2) employing multiple binary activations to alleviate information loss. The implementation of the resulting binary CNN, denoted as ABC-Net, is shown to achieve much closer performance to its full-precision counterpart, and even reach the comparable prediction accuracy on ImageNet and forest trail datasets, given adequate binary weight bases and activations.

Towards Accurate Binary Convolutional Neural Network

Abstract: We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to \{-1,+1\} at run-time. It has been known that using binary weights and activations drastically reduce memory size and accesses, and can replace arithmetic operations with more efficient bitwise operations, leading to much faster test-time inference and lower power consumption. However, previous works on binarizing CNNs usually result in severe prediction accuracy degradation. In this paper, we address this issue with two major innovations: (1) approximating full-precision weights with the linear combination of multiple binary weight bases; (2) employing multiple binary activations to alleviate information loss. The implementation of the resulting binary CNN, denoted as ABC-Net, is shown to achieve much closer performance to its full-precision counterpart, and even reach the comparable prediction accuracy on ImageNet and forest trail datasets, given adequate binary weight bases and activations.

Adversarial and Clean Data Are Not Twins

Abstract: Adversarial attack has cast a shadow on the massive success of deep neural networks. Despite being almost visually identical to the clean data, the adversarial images can fool deep neural networks into wrong predictions with very high confidence. In this paper, however, we show that we can build a simple binary classifier separating the adversarial apart from the clean data with accuracy over 99%. We also empirically show that the binary classifier is robust to a second-round adversarial attack. In other words, it is difficult to disguise adversarial samples to bypass the binary classifier. Further more, we empirically investigate the generalization limitation which lingers on all current defensive methods, including the binary classifier approach. And we hypothesize that this is the result of intrinsic property of adversarial crafting algorithms.

Detecting Binary Compact-object Mergers with Gravitational Waves: Understanding and Improving the Sensitivity of the PyCBC Search

Abstract: We present an improved search for binary compact-object mergers using a network of ground-based gravitationalwave detectors. We model a volumetric, isotropic source population and incorporate the resulting distribution over signal amplitude, time delay, and coalescence phase into the ranking of candidate events. We describe an improved modeling of the background distribution, and demonstrate incorporating a prior model of the binary mass distribution in the ranking of candidate events. We find an ~10% and ~20% increase in detection volume for simulated binary neutron star and neutron star black hole systems, respectively, corresponding to a reduction of the false alarm rates assigned to signals by between one and two orders of magnitude.

Deep Hashing for Scalable Image Search

Abstract: In this paper, we propose a new deep hashing (DH) approach to learn compact binary codes for scalable image search. Unlike most existing binary codes learning methods, which usually seek a single linear projection to map each sample into a binary feature vector, we develop a deep neural network to seek multiple hierarchical non-linear transformations to learn these binary codes, so that the non-linear relationship of samples can be well exploited. Our model is learned under three constraints at the top layer of the developed deep network: 1) the loss between the compact real-valued code and the learned binary vector is minimized, 2) the binary codes distribute evenly on each bit, and 3) different bits are as independent as possible. To further improve the discriminative power of the learned binary codes, we extend DH into supervised DH (SDH) and multi-label SDH by including a discriminative term into the objective function of DH, which simultaneously maximizes the inter-class variations and minimizes the intra-class variations of the learned binary codes with the single-label and multi-label settings, respectively. Extensive experimental results on eight widely used image search data sets show that our proposed methods achieve very competitive results with the state-of-the-arts.

Waveform model for an eccentric binary black hole based on the effective-one-body-numerical-relativity formalism

Abstract: Binary black hole systems are among the most important sources for gravitational wave detection. They are also good objects for theoretical research for general relativity. A gravitational waveform template is important to data analysis. An effective-one-body-numerical-relativity (EOBNR) model has played an essential role in the LIGO data analysis. For future space-based gravitational wave detection, many binary systems will admit a somewhat orbit eccentricity. At the same time, the eccentric binary is also an interesting topic for theoretical study in general relativity. In this paper, we construct the first eccentric binary waveform model based on an effective-one-body-numerical-relativity framework. Our basic assumption in the model construction is that the involved eccentricity is small. We have compared our eccentric EOBNR model to the circular one used in the LIGO data analysis. We have also tested our eccentric EOBNR model against another recently proposed eccentric binary waveform model; against numerical relativity simulation results; and against perturbation approximation results for extreme mass ratio binary systems. Compared to numerical relativity simulations with an eccentricity as large as about 0.2, the overlap factor for our eccentric EOBNR model is better than 0.98 for all tested cases, including spinless binary and spinning binary, equal mass binary, and unequal mass binary. Hopefully, our eccentric model can be the starting point to develop a faithful template for future space-based gravitational wave detectors.

Hardware implementation of pseudo-random number generators based on chaotic maps

Abstract: We show the usefulness of bifurcation diagrams to implement a pseudo-random number generator (PRNG) based on chaotic maps. We provide details on the selection of the best parameter values to obtain high entropy and positive Lyapunov exponent from the bifurcation diagram of four chaotic maps, namely: Bernoulli shift map, tent, zigzag, and Borujeni maps. The binary sequences obtained from these maps are analyzed to implement a PRNG both in software and in hardware. The software implementation is realized using 32 and 64 bits microprocessor architectures, and with floating point and fixed point computer arithmetic. The hardware implementation is done by using a field-programmable gate array (FPGA) architecture. We developed a serial communication interface between the PRNG on the FPGA and a personal computer to obtain the generated sequences. We validate the randomness of the generated binary sequences with the NIST test suite 800-22-a both in floating point and fixed point arithmetic. At the end, we show that those chaotic maps are suitable to implement a PRNG but according to the hardware resources, the one based on the Bernoulli shift map is better. In addition, another advantage is that the required initial value for the sequences can be within the whole interval $$[-1,1]$$ , including its bounds.

Real-time fast physical random number generator with a photonic integrated circuit

Abstract: Random number generators are essential for applications in information security and numerical simulations. Most optical-chaos-based random number generators produce random bit sequences by offline post-processing with large optical components. We demonstrate a real-time hardware implementation of a fast physical random number generator with a photonic integrated circuit and a field programmable gate array (FPGA) electronic board. We generate 1-Tbit random bit sequences and evaluate their statistical randomness using NIST Special Publication 800-22 and TestU01. All of the BigCrush tests in TestU01 are passed using 410-Gbit random bit sequences. A maximum real-time generation rate of 21.1 Gb/s is achieved for random bit sequences in binary format stored in a computer, which can be directly used for applications involving secret keys in cryptography and random seeds in large-scale numerical simulations.

Effective-one-body waveforms for binary neutron stars using surrogate models

Abstract: Gravitational-wave observations of binary neutron star systems can provide information about the masses, spins, and structure of neutron stars. However, this requires accurate and computationally efficient waveform models that take ≲1 s to evaluate for use in Bayesian parameter estimation codes that perform 10^7–10^8 waveform evaluations. We present a surrogate model of a nonspinning effective-one-body waveform model with l=2 , 3, and 4 tidal multipole moments that reproduces waveforms of binary neutron star numerical simulations up to merger. The surrogate is built from compact sets of effective-one-body waveform amplitude and phase data that each form a reduced basis. We find that 12 amplitude and 7 phase basis elements are sufficient to reconstruct any binary neutron star waveform with a starting frequency of 10 Hz. The surrogate has maximum errors of 3.8% in amplitude (0.04% excluding the last 100M before merger) and 0.043 rad in phase. This leads to typical mismatches of 10^(−5)−10^(−4) for Advanced LIGO depending on the component masses, with a worst case match of 7×10^(−4) when both stars have masses ≥2 M⊙ . The version implemented in the LIGO Algorithm Library takes ∼0.07 s to evaluate for a starting frequency of 30 Hz and ∼0.8 s for a starting frequency of 10 Hz, resulting in a speed-up factor of O(10^3) relative to the original MATLAB code. This allows parameter estimation codes to run in days to weeks rather than years, and we demonstrate this with a nested sampling run that recovers the masses and tidal parameters of a simulated binary neutron star system.

Learning Rotation-Invariant Local Binary Descriptor

Abstract: In this paper, we propose a rotation-invariant local binary descriptor (RI-LBD) learning method for visual recognition. Compared with hand-crafted local binary descriptors, such as local binary pattern and its variants, which require strong prior knowledge, local binary feature learning methods are more efficient and data-adaptive. Unlike existing learning-based local binary descriptors, such as compact binary face descriptor and simultaneous local binary feature learning and encoding, which are susceptible to rotations, our RI-LBD first categorizes each local patch into a rotational binary pattern (RBP), and then jointly learns the orientation for each pattern and the projection matrix to obtain RI-LBDs. As all the rotation variants of a patch belong to the same RBP, they are rotated into the same orientation and projected into the same binary descriptor. Then, we construct a codebook by a clustering method on the learned binary codes, and obtain a histogram feature for each image as the final representation. In order to exploit higher order statistical information, we extend our RI-LBD to the triple rotation-invariant co-occurrence local binary descriptor (TRICo-LBD) learning method, which learns a triple co-occurrence binary code for each local patch. Extensive experimental results on four different visual recognition tasks, including image patch matching, texture classification, face recognition, and scene classification, show that our RI-LBD and TRICo-LBD outperform most existing local descriptors.

Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation, and effective one-body theory

Abstract: A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the ``scattering holonomy'', i.e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i.e. first order in $G$ and all orders in $v/c$), of the values of the two gyrogravitomagnetic ratios describing spin-orbit coupling in the effective one-body formalism. These gyrogravitomagnetic ratios are found to tend to zero in the ultrarelativistic limit.

Embedded Systems Design with Special Arithmetic and Number Systems

Abstract: This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems.

Testing intermediate representations for binary analysis

Abstract: Binary lifting, which is to translate a binary executable to a high-level intermediate representation, is a primary step in binary analysis. Despite its importance, there are only few existing approaches to testing the correctness of binary lifters. Furthermore, the existing approaches suffer from low test coverage, because they largely depend on random test case generation. In this paper, we present the design and implementation of the first systematic approach to testing binary lifters. We have evaluated the proposed system on 3 state-of-the-art binary lifters, and found 24 previously unknown semantic bugs. Our result demonstrates that writing a precise binary lifter is extremely difficult even for those heavily tested projects.

Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem

Abstract: The residue number system (RNS) is an unconventional number system which can lead to parallel and fault-tolerant arithmetic operations. However, the complexity of residue-to-binary conversion for large number of moduli reduces the overall RNS performance, and makes it inefficient for nowadays high-performance computation systems. In this paper, we present an improved approximate Chinese remainder theorem (CRT) with the aim of performing efficient residue-to-binary conversion for general RNS moduli sets. To achieve this aim, the required number of fraction bits for accurate residue-to-binary conversion is derived. Besides, a method is proposed to substitute fractional calculations by similar computations based on integer numbers to have a hardware amenable algorithm. The proposed approach results in high-speed and low-area residue-to-binary converters for general RNS moduli sets. Therefore, with this conversion method, high dynamic range residue number systems suitable for cryptography and digital ...

Detecting binary compact-object mergers with gravitational waves: Understanding and Improving the sensitivity of the PyCBC search

Abstract: We present an improved search for binary compact-object mergers using a network of ground-based gravitational-wave detectors. We model a volumetric, isotropic source population and incorporate the resulting distribution over signal amplitude, time delay, and coalescence phase into the ranking of candidate events. We describe an improved modeling of the background distribution, and demonstrate incorporating a prior model of the binary mass distribution in the ranking of candidate events. We find a $\sim 10\%$ and $\sim 20\%$ increase in detection volume for simulated binary neutron star and neutron star--binary black hole systems, respectively, corresponding to a reduction of the false alarm rates assigned to signals by between one and two orders of magnitude.

Secret Key Generation With Limited Interaction

Abstract: A basic two-terminal secret key generation model is considered, where the interactive communication rate between the terminals may be limited, and in particular may not be enough to achieve the maximum key rate. We first prove a multi-letter characterization of the key-communication rate region (where the number of auxiliary random variables depends on the number of rounds of the communication), and then provide an equivalent but simpler characterization in terms of concave envelopes in the case of unlimited number of rounds. Two extreme cases are given special attention. First, in the regime of very low communication rates, the key bits per interaction bit (KBIB) is expressed with a new “symmetric strong data processing constant”, which has a concave envelope characterization analogous to that of the conventional strong data processing constant. The symmetric strong data processing constant can be upper bounded by the supremum of the maximal correlation coefficient over a set of distributions, which allows us to determine the KBIB for binary symmetric sources, and conclude, in particular, that the interactive scheme is not more efficient than the one-way scheme at least in the low communication-rate regime. Second, a new characterization of the minimum interaction rate needed for achieving the maximum key rate (MIMK) is given, and we resolve a conjecture by Tyagi regarding the MIMK for (possibly nonsymmetric) binary sources. We also propose a new conjecture for binary symmetric sources that the interactive scheme is not more efficient than the one-way scheme at any communication rate.

Hybrid geometric-random template-placement algorithm for gravitational wave searches from compact binary coalescences

Abstract: Astrophysical compact binary systems consisting of neutron stars and black holes are an important class of gravitational wave (GW) sources for advanced LIGO detectors. Accurate theoretical waveform models from the inspiral, merger, and ringdown phases of such systems are used to filter detector data under the template-based matched-filtering paradigm. An efficient grid over the parameter space at a fixed minimal match has a direct impact on the overall time taken by these searches. We present a new hybrid geometric-random template placement algorithm for signals described by parameters of two masses and one spin magnitude. Such template banks could potentially be used in GW searches from binary neutron stars and neutron star--black hole systems. The template placement is robust and is able to automatically accommodate curvature and boundary effects with no fine-tuning. We also compare these banks against vanilla stochastic template banks and show that while both are equally efficient in the fitting-factor sense, the bank sizes are $\ensuremath{\sim}25%$ larger in the stochastic method. Further, we show that the generation of the proposed hybrid banks can be sped up by nearly an order of magnitude over the stochastic bank. Generic issues related to optimal implementation are discussed in detail. These improvements are expected to directly reduce the computational cost of gravitational wave searches.

Fast Binary Counters Based on Symmetric Stacking

Abstract: In this brief, a new binary counter design is proposed. It uses 3-bit stacking circuits, which group all of the “1” bits together, followed by a novel symmetric method to combine pairs of 3-bit stacks into 6-bit stacks. The bit stacks are then converted to binary counts, producing 6:3 counter circuits with no xor gates on the critical path. This avoidance of xor gates results in faster designs with efficient power and area utilization. In VLSI simulations, the proposed counters are 30% faster than existing parallel counters and also consume less power than other higher order counters. Additionally, using the proposed counters in existing counter-based Wallace tree multiplier architectures reduces latency and power consumption for 64 and 128-bit multipliers.

Evolution of Binary Supermassive Black Holes in Rotating Nuclei

Abstract: The interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binary's orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binary's orbital eccentricity as well. We present a general treatment of this problem based on the Fokker–Planck equation for f, defined as the probability distribution for the binary's orbital elements. First- and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analytic approximations are presented for some of these coefficients. Solutions of the Fokker–Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: (1) the orientation of the binary's orbit evolves toward alignment with the plane of rotation of the nucleus and (2) binary orbital eccentricity decreases for aligned binaries and increases for counteraligned ones. We find that the diffusive (random-walk) component of a binary's evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity, and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets.

Learning Efficient Binary Codes From High-Level Feature Representations for Multilabel Image Retrieval

Abstract: Due to the efficiency and effectiveness of hashing technologies, they have become increasingly popular in large-scale image semantic retrieval. However, existing hash methods suppose that the data distributions satisfy the manifold assumption that semantic similar samples tend to lie on a low-dimensional manifold, which will be weakened due to the large intraclass variation. Moreover, these methods learn hash functions by relaxing the discrete constraints on binary codes to real value, which will introduce large quantization loss. To tackle the above problems, this paper proposes a novel unsupervised hashing algorithm to learn efficient binary codes from high-level feature representations. More specifically, we explore nonnegative matrix factorization for learning high-level visual features. Ultimately, binary codes are generated by performing binary quantization in the high-level feature representations space, which will map images with similar (visually or semantically) high-level feature representations to similar binary codes. To solve the corresponding optimization problem involving nonnegative and discrete variables, we develop an efficient optimization algorithm to reduce quantization loss with guaranteed convergence in theory. Extensive experiments show that our proposed method outperforms the state-of-the-art hashing methods on several multilabel real-world image datasets.

Principal weighted support vector machines for sufficient dimension reduction in binary classification.

Abstract: Sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.

Learning Effective Binary Descriptors via Cross Entropy

Abstract: Binary descriptors not only are beneficial for similarity search, they are also capable of serving as discriminant features for classification purpose. In this paper we propose a new algorithm based on cross entropy to learn effective binary descriptors, dubbed CE-Bits, providing an alternative to L-2 and hinge loss learning. Because of the usage of cross entropy, a min-max binary NP-hard problem is raised to optimize the binary code during training. We provide a novel solution by breaking the binary code into independent blocks and optimize them individually. Although sub-optimal, our method converges very fast and outperforms its L-2 and hinge loss counterparts. By conducting extensive experiments on several benchmark datasets, we show that CE-Bits efficiently generates effective binary descriptors for both classification and retrieval tasks and outper-forms state-of-the-art supervised hashing algorithms.

Gravitational wave source localization for eccentric binary coalesce with a ground-based detector network

Abstract: The gravitational wave source localization problem is important in gravitational wave astronomy. About the source localization problem of ground-based detectors, almost all of the previous investigations only considered the arrival time difference. Within the matched filtering framework, the information beside the arrival time difference can possibly also help with source localization. Especially when an eccentric binary is considered, the character involved in the gravitational waveform may improve the source localization. We investigate this effect systematically in the current paper. During the investigation, the enhanced postcircular waveform model is used to describe the eccentric binary coalesce. We find that the source localization accuracy does increase along with the eccentricity increases. But such improvement depends on the total mass of the binary. For total mass $100{M}_{\ensuremath{\bigodot}}$ binary, the source localization accuracy may be improved about two times in general when the eccentricity increases from 0 to 0.4. For a total mass $65{M}_{\ensuremath{\bigodot}}$ binary (GW150914-like binary), the improvement factor is about 1.3 when the eccentricity increases from 0 to 0.4. For a total mass $22{M}_{\ensuremath{\bigodot}}$ binary (GW151226-like binary), such improvement is ignorable.

Double-pattern triangular pulse width modulation technique for high-accuracy high-speed 3D shape measurement.

Abstract: Using 1-bit binary patterns for three-dimensional (3D) shape measurement has been demonstrated as being advantageous over using 8-bit sinusoidal patterns in terms of achievable speeds. However, the phase quality generated by binary pattern(s) typically are not high if only a small number of phase-shifted patterns are used. This paper proposes a method to improve the phase quality by representing each pattern with the difference of two binary patterns: the first binary pattern is generated by triangular pulse width modulation (TPWM) technique, and the second being π shifted from the first pattern that is also generated by TPWM technique. The phase is retrieved by applying a three-step phase-shifting algorithm to the difference patterns. Through optimizing the modulation frequency of the triangular carrier signal, we demonstrate that a high-quality phase can be generated for a wide range of fringe periods (e.g., from 18 to 1140 pixels) with only six binary patterns. Since only 1-bit binary patterns are required for 3D shape measurement, this paper will present a real-time 3D shape measurement system that can achieve 30 Hz.

Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6

Abstract: The maximum size $A_2(8,6;4)$ of a binary subspace code of packet length $v=8$, minimum subspace distance $d=6$, and constant dimension $k=4$ is $257$, where the $2$ isomorphism types are extended lifted maximum rank distance codes. In Finite Geometry terms the maximum number of solids in $\operatorname{PG}(7,2)$, mutually intersecting in at most a point, is $257$. The result was obtained by combining the classification of substructures with integer linear programming techniques. This implies that the maximum size $A_2(8,6)$ of a binary mixed-dimension code of packet length $8$ and minimum subspace distance $6$ is also $257$.

Worst-case Redundancy of Optimal Binary AIFV Codes and Their Extended Codes

Abstract: Binary almost instantaneous fixed-to-variable length (AIFV) codes are lossless codes that generalize the class of instantaneous fixed-to-variable length codes. The code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain better compression ratio than Huffman codes. Nevertheless, an upper bound on the redundancy of optimal binary AIFV codes is only known to be 1, which is the same as the bound of Huffman codes. In this paper, the upper bound is improved to 1/2, which is shown to coincide with the worst-case redundancy of the codes. Along with this, the worst-case redundancy is derived for sources with $p_{\max }\geq 1$ /2, where $p_{\max }$ is the probability of the most likely source symbol. In addition, we propose an extension of binary AIFV codes, which use $m$ code trees and allow at most $m$ -bit decoding delay. We show that the worst-case redundancy of the extended binary AIFV codes is $1/m$ for $m \leq 4$ .

Design of Approximate High-Radix Dividers by Inexact Binary Signed-Digit Addition

Abstract: Approximate high radix dividers (HR-AXDs) are proposed and investigated in this paper. High-radix division is reviewed and inexact computing is introduced at different levels. Design parameters such as number of bits (N) and radix (r) are considered in the analysis; the replacement schemes with inexact cells and truncation schemes of exact cells in the binary signed-digit adder array is introduced. Circuit-level performance and the error characteristics of the inexact high radix dividers are analyzed for the proposed designs. The combined assessment of the normal error distance, power dissipation and delay is investigated and applications of approximate high-radix dividers are treated in detail. The simulation results show that the proposed approximate dividers offer extensive saving in terms of power dissipation, circuit complexity and delay, while only incurring in a small degradation in accuracy thus making them possibly suitable and interesting to some applications and domains such as low power/mobile computing.

A Reconfigurable Optical Logic Gate With up to 25 Logic Functions Based on Polarization Modulation With Direct Detection

Abstract: We propose and investigate a new scheme to realize optical logic gates using polarization addition with direct detection. Two polarizations of an optical signal are modulated, respectively, by independent binary inputs to represent four different states, while direct detection is used to map the four states to the corresponding binary output. Up to 25 logic gates, including all the basic logic gates, can be implemented by adjusting bias voltages of the two modulators, peak–peak voltages of the driving signals, and the rotation angle between the two polarizations. A modified Poincare sphere and a simplified 2-D description are developed to illustrate the principle of the proposed scheme. Experiments are successfully carried out to realize all of the six basic logic gates at 1 Gb/s. Influences on the performance of logic gates are also studied by considering some key factors, such as the extinction ratio of Mach–Zehnder modulator (MZM), input power, and rotation-angle deviation.

Approximate-computation-based binary weight convolution neural network hardware accelerator calculating module

Abstract: The invention discloses an approximate-computation-based binary weight convolution neural network hardware accelerator calculating module. The hardware accelerator calculating module is able to receive the input neural element data and binary convolution kernel data and conducts rapid convolution data multiplying, accumulating and calculating. The calculation module utilizes the complement data representation, and includes mainly an optimized approximation binary multiplier, a compressor tree, an innovative approximation adder, and a temporary register for the sum of the serially adding part. In addition, targeted to the optimized approximation binary multiplier, two error compensation schemes are proposed, which reduces or completely eliminates the errors brought about from the optimized approximation binary multiplier under the condition of only slightly increasing the hardware resource overhead expense. Through the optimized calculating units, the key paths for the binary weight convolution neural network hardware accelerator using the computation module are shortened considerably, and the size loss and power loss are also reduced, making the module suitable for a low power consuming embedded type system in need of using the convolution neural network.