Digit Generation Research Articles

A 1T1M-based efficient probability storage and computing cell for the VAE-SBN hybrid model

Abstract Bayesian network are crucial components for uncertainty reasoning and knowledge representation in probabilistic graphical models. As model complexity increases, traditional digital methods face challenges in efficiency and resource utilization. In this work, a novel Bayesian network optimization method based on one-transistor one-memristor (1T1M) units for storing and accessing probability values was proposed. This method leverages the sigmoid-like characteristics of 1T1M for computational optimization, integrates probability storage into sigmoid belief network (SBN), and extends to the variational autoencoder (VAE) framework. By storing and manipulating probabilities at hardware level, this approach enhances storage efficiency and access speed while enhancing computational precision and model expressiveness through the sigmoid-like space of 1T1M. Validation experiments using the MNIST digit generation task demonstrate that this method exhibits unique advantages in SBN structures, particularly in handling complex conditional probabilities and inference tasks. Compared to traditional digital implementations, the proposed method exhibits potential advantages in inference speed and hardware utilization.

A practical Approach to Handwritten Digit Generation with Generative Adversarial Networks on MNIST

Implementation of a Generative Adversarial Network (GAN) utilizing the MNIST (Modified National Institute of Standards and Technology database) dataset of handwritten digits, the GAN comprises a generator creating synthetic images from random noise and a discriminator to classifying these images as real or fake. The Generator utilizes leaky ReLU (rectified linear unit) activations, Batch normalization and reshaping to produce 28x28 grayscale images, while the Discriminator uses dense layers, leaky ReLU, and dropout to enhance classification accuracy. Both networks are trained using the Adam optimizer to improve stability and performance. The GAN is trained in an adversarial setup where the Generator seeks to create convincing images and the Discriminator aims to correctly classify them. Results demonstrate the GAN's ability to generate high-quality handwritten digit images, displaying its effectiveness and providing valuable insights into best practices for GAN implementation and training.

Photonic probabilistic machine learning using quantum vacuum noise

Probabilistic machine learning utilizes controllable sources of randomness to encode uncertainty and enable statistical modeling. Harnessing the pure randomness of quantum vacuum noise, which stems from fluctuating electromagnetic fields, has shown promise for high speed and energy-efficient stochastic photonic elements. Nevertheless, photonic computing hardware which can control these stochastic elements to program probabilistic machine learning algorithms has been limited. Here, we implement a photonic probabilistic computer consisting of a controllable stochastic photonic element – a photonic probabilistic neuron (PPN). Our PPN is implemented in a bistable optical parametric oscillator (OPO) with vacuum-level injected bias fields. We then program a measurement-and-feedback loop for time-multiplexed PPNs with electronic processors (FPGA or GPU) to solve certain probabilistic machine learning tasks. We showcase probabilistic inference and image generation of MNIST-handwritten digits, which are representative examples of discriminative and generative models. In both implementations, quantum vacuum noise is used as a random seed to encode classification uncertainty or probabilistic generation of samples. In addition, we propose a path towards an all-optical probabilistic computing platform, with an estimated sampling rate of ~1 Gbps and energy consumption of ~5 fJ/MAC. Our work paves the way for scalable, ultrafast, and energy-efficient probabilistic machine learning hardware.

Enhanced diffusion model based on similarity for handwritten digit generation

In recent years with the rise of deep learning, there has been a major revolution in image generation technology. Deep learning models, especially the diffusion model. have brought about breakthrough progress in image generation. Various deep generation models have recently demonstrated a wide variety of high-quality sample data patterns. Although image generation technology has achieved remarkable achievement. There are still challenges and issues, such as quality control in generated images. In order to improve the robustness and performance of diffusion model in image generation, an enhanced diffusion model based on similarity is proposed in this paper. Based on the original diffusion model, the similarity loss function is added to narrow the semantic distance between the original image and the generated image, so that the generated image is more robust. Extensive experiments were carried out on the MINIST dataset, and the experimental results showed that compared with the other generation models, the enhanced diffusion model based on similarity obtained the best scores of IS=31.61 and FID=175.21, which verified the validity of the similarity loss.

Dzongkha Handwritten Digit Recognition using Machine Learning Techniques

Handwritten digit recognition has recently gained importance, attracting many researchers due to its use in various machine learning and computer vision applications. As technology and science progressing, there is a need for a system to recognize the handwritten script in several real-time applications to reduce human effort. There a lot of work has been done on the recognition and generation of handwritten digits of high-resource languages such as English. However, insufficient work has been done on Dzongkha digits recognition, as Dzongkha digits are low-resource and more complex than English patterns. This paper aims to perform handwritten character recognition of Dzongkha digit using several machine learning techniques. The unavailability of the Dzongkha handwritten digit dataset is the prime motivation behind this work. To facilitates the recognition of Dzongkha handwritten digit, we have collected the data of Dzongkha handwritten digit from indigenous and non-indigenous people of Bhutan and provided the dataset for further research. Moreover, we have used several machine algorithms, including a support vector machine, K-nearest neighbor, and decision tree. Among these algorithms, the support vector machine classification algorithm has achieved a remarkable result with an accuracy of 98.29%.

Generation of High-Resolution Handwritten Digits with an Ion-Trap Quantum Computer

Generating high-quality data (e.g., images or video) is one of the most exciting and challenging frontiers in unsupervised machine learning. Utilizing quantum computers in such tasks to potentially enhance conventional machine-learning algorithms has emerged as a promising application but poses big challenges due to the limited number of qubits and the level of gate noise in available devices. In this work, we provide the first practical and experimental implementation of a quantum-classical generative algorithm capable of generating high-resolution images of handwritten digits with state-of-the-art gate-based quantum computers. In our quantum-assisted machine-learning framework, we implement a quantum-circuit-based generative model to learn and sample the prior distribution of a generative adversarial network. We introduce a multibasis technique which leverages the unique possibility of measuring quantum states in different bases, hence enhancing the expressivity of the prior distribution. We train this hybrid algorithm on an ion-trap device based on Yb+171 ion qubits to generate high-quality images and quantitatively outperform comparable classical generative adversarial networks trained on the popular MNIST dataset for handwritten digits.1 MoreReceived 26 November 2021Revised 19 April 2022Accepted 1 June 2022DOI:https://doi.org/10.1103/PhysRevX.12.031010Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMachine learningQuantum algorithmsQuantum Information

LayoutGAN: Synthesizing Graphic Layouts With Vector-Wireframe Adversarial Networks.

Layout is important for graphic design and scene generation. We propose a novel Generative Adversarial Network, called LayoutGAN, that synthesizes layouts by modeling geometric relations of different types of 2D elements. The generator of LayoutGAN takes as input a set of randomly-placed 2D graphic elements, represented by vectors and uses self-attention modules to refine their labels and geometric parameters jointly to produce a realistic layout. Accurate alignment is critical for good layouts. We, thus, propose a novel differentiable wireframe rendering layer that maps the generated layout to a wireframe image, upon which a CNN-based discriminator is used to optimize the layouts in image space. We validate the effectiveness of LayoutGAN in various experiments including MNIST digit generation, document layout generation, clipart abstract scene generation, tangram graphic design, mobile app layout design, and webpage layout optimization from hand-drawn sketches.

Age-related cognitive task effects on gait characteristics: do different working memory components make a difference?

BackgroundThough it is well recognized that gait characteristics are affected by concurrent cognitive tasks, how different working memory components contribute to dual task effects on gait is still unknown. The objective of the present study was to investigate dual-task effects on gait characteristics, specifically the application of cognitive tasks involving different working memory components. In addition, we also examined age-related differences in such dual-task effects.MethodsThree cognitive tasks (i.e. ‘Random Digit Generation’, ‘Brooks’ Spatial Memory’, and ‘Counting Backward’) involving different working memory components were examined. Twelve young (6 males and 6 females, 20 ~ 25 years old) and 12 older participants (6 males and 6 females, 60 ~ 72 years old) took part in two phases of experiments. In the first phase, each cognitive task was defined at three difficulty levels, and perceived difficulty was compared across tasks. The cognitive tasks perceived to be equally difficult were selected for the second phase. In the second phase, four testing conditions were defined, corresponding to a baseline and the three equally difficult cognitive tasks. Participants walked on a treadmill at their self-selected comfortable speed in each testing condition. Body kinematics were collected during treadmill walking, and gait characteristics were assessed using spatial-temporal gait parameters.ResultsApplication of the concurrent Brooks’ Spatial Memory task led to longer step times compared to the baseline condition. Larger step width variability was observed in both the Brooks’ Spatial Memory and Counting Backward dual-task conditions than in the baseline condition. In addition, cognitive task effects on step width variability differed between two age groups. In particular, the Brooks’ Spatial Memory task led to significantly larger step width variability only among older adults.ConclusionThese findings revealed that cognitive tasks involving the visuo-spatial sketchpad interfered with gait more severely in older versus young adults. Thus, dual-task training, in which a cognitive task involving the visuo-spatial sketchpad (e.g. the Brooks’ Spatial Memory task) is concurrently performed with walking, could be beneficial to mitigate impairments in gait among older adults.Electronic supplementary materialThe online version of this article (doi:10.1186/1743-0003-11-149) contains supplementary material, which is available to authorized users.

Continued fractions without fractions: Lagrange theorem and Pell equations

Quadratic irrationals and their representation as continued fractions are investigated by means of proper tools of Discrete Dynamical Systems theory. This is done by recasting the process of generation of digits in the continued fraction expansion of a real number as a suitable discrete nonlinear system whose asymptotic behavior is to be studied. Such an approach allows, on the one hand, to retrieve well known results in the literature, the most relevant being the Lagrange theorem, and on the other hand it aims to give more insight into some related issues.

Semantic, perceptual and number space: Relations between category width and spatial processing

Coarse semantic encoding and broad categorization behavior are the hallmarks of the right cerebral hemisphere's contribution to language processing. We correlated 40 healthy subjects’ breadth of categorization as assessed with Pettigrew's category width scale with lateral asymmetries in perceptual and representational space. Specifically, we hypothesized broader category width to be associated with larger leftward spatial biases. For the 20 men, but not the 20 women, this hypothesis was confirmed both in a lateralized tachistoscopic task with chimeric faces and a random digit generation task; the higher a male participant's score on category width, the more pronounced were his left-visual field bias in the judgement of chimeric faces and his small-number preference in digit generation (“small” is to the left of “large” in number space). Subjects’ category width was unrelated to lateral displacements in a blindfolded tactile-motor rod centering task. These findings indicate that visual-spatial functions of the right hemisphere should not be considered independent of the same hemisphere's contribution to language. Linguistic and spatial cognition may be more tightly interwoven than is currently assumed.

Exploring number space by random digit generation

There is some evidence that human subjects preferentially select small numbers when asked to sample numbers from large intervals "at random". A retrospective analysis of single digit frequencies in 16 independent experiments with the Mental Dice Task (generation of digits 1-6 during 1 min) confirmed the occurrence of small-number biases (SNBs) in 488 healthy subjects. A subset of these experiments suggested a spatial nature of this bias in the sense of a "leftward" shift along the number line. First, individual SNBs were correlated with leftward deviations in a number line bisection task (but unrelated to the bisection of physical lines). Second, in 20 men, the magnitude of SNBs significantly correlated with leftward attentional biases in the judgment of chimeric faces. Finally, cognitive activation of the right hemisphere enhanced SNBs in 20 different men, while left hemisphere activation reduced them. Together, these findings provide support for a spatial component in random number generation. Specifically, they allow an interpretation of SNBs in terms of "pseudoneglect in number space." We recommend the use of random digit generation for future explorations of spatial-attentional asymmetries in numerical processing and discuss methodological issues relevant to prospective designs.

Executive processes in visual and spatial working memory tasks

Three experiments are reported, which have investigated the nature of the cognitive mechanisms that underlie performance on specific visuo-spatial working memory tasks, with the emphasis on exploring the extent of central executive involvement. Experiments 1 and 2 employed oral random digit generation as an executive task within a dual-task paradigm. The results of both experiments indicated that visuo-spatial tasks that involve sequential processing of information show more interference with random digit generation than do visuo-spatial tasks that involve simultaneous processing. The third experiment substituted oral random digit generation for executive tasks that did not involve memory for serial order (vigilance tasks adapted from Vandierendonck, De Vooght, & Van der Goten, 1998b). The results indicated significant interference between the vigilance tasks and the sequential visuo-spatial task, but not with the simultaneous visuo-spatial task. Overall the results of the three experiments are interpreted as indicating that serial sequential visuo-spatial tasks involve executive resources to a significantly greater extent than do simultaneous visuo-spatial tasks, and that this can have implications for studies that attempt to make use of such tasks to fractionate separable visual and spatial components within working memory.

Generation of physical random digits using diode noise and its statistical properties

AbstractThis study deals with a method of random number generation using hardware as a source of random signals. The random signals are produced by shot noise generated by a Zener diode and are converted into sequences of high‐quality random numbers. The proposed method is an improvement compared to conventional hardware‐based methods due to the fact that randomness of generated numbers is not affected by irregular performance characteristics of the hardware. This new method was verified by generating approximately 1.2 × 109 decimal random integers and by testing such characteristics of the generated random number sequences as their uniformity and independence by statistical methods. Results of the verification confirmed that characteristics of the random sequences obtained by this method were most satisfactory. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 29–36, 2001

Random generation and the executive control of working memory.

A series of experiments explores the capacity for generating sequences of random responses, relating it to the central executive component of working memory. Experiment 1 shows a broadly similar pattern of redundancy increasing with speed of generation for both the verbal generation of digits and the manual pressing of keys. In both cases deviations from randomness are shown to reflect the increasing use of a limited number of stereotyped response sets. The remaining experiments use keyboard generation. Experiment 2 demonstrates that concurrent immediate serial recall decreases randomness, and that longer recall sequences produce less random output. Experiments 3 and 4 show that whereas simple counting has no effect on randomness, serial recall, semantic category generation, and concurrent digit generation have substantial effects, and a concurrent fluid intelligence test has the greatest influence on the randomness of key pressing. It is suggested that the task of random generation resembles that of category fluency because it requires the subject to switch retrieval plans and inhibit repetition. On this basis it is predicted that a task involving repeated switching of categories will interfere with generation, despite being predictable and having a low memory load. Experiments 5 and 6 confirm this prediction. Strengths and limitations of the switching hypothesis are discussed, as are the implications of our results for the analysis of executive processes.

Random Generation and the Executive Control of Working Memory

A series of experiments explores the capacity for generating sequences of random responses, relating it to the central executive component of working memory. Experiment 1 shows a broadly similar pattern of redundancy increasing with speed of generation for both the verbal generation of digits and the manual pressing of keys. In both cases deviations from randomness are shown to reflect the increasing use of a limited number of stereotyped response sets. The remaining experiments use keyboard generation. Experiment 2 demonstrates that concurrent immediate serial recall decreases randomness, and that longer recall sequences produce less random output. Experiments 3 and 4 show that whereas simple counting has no effect on randomness, serial recall, semantic category generation, and concurrent digit generation have substantial effects, and a concurrent fluid intelligence test has the greatest influence on the randomness of key pressing. It is suggested that the task of random generation resembles that of category fluency because it requires the subject to switch retrieval plans and inhibit repetition. On this basis it is predicted that a task involving repeated switching of categories will interfere with generation, despite being predictable and having a low memory load. Experiments 5 and 6 confirm this prediction. Strengths and limitations of the switching hypothesis are discussed, as are the implications of our results for the analysis of executive processes.

Evaluation of a Simulation of Human Performance on Random-Digit Generation: Measures of Concept and Redundancy

Ginsburg and Karpiuk in 1995 introduced an algorithm that simulates human performance in tasks of generating random digits. We have compared sequences produced by this algorithm with human performance and truly random sequences. It is shown that the algorithm can be used to simulate human performance according to the measures on which it had been constructed. However, other peculiarities of human performance are not captured by the algorithm. The results are discussed with regard to current theories of human random digit generation.

Estimates of Driver Mental Workload: A Long-Term Field Trial of Two Subsidiary Tasks

Two auditory subsidiary task measures of driver mental workload---delayed digit recall and random digit generation---were evaluated in a four-year field trial. Van pool members performed the tasks for 2-min periods while driving a mix of rural secondary roads, limited access expressways, high-density, limited-access urban drives, and downtown city streets on a daily commute from upstate New York to New York City. Data collected included the roadway being traveled, time of day, traffic conditions, vehicle density, speed, weather, brake applications, and driver's subjective difficulty rating. Subsidiary task degradation was a function of traffic density, average speed, and uncertainty (estimated by the number of brake depressions). Weather conditions moderated these variables. Unpredictability of traffic appeared to be the major determinant of perceived difficulty. The digit recall task correlated (r = 0.784) with driver ratings of task difficulty and (r = 0.808) with a calculated driver workload index based on brake actuations per minute plus the log2 of vehicle speed. Although subjective difficulty ratings correlated with subsidiary task performance and with objective criteria of traffic density and speed, some dissociation was noted. Indications of workload homeostasis were evident, as drivers appeared to modify their performance to keep workload within a comfortable range.

Components of Random Generation by Normal Subjects and Patients with Dysexecutive Syndrome

The study presents a hypothesis on how randomness could be simulated by human subjects. Three sources of deviation from randomness are predicted: (1) the preferred application of overlearned production schemata for producing sequences of digits, (2) a wrong concept of randomness, and (3) the impossibility to monitor for redundancies of higher- than those of first-order. Deviations of random generation of digits produced by healthy subjects, patients with chronic frontal lobe damage, and patients with Parkinson′s disease from random sequences produced by a computer program can be explained by the differential influence of these factors. Whereas incorrect concepts of randomness and limits on monitoring capacity distinguished all sequences produced by humans from actual random sequences, persistence on a single production strategy distinguished brain-damaged patients from controls. Random generation of digits appears to be a theoretically transparent and clinically useful test of executive function.

Improving the division instruction of application-specific RISCs

This paper presents the development and application of a signed radix-4 division algorithm to a RISC architecture, where the internal ALU Manchester Carry adder is used to maintain the partial remainder in irredundant form. There are division algorithms which are faster than the one described in this paper, however, they usually make use of a redundant representation of the partial remainder and require carry-save adders which are not normally used in the integer execution unit of RISCs. The method presented in this contribution employs 3x divisor multiples and uses a reduced next divisor multiple estimate table which is implemented by a small and fast logic. Alternative radix-4 schemes with quotient digits {-2,-1,0,1,2} require large and slow PLAs for quotient digit generation. Additionally, there is no need for positive and negative quotient registers because quotient bits are generated on-the-fly by a small-sized logic, concurrently with partial remainder formation. This method also deals directly with signed two's complement numbers, eliminating the need for additional instructions for sign conversion. The application of this radix-4 division algorithm provides a two-bits-at-a-time division instruction, instead of the traditional single bit approach used in some RISCs. The speedup achieved can be very important in many numeric intensive applications, in which the use of floating-point units is not essential.

Fast Iterative Division of p-adic Numbers

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.