There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Convex Analysisの二,三の進展について

Major advancements in building general-purpose and customized hardware have been one of the key enablers of versatility and pervasiveness of machine learning models such as deep neural networks. To sustain this ubiquitous deployment of machine learning models and cope with their computational and storage complexity, several solutions such as low-precision representation of model parameters using fixed-point representation and deploying approximate arithmetic operations have been employed. Studying the potency of such solutions in different applications requires integrating them into existing machine learning frameworks for high-level simulations as well as implementing them in hardware to analyze their effects on power/energy dissipation, throughput, and chip area. Lop is a library for design space exploration that bridges the gap between machine learning and efficient hardware realization. It comprises a Python module, which can be integrated with some of the existing machine learning frameworks and implements various customizable data representations including fixed-point and floating-point as well as approximate arithmetic operations.Furthermore, it includes a highly-parameterized Scala module, which allows synthesizing hardware based on the said data representations and arithmetic operations. Lop allows researchers and designers to quickly compare quality of their models using various data representations and arithmetic operations in Python and contrast the hardware cost of viable representations by synthesizing them on their target platforms (e.g., FPGA or ASIC). To the best of our knowledge, Lop is the first library that allows both software simulation and hardware realization using customized data representations and approximate computing techniques.

Deploying Customized Data Representation and Approximate Computing in Machine Learning Applications

A Flow-Oriented Approach to the Placement of Boolean Networks.

In this article, we investigate the application of different techniques for mitigating the impact of process variations on the custom functional unit (CFU) of extensible processors. The techniques include using extra cycles for the CFU and extending the clock period for the extensible processor. The former technique is based on providing an extra clock cycle to those custom instructions (CIs) that have timing yields smaller than one. For this purpose, we make use of a lookup table (LUT) for each fabricated processor. Based on a post-fabrication analysis, the need for an extra clock cycle for some CIs is determined. Consequently, the CI timing violations are prevented, and all manufactured extensible processors will work with a predefined clock cycle time. To study the effect of the objective function (used during the CI selection phase) on the efficacy of the suggested architectural technique, we investigate three different objective functions. In the second technique, the clock period extension is used to guarantee a design yield of one. Our results demonstrate that combining both techniques helps increase the speedup achieved by the extensible processor. To assess the efficacies of the proposed methods, several benchmarks from different application domains are used. Results of the study reveal that the suggested techniques provide considerable improvements in the speedups of the extensible processors when compared to those of approaches that do not consider the impact of process variations.

Yield and Speedup Improvements in Extensible Processors by Allocating Extra Cycles to Some Custom Instructions

With the emergence of many-core multiprocessor system-on-chips (MPSoCs), on-chip networks are facing serious challenges in providing fast communication among various tasks and cores. One promising on-chip network design approach shown in recent studies is to add express channels to traditional mesh network as shortcuts to bypass intermediate routers, thereby reducing packet latency. This approach not only changes the packet latency models, but also greatly affects network traffic behaviors, both of which have not been fully exploited in existing mapping algorithms. In this article, we explore the opportunities in optimizing application mapping for flattened butterfly, a popular express channel-based on-chip network. Specifically, we identify the unique characteristics of flattened butterfly, analyze the opportunities and new challenges, and propose an efficient heuristic mapping algorithm. The proposed algorithm Contention-Aware Latency Minimal (CALM) is able to reduce unnecessary turns that would otherwise impose additional router pipeline latency to packets, as well as adjust forwarding traffic to reduce network contention latency. Simulation results show that the proposed algorithm can achieve, on average, 3.4X reduction in the number of turns, 24.8% reduction in contention latency, and 14.12% reduction in the overall packet latency.

CALM: Contention-Aware Latency-Minimal Application Mapping for Flattened Butterfly On-Chip Networks

Traditional logical equivalence checking (LEC), which plays a major role in the entire chip design process, faces challenges of meeting the requirements demanded by the many emerging technologies that are based on logic models different from the standard complementary metal oxide semiconductor (CMOS). In this article, we propose an LEC framework to be employed in the verification process of superconducting electronics (SCE). Our LEC framework is compatible with the existing CMOS technologies and can also check features and capabilities that are unique to SCE. For instance, the performance of nonresistively biased single-flux quantum (SFQ) circuits benefits from ultradeep pipelining, and verification of such circuits requires new models and algorithms. We, therefore, present the multicycle input dependency circuit model which is a novel model representation of design to explicitly capture the dependency of primary outputs of the circuit on sequences of internal signals and inputs. Embedding the proposed circuit model and several structural checking modules, the process of verification can be independent of the underlying technology and signaling. We benchmark the proposed framework on postsynthesis SFQ and 4-phase adiabatic quantum flux parametron netlists. Results show a comparative verification time of SFQ circuit benchmark, including 16-bit integer divider and ISCAS’85 circuits with respect to the ABC tool for similar CMOS circuits.

Massoud Pedram

Papers

Deploying Customized Data Representation and Approximate Computing in Machine Learning Applications

A Flow-Oriented Approach to the Placement of Boolean Networks.

Yield and Speedup Improvements in Extensible Processors by Allocating Extra Cycles to Some Custom Instructions

CALM: Contention-Aware Latency-Minimal Application Mapping for Flattened Butterfly On-Chip Networks

A Logic Verification Framework for SFQ and AQFP Superconducting Circuits