Block Format Error Bounds and Optimal Block Size Selection

The amounts of data that need to be transmitted, processed, and stored by the modern deep neural networks have reached truly enormous volumes in the last few years calling for the invention of new paradigms both in hardware and software development. One of the most promising and rapidly advancing frontiers here is the creation of new numerical formats. In this work we focus on the family of block floating point numerical formats due to their combination of wide dynamic range, numerical accuracy, and efficient hardware implementation of inner products using simple integer arithmetic. These formats are characterized by a block of mantissas with a shared scale factor. The basic Block Floating Point (BFP) format quantizes the block scales into the nearest powers of two on the right. Its simple modification - Scaled BFP (SBFP) - stores the same scales in full precision and thus allows higher accuracy. In this paper, we study the statistical behavior of both these formats rigorously. We develop asymptotic bounds on the inner product error in SBFP- and BFP-quantized normally distributed vectors. Next, we refine those asymptotic results to finite dimensional settings and derive high-dimensional tight bounds for the same errors. Based on the obtained results we introduce a performance measure assessing accuracy of any block format. This measure allows us to determine the optimal parameters, such as the block size, yielding highest accuracy. In particular, we show that if the precision of the BFP format is fixed at 4 bits, the optimal block size becomes 64. All theoretical derivations are supported by numerical experiments and studies on the weights of publicly available pretrained neural networks

Toward far infrared quantum well lasers

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 113-121).by Ilya Lyubomirsky.Ph.D

Quantum reality and squeezed states of light

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 67-71).by Ilya Lyubomirsky.M.S

Millimeter-wave, Terahertz, and Infrared Devices

Contains an introduction, reports on two research projects and a list of publications.National Aeronautics and Space Administration Grant NAGW-4691National Science Foundation Grant AST 94-23608U.S. Army Research Office Grant DAAH04-95-1-0610AASERT/U.S. Army Research Office Grant DAAHO4-94-G-0167Hertz Foundation FellowshipU.S. Army Research Laboratory - Federated Laboratories Grant QK-881

Reach Extension and Capacity Enhancement of VCSEL-Based Transmission Over Single-Lane MMF Links

This paper reviews and examines several techniques for expanding the carrying capacity of multimode fiber (MMF) using vertical cavity surface emitting lasers (VCSELs). The first approach utilizes short wavelength division multiplexing in combination with MMF optimized for operation between 850 and 950 nm. Both nonreturn to zero (NRZ) and four-level pulse amplitude modulation (PAM4) signaling are measured and demonstrate up to 170-Gb/s postforward error correction transmission over 300 m. For single wavelength transmission, the use of selective modal launch to increase the optical bandwidth of a standard OM3 MMF to more than 2.1 GHzkm for standard MMF is presented. A statistical model is used to predict the bandwidth enhancement of installed MMF and indicates that significant link extension can be achieved using selective modal launch techniques. These results demonstrate the continued effectiveness of VCSEL-based MMF links in current and future data center environments

High-Frequency (> 100 GHz) and High-Speed (< 10 ps) Electronic Devices

Contains an introduction, reports on four research projects and a list of publications.Defense Advanced Research Projects Agency Contract MDA972-90-C-0021National Aeronautics and Space Administration Grant NAGW-4691National Aeronautics and Space Administration Grant 959705National Science Foundation Grant AST 94-23608National Science Foundation/MRSEC Grant DMR 94-00334MIT Lincoln Laboratory Advanced Concept Program Grant BX-5464U.S. Army Research Office Grant DAAH04-95-1-0610Hertz Foundation FellowshipU.S. Army - Office of Scientific Research Grant DAAH04-94-G-016

High-Frequency (>100 GHz) and High-Speed (<1 ps) Electronic Devices

Contains an introduction, reports on three research projects and a list of publications.Advanced Research Projects Agency Contract MDA972-90-C-0021National Aeronautics and Space Administration Grant NAG2-693National Aeronautics and Space Administration Contract 959705National Science Foundation/MRSEC Grant DMR 94-00334MIT Lincoln Laboratory Advanced Concept Program Contract BX-5464MIT Research Laboratory of Electronics Postdoctoral FellowshipRome Air Force Laboratory Graduate FellowshipU.S. Army Research Office Grant DAAL03-92-G-0251Hertz Foundation FellowshipU.S. Army Research Office/ASSERT Grant DAAH04-94-G-016

Electromagnetic Wave Theory and Applications

Contains table of contents for Section 3 and reports on five research projects.U.S. Department of Transportation Contract DTRS-57-88-C-00078TTD13U.S. Department of Transportation Contract DTRS-57-88-C-00078TTD30Defense Advanced Research Projects Agency Contract MDA972-90-C-0021Digital Equipment CorporationIBM CorporationJoint Services Electronics Program Contract DAAL03-89-C-0001Joint Services Electronics Program Contract DAAL03-92-C-0001Schlumberger-Doll ResearchU.S. Navy - Office of Naval Research Grant N00014-90-J-1002U.S. Navy - Office of Naval Research Grant N00014-89-J-1019National Aeronautics and Space Administration Grant NAGW-1617National Aeronautics and Space Administration Grant 958461National Aeronautics and Space Administration Grant NAGW-1272U.S. Army Corp of Engineers Contract DACA39-87-K-0022U.S. Navy - Office of Naval Research Grant N00014-89-J-110

Optics and Quantum Electronics

Contains table of contents for Section 3, reports on twenty-one research projects and a list of publications and meeting papers.Joint Services Electronics Program Contract DAAL03-92-C-0001U.S. Air Force - Office of Scientific Research Contract F49620-91-C-0091Charles S. Draper Laboratories Contract DL-H-441692MIT Lincoln LaboratoryNational Science Foundation Grant ECS 90-12787Fujitsu LaboratoriesU.S. Navy - Office of Naval Research Grant N00014-92-J-1302National Center for Integrated Photonic TechnologyNational Science Foundation Grant ECS 85-52701U.S. Navy - Office of Naval Research (MFEL) Grant N00014-91-C-0084U.S. Navy - Office of Naval Research (MFEL) Grant N00014-91-J-1956National Institutes of Health Grant R01-GM35459-08U.S. Air Force - Office of Scientific Research Grant F49620-93-1-0301MIT Lincoln Laboratory Contract BX-5098Electric Power Research Institute Contract RP3170-2

Optics and Quantum Electronics

Contains table of contents for Section 3 and reports on twenty-three research projects.Joint Services Electronics Program Contract DAAL03-92-C-0001U.S. Air Force - Office of Scientific Research Contract F49620-91-C-0091Charles S. Draper Laboratories Contract DL-H-441629MIT Lincoln LaboratoryNational Science Foundation Grant ECS 90-12787Fujitsu LaboratoriesU.S. Navy - Office of Naval Research Grant N00014-92-J-1302National Center for Integrated PhotonicsNational Center for Integrated Photonics TechnologyNational Science Foundation Grant EET 88-15834Joint Services Electronics Program Contract DAAL03-91-C-0001National Science Foundation Fellowship ECS-85-52701U.S. Navy - Office of Naval Research (MGH) Contract N00014-91-C-0084U.S. Navy - Office of Naval Research Grant N00014-91-J-1956National Institutes of Health Grant NIH-5-RO1-GM35459-08Bose CorporationLawrence Livermore National Laboratories Subcontract B160530U.S. Department of Energy Grant DE-FG02-89-ER14012Rockwell International CorporationSpace Exploration AssociatesFuture Energy Applied Technology, Inc