Computer Arithmetic for the Next Generation of Integrated Circuits

Are you keen on spearheading a new era of high-performance computing? Then come and join the Leeds Mathematical Software and Hardware Lab! Seize this opportunity to harness the untapped potential of existing hardware and explore the needs of the next generation of integrated circuits. You will have a chance to work with cutting-edge technology, propose groundbreaking algorithms that redefine traditional paradigms, and inform the future of computer arithmetic.<br /> <br /> This is an ideal moment to pursue a PhD in this area. The growing importance of artificial intelligence is fostering a paradigm shift in the world of hardware design. The increasing complexity of deep-learning models demands computers faster and more powerful than ever before. At the same time, the numerical formats available in conventional hardware are often too accurate for the needs of machine learning: they do not improve the quality of the trained model but may deteriorate it by causing overfitting of the training data.<br /> <br /> Hardware vendors have thus begun to design specialised hardware accelerators that can perform very efficiently a limited range of operations using low-precision formats such as FP8, binary16, BFLOAT16, TensorFloat-32, and a number of other custom fewer-than-32-bit formats. At present, there is no widely-adopted standard that systematises low-precision computer arithmetic, thus different hardware vendor may decide to implement a same format slightly differently, leading to irreproducible results, non-portable code, hard-to-find bugs, and other unexpected behaviours.<br /> <br /> Such problems are hard to detect. The exact design of commercial hardware is a jealously guarded secret, and the numerical behaviour of a specific device has to be probed by a combination of theoretical analysis and reverse engineering. To further complicate the situation, some key operations may involve inputs and outputs in different formats, making the behaviour of the hardware even more difficult to describe exactly. Hardware accelerators that support mixed-precision computations are becoming increasingly prevalent, as they more and more often complement traditional high-end CPUs in top-tier supercomputers. Exploiting all available precisions will be key to harnessing the full potential of these high-performance computing facilities, and the need for such approaches will become ever more pressing as we enter the exascale era.<br /> <br /> This degree will open doors to a myriad of opportunities to shape the future of computing. If this resonates with you, please get in touch!

<h2>Possible research topics</h2> <p>This is an indicative range of subjects you might wish to consider if you are planning to apply for this position. Do not worry if what you have in mind is not listed below: you will have a chance to define a project that resonates with your personal interests, leverages your existing skills, and provides room to develop the skills you wish to learn.</p> <ul> <li>Developing novel, mixed-precision algorithms that exploit a wide range of floating-point formats to solve large-scale problems more efficiently without sacrificing accuracy.</li> <li>Characterising the numerical behaviour of existing hardware through automated testing.</li> <li>Developing high-performance libraries that exploit features of mixed-precision hardware to achieve better performance.</li> <li>Developing new algorithms to solve a variety of problems in heterogeneous CPU/GPU/DPU/FPGA environments.</li> <li>Contributing to the standardisation of new floating-point formats and arithmetics, with the possibility to join the IEEE Working Group P3109 on Arithmetic Formats for Machine Learning and the IEEE Study Group set to deliver the next revision of the IEEE 754 Standard for Floating-Point Arithmetic (IEEE 754-2029).</li> <li>Analysing the behaviour of numerical algorithms on different hardware units, with the aim of discovering and understanding unexpected features.</li> <li>Designing alternative arithmetic formats that can better exploit a very low number of bits.</li> </ul> <h2>Skills and career prospects</h2> <p>Depending on the specific PhD topic you choose, you will develop a number of field-specific skills, such as:</p> <ul> <li>a deep understanding of computer arithmetic;</li> <li>a broad grasp of hardware design issues and trade-offs, with particular emphasis on the design of floating-point units;</li> <li>a familiarity with numerical phenomena such as rounding and numerical errors;</li> <li>a sense for the analysis of errors striking complex computations.</li> </ul> <p>By pairing research and hands-on experience, a PhD degree in computer arithmetic will expand your career prospects, preparing you not only for academia, but also for Research &amp; Development roles in cutting-edge semiconductor companies. You will develop a skill set that aligns with the demands of the evolving technology sector, as hardware manufacturers increasingly seek figures with a solid understanding of low-precision arithmetic. And over the course of the PhD, you will have many opportunities to build a network of meaningful connections within both industry and academia.</p> <p>Finally, you will acquire a number of transferable skills which will serve you well in a variety of roles, regardless of the career path you decide to choose. For example, you will enhance your ability to understand and solve complex problems, you will develop a research-oriented mindset that will enable you to propose innovative solutions that go beyond traditional approaches, and you will improve your ability to communicate with others efficiently and effectively. You will also learn how to plan a long and complex project, how to keep it on track, and how to manage your time effectively to complete it on time.</p>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>. Please state clearly in the Planned Course of Study section that you are applying for <strong><em>PHD Computing FT</em></strong>, in the research information section, please state clearly that the research project you wish to be considered for is <strong><em>Computer arithmetic for the next generation of integrated circuits</em></strong>, and mention <em><a href="https://eps.leeds.ac.uk/computing/staff/14034/massimiliano-fasi">Massimiliano Fasi</a></em> as your proposed supervisor and in the&nbsp;finance section, please state clearly&nbsp;<em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p style="margin-bottom:11px"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered on an ongoing basis. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of 31 May 2024:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.5 overall with at least 6.5 in writing and at least 6.0 in reading, listening and speaking or equivalent. The test must be dated within two years of the start date of the course in order to be valid.

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>&nbsp;and&nbsp;<a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>&nbsp;are available for UK applicants (will reopen in October 2024 for 2025/26 entry, starting October 2025).&nbsp;&nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a>&nbsp;is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong>&nbsp;&ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China (will reopen in October 2024 for 2025/26 entry, starting October 2025). The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a>&nbsp;is available to graduates of the University of Leeds.</p> <p><strong>Important:&nbsp;</strong>&nbsp;Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are not covered under this studentship.</p> <p>Please refer to the&nbsp;<a href="https://www.ukcisa.org.uk/">UKCISA</a>&nbsp;website for information regarding Fee Status for Non-UK Nationals.</p> <h2>&nbsp;</h2>

<p>For further information about this project, please contact Massimiliano Fasi at <a href="mailto:m.fasi@leeds.ac.uk?subject=%5BPhD%20contact%5D%20Computer%20arithmetic%20for%20the%20next%20generation%20of%20integrated%20circuits">M.Fasi@leeds.ac.uk</a>.</p> <p>For further information about your application, please contact the&nbsp;Postgraduate Research Admissions team at <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a>.</p>