Computer Arithmetic for the Next Generation of Integrated Circuits

The growing importance of artificial intelligence is fostering a paradigm shift in the world of hardware design. On the one hand, the increasing complexity of deep-learning models demands computers faster and more powerful than ever before. On the other hand, 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 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, and two hardware vendors 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 /> On the backdrop of this complex hardware landscape, this PhD project can explore one or more of several directions.<br /> <br /> 1. 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, in particular for operations that involve inputs and outputs in different formats. Currently, this probing must be done manually and on a case by case basis – a process that is long, tedious, and prone to errors. We can streamline this process, to make it more accessible to users without deep floating-point knowledge.<br /> <br /> 2. One can leverage low-precision accelerators for scientific computing by using a number of tricks, known as "mixed-precision" algorithms. Developing such algorithms is far from trivial. We can look at computational kernels that are common in scientific workloads and rewrite them to achieve better performance while delivering high accuracy despite running on low-precision hardware.<br /> <br /> 3. Hardware is designed to cater for specific applications, but this is only effective if the requirements of the application are fully specified. By means of a theoretical and experimental study, we can better understand the specific needs of different applications, and we can use this knowledge to inform the development of tomorrow's hardware. A typical outcome of this line of work is the design of ISA extensions, and a particularly suitable starting point for this is the RISC-V ISA.

<h2>Possible research topics</h2> <p>This is an indicative range of topics you might wish to consider if you are planning to apply for this opportunity. 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>Characterising the numerical behaviour of existing hardware through fully automated testing.</li> <li>Analysing the behaviour of numerical algorithms on different hardware units, with the aim of discovering and understanding unexpected features.</li> <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>Developing high-performance libraries that exploit features of mixed-precision hardware to achieve better performance.</li> <li>Developing new algorithms to solve scientific computing problems in a variety of heterogeneous CPU/GPU/DPU/FPGA environments.</li> <li>Designing alternative arithmetic formats that can better exploit a very low number of bits.</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> </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 & 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 <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <strong><em>PHD Computer Science 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 finance section, please state clearly <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'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.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  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 style="margin-bottom:11px"><strong>Please ensure you provide your supporting documents by the closing date of Friday 3 January 2025: </strong></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 style="margin-bottom:11px">A highly competitive School of Computer Science Studentship providing the award of full academic fees, together with a tax-free maintenance grant at the standard UKRI rate (£19,237 in academic session 2024/25) for 3.5 years. There are no additional allowances for travel, research expenses, conference attendance or any other costs.</p> <p style="margin-bottom:11px">You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p style="margin-bottom:11px">Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p> <p style="margin-bottom:11px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p style="margin-bottom:11px"><strong>Competition Funding</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a> <strong>(closing date: Monday 3 February 2025)</strong> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: Tuesday 1 April 2025)</strong> are available to UK applicants.  <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> – The <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> is available to nationals of China <strong>(closing date: Monday 6 January 2025)</strong>. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not </strong></em>cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<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 Postgraduate Research Admissions team at <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a>.</p>