This week, I attended my first Asilomar Conference on Circuits, Signals and Computers, a very long-running conference series of the IEEE Signal Processing Society, with a very broad range of topics. I decided to attend Asilomar after being invited to give not just one talk, but two, once by my friend and collaborator Miloš Ercegovac from UCLA, and once by my good colleague Zhiru Zhang from Cornell.

No discussion of highlights of Asilomar can go without pointing out the extraordinarily beautiful setting of a conference centre right on Asilomar Beach. I can certainly see why the conference organisers keep coming back year after year – since the 1970s for Miloš and even earlier for my old friend fred harris, who I met there by surprise.

 

Distinguished Lecture

The conference opened with distinguished lecture by Helmut Bölcskei from ETH Zurich, who gave a wonderful talk about the fundamental limits of deep learning. The key results he presented were about neural networks built of linear computational units and ReLU functions, and he showed how they can approximate a range of different functions. I was already familiar with asymptotic results for infinite depth or infinite width networks, but Bölcskei’s results were different – they showed how the approximation quality can be traded against a metric of neural network complexity that captured the number of bits needed to store the topology and the weights of the network. He was able to show the power of such neural networks across an extremely broad class of functions, and to explain how this comes about.

Compilation for Spatial Computing Architectures

This session was organised by Zhiru Zhang from Cornell and Hongbo Rong from Intel. The first talk, given by Yi-Hsiang Lai from Cornell, described the HeteroCL infrastructure, about which I’ve previously blogged in my description of FPGA 2019. Very closely related to this was Hongbo’s own work at Intel Labs, which makes heavy use of polyhedral methods, and work from the systolic array community on affine and uniform recurrence equations.

I then gave a talk about some of the work my research group has been doing over the past 12+ years in analysis of memory access patterns for High-Level Synthesis, taking in my early foundational work in bringing the polyhedral model to HLS with Qiang Liu (now at Tianjin University), our work on Separation Logic in HLS (now also a book by Felix Winterstein, my former PhD student who leads Xelera Technologies), and our recent work on utilising Microsoft Boogie in this context for multi-threaded HLS by my current PhD student Jianyi Cheng.

Finally, Thierry Moreau from the University of Washington presented his very interesting work on a hardware-software open-source stack for modern deep learning (see the TVM website).

Computer Arithmetic

This session was organised by Miloš Ercegovac from UCLA and Earl Swartzlander from UT Austin. The first talk in this session was from Fredrik Dahlqvist, a postdoc in my group, who spoke about our work together with Rocco Salvia marrying ideas from probabilistic programming with rounding error analysis.

Miloš Ercegovac from UCLA and James Stine from Oklahoma State University looked at how digit iteration techniques for division compare to multiplication-based techniques. Alexander Groszewski and Earl Swartzlander from UT Austin discussed their results from deterministic unary arithmetic inspired by stochastic computing; Keshab Parhi from the audience raised the interesting point of the importance of preservation of temporal structure in specially designed deterministic sequences for purposes of compositionality.

I really enjoyed the unusual talk by Keshab Parhi (U. Minnesota) on Molecular Computing Inspired by Stochastic Logic (see here for more details) via Fractional Coding, building on Soloveichik, Seelig and Winfree. If digits are encoded as relative concentrations of molecules, the problem of signal correlation, which tends to take the shine off stochastic computing work, can be avoided. He proposed computation using molecular reaction rates, and showed how to encode values as concentrations of two different molecules; his techniques have been verified in simulation – I would love to see this in a test-tube.

Theory of Deep Learning

This session was organised by Richard Baraniuk and Santiago Segarra (Rice University.)

There was a very enjoyable talk by Alessandro Achille from UCLA on studying deep neural networks from an information-theoretic perspective. He pointed out that real-valued weights appear to contain infinite information, but that by using the principle that small perturbations in weights should not throw-off the classification result completely, we can recover a finite weight encoding. He then moved on to show using a PAC-Bayes bound that good generalisation comes from low weight information. He demonstrated that Stochastic Gradient Descent implicitly minimises Fisher information, but that for generalisation performance, it is Shannon information that should be bounded – he then derived a connection between the two under some conditions.

Tom Goldstein (University of Maryland) gave a stunningly illustrated talk on Understanding Generalization in Neural Nets via Visualization, based on his co-authored paper on the topic. He sought to empirically understand how the continuous piecewise linear functions of modern DNNs, when combined with SGD-based optimisation, lead to functions that generalise well. This was done via a clever process of “poisoning” training data to obtain badly generalising minima.

AI/ML Architectures

This session was organised by Keshab Parhi (University of Minnesota.)

Danny Bankman gave a talk about Stanford’s RRAM-based DNNs. He showed that register-file access accounts for the majority of energy in standard CMOS processor-like architectures, and drew the conclusion that architectures should be “memory-like” in their design, using “conductance-mode arithmetic” with very low precision integer activations, and put the necessary ramp generator for their ADC right inside the RRAM array. Results are verified using SPICE. I know little about RRAM technology, but talking with my colleagues Themis Prodromakis and Tony Kenyon has got me intrigued.

Deep Learning Theory

This session was organised by Tom Goldstein (University of Maryland.)

My favourite talk in this session was by Tom himself, in which he presented an analysis of adversarial attacks in DNNs, again beautifully illustrated – based on his co-authored paper. He showed that due to the high dimensionality of the spaces involved, you are extremely likely to hit – at random – a point in the input space that can be adversarially perturbed. He demonstrated – using the audience as guinea pigs – that adversarial perturbation can also trick humans quite easily on the CIFAR-10 data set. Perhaps my favourite twist on the talk was that he gave the talk wearing an “invisibility cloak” which – if worn – tricks YOLO into not identifying the wearer.

Reflections on Asilomar

I’ve sent PhD students to Asilomar before, but this was the first time I attended myself. It’s a very broad conference, in a beautiful setting. It seems to be a great venue to complement the more technically homogeneous conferences like FPGA which I help to organise – they serve different purposes. Asilomar is a great conference to have your work seen by people who wouldn’t usually follow your work, and to pick up ideas from neighbouring fields.

I was kindly invited to speak at a Royal Society Discussion Meeting before Easter, entitled “Numerical Algorithms for High-Performance Computational Science”, organised by Nick Higham, Laura Grigori and Jack Dongarra. This blog post summarises some of the discussion at the meeting.

I very much enjoyed the format of the meeting: select interesting speakers and allow them 30 minutes to talk about a topic of their choosing related to the theme of the meeting, with 10 full minutes for discussion and in-depth questions after each talk. Posters were also presented by a wide variety of researchers, with each poster presenter given a one-minute lightning-talk slot. Two of my PhD students, Erwei Wang and He Li, took this opportunity. Erwei presented a preview of our LUTNet paper appearing at FCCM very soon (separate blog post to follow), while He presented some of our work on arbitrary precision iterative compute.

 

Talks by others included:

• David Keyes (KAUST) on the topic “Hierarchical algorithms on hierarchical architectures”. He discussed some very interesting hierarchical low-rank decompositions and also hierarchies of numerical precision.
• Kathy Yelick (Berkeley) spoke on “Antisocial parallelism: avoiding, hiding and managing communication”, a very fruitful area of research in recent years. A few years ago, Abid Rafique, one of my former PhD students (joint with Nachiket Kapre) made use of this work, and it was good to catch up with the current state of research.
• Anna Scaife (Manchester) gave a fascinating insight into the Square Kilometre Array. The sheer volumes of data are mind boggling (zettabytes annually) and pose unique algorithmic challenges.
• Michela Taufer (UTK) discussed molecular dynamics workflows, and how we may be able to harness machine learning to reduce the human bottlenecks in such workflows in the future.
• Rick Stevens (Argonne) gave a very engaging talk about the intersection of machine learning with computational science, exemplified by the Candle project, using deep learning in cancer research. He mentioned many of the emerging architectures for deep learning and their optimisation for low-precision compute. Interested readers may also like our recent survey article on the topic.
• Jack Poulson (Hodge Star) spoke about sampling Determinantal Point Processes, and how links to matrix decomposition algorithms can be used to radically accelerate this process.
• John Shalf (LBNL) spoke about alternative computational models beyond CMOS, new materials for switches, and the growth of hardware specialisation. He proposed the strategy of: hardware-driven algorithm design, algorithm-driven hardware design, and co-design of hardware and algorithm. Having worked in the FPGA community for decades where this has been our mantra, it is great to see hardware specialisation spreading the message of co-design into the HPC community.
• Doug Kothe (ORNL) provided a very interesting insight into exascale computational motifs at the DOE.
• Tony Hey (STFC) set out a compelling argument that academics in applied deep learning should focus on deep learning for scientific data, on the basis that (i) scientific data sets are huge and open and (ii) head-to-head competition with industrial giants on profit-oriented deep-learning applications, without access to their data sets, is a poor choice for academia. I think the same argument could be made for academic computer architecture too. His team are developing benchmarks for scientific machine learning, complementary to MLPerf.
• Erin Carson (Charles University) presented an enchanting talk on iterative linear algebra in low and multiple precision compute. I’m a fan of her earlier work with Nick, and it was great to hear her current thinking and discussion of least-squares iterative refinement.
• Steve Furber (Manchester) spoke about arithmetic in the context of the SpiNNaker machine, and a particular approach they have taken to numerical solution of neural ODEs in fixed-point arithmetic, demonstrating that stochastic rounding can radically improve the quality of their results.
• Tim Palmer (Oxford) argued for low precision compute in weather and climate models, allowing the recouped computational cost to be recycled into better resolution weather models, resulting in higher overall accuracy. This reminded me of the argument I made with my PhD student Antonio Roldão Lopes and collaborator Eric Kerrigan in our paper More FLOPS or More Precision?
• Guillaume Aupy (INRIA) discussed memory-efficient approaches for automatic differentiation and back-propagation.
• Satoshi Matsuoka (RIKEN Centre) took us through the work being done on Post-K, a new Japanese supercomputer being designed to provide compute infrastructure for future workloads at the intersection of big data and AI/ML.
• Mike Heroux (Sandia) spoke about his work developing programming infrastructure for future HPC, in particular for performance portability and for system reliability.

My own talk was entitled “Rethinking Deep Learning: Architectures and Algorithms” – I will save summarising the content for a future blog post. Slides for all these talks will appear on the Manchester Numerical Linear Algebra group website. In addition, each speaker has received an invitation to author an article for a special issue of Philosophical Transactions A – this should be a very interesting read.

I was impressed by the great attendance at the meeting and by the quality of the technical interaction; I met several new and interesting people at the intersection of numerical analysis and scientific computing.

Special thanks to the organisers, Nick, Laura, and Jack for putting an excellent programme together. And congratulations to Jack for the news – a few days after the meeting – of his election to Foreign Member of the Royal Society!

This week, I attended the Design, Automation & Test in Europe (DATE) conference in Florence, Italy. DATE is a large conference, which I have attended irregularly since I was a PhD student. This year, the general chair was a long-standing colleague from the FPGA community, Jürgen Teich.

Readers can find a summary of some of the talks I found most interesting below.

On Tuesday, my colleague Martin Trefzer chaired a session on Computational and Resource-efficiency in Quantum and Approximate Computing. The work by Sekanina was  interesting, using information on data distribution to drive the construction of approximate circuits. Circuits are constructed from the baseline using a technique called Cartesian Genetic Programming. I have recently been collaborating with Ilaria Scarabottolo and others from Laura Pozzi‘s group on a related problem – see our DAC 2019 paper (to appear) for details – so this was of particular interest.

On Wednesday, I chaired a session When Approximation Meets Dependability, together with my colleague Rishad Shafik. Ioannis Tsiokanos from Queen’s University Belfast presented an interesting approach that dynamically truncates precision in order to avoid timing violations. This is interestingly complementary to the approach I developed with my former PhD student Kan Shi where we first simply allowed timing violations [FCCM 2013], and secondly redesigned data representation based on Ercegovac‘s online arithmetic, so that timing violations caused low-magnitude error [DAC 2014].

David Pellerin from Amazon gave an interesting keynote address which very heavily emphasised Amazon’s F1 FPGA offering, which was – of course – music to my ears.

On Thursday morning, I attended the session Architectures for Emerging Machine Learning Techniques. Interestingly, there was a paper there making use of Gustafson’s posits within hardware-accelerated deep learning, a technique they dub Deep Positron.

The highlight talk for me was Ed Lee‘s Thursday keynote, A Fundamental Look at Models and Intelligence. Although I’ve been aware of Lee’s work, especially on Ptolemy, since I did my own PhD, I don’t think I’ve ever had the pleasure of hearing him lecture before. It was insightful and entertaining. A central theme of the talk was that models mean two different things for scientists and engineers: a scientist builds a model to correspond closely to a ‘thing’; an engineer builds a ‘thing’ to correspond closely to a model. He used dichotomy to illuminate some of the differences we see between neuroscience-inspired artificial intelligence and the kind of AI we see as very popular at the moment, such as deep learning. Lee’s general-readership book Plato and the Nerd – which has been on my “to read” list since my colleague and friend Steve Neuendorffer mentioned it to me a few years ago – has just climbed several notches up that list!

On Thursday afternoon, I attended the session on The Art of Synthesizing Logic. My favourite talk in this session was from Heinz Reiner, who presented a collaboration between EPFL and UC Berkeley on Boolean rewriting for logic synthesis, in which exact synthesis methods are used to replace circuit cuts, rather than resorting to a pre-computed database of optimal function implementations. During the talk, Reiner also pointed the audience to an impressive-looking GitHub repo, featuring what looks like some very useful tools.

Friday is always workshop day at DATE, featuring a number of satellite workshops.  I attended the workshop entitled Quo Vadis, Logic Synthesis?, organised by Tiziano Villa and Luca Carloni. This was a one-off workshop in celebration of the 35th anniversary of the publication of the influential Espresso book on two-level logic minimisation.

Villa talked the audience through the history of logic synthesis, starting with the Quine-McCluskey method.

My favourite talk in this workshop was from Jordi Cortadella, who spoke about a method for synthesising Boolean relations. This is the problem of synthesising a the cheapest implementation of a function , which one is free to choose from amongst the given relation , i.e. viewing as a relation , one is free to chose – and its implementation – subject to the requirement that for some given relation (not necessarily a function). This is a strict generalisation of the well-known problem of Boolean ‘don’t care’ conditions, a.k.a. incompletely specified functions. Cortadella presented a method leveraging the known approaches to this latter problem, by exploring the semi-lattice of relations between these sets generated by in a structured way, using a form of branch-and-bound.

Soeken also presented a very interesting summary of three uses of SAT within logic synthesis, namely Schmitt’s ASP-DAC paper on SAT-based LUT mapping, Eén’s paper on using logic synthesis for efficient SAT (rather than SAT for efficient logic synthesis) and Haaswijk‘s recent PhD on making exact logic synthesis more scalable by providing partial topological information – a topic that interestingly has some echoes in work I’m soon to present at the Royal Society.

The workshop was an enjoyable way to end DATE, and I was disappointed to have to leave half-way through – there may well have been other interesting talks presented in the afternoon.

Over the second half of this week, I’ve been attending the SIAM Computational Science and Engineering conference in Spokane, Washington – a short flight north (and a radical change in weather) from my earlier conference in California this week.

This was my first SIAM conference. I was kindly invited to speak on the topic of floating-point error analysis by Pierre Blanchard, Nick Higham and Theo Mary. I very much enjoyed the sessions they organised and indeed the CSE conference, which I hope to be able to attend more regularly from now on.

My own talk was entitled Approximate Arithmetic – A Hardware perspective. I spoke about the rise of architecture specialisation as driving the need for closer collaboration between computer architects and numerical analysts, about some of our work on automatic error bounds Boland and Constantinides (2011) and Magron, Constantinides and Donaldson (2017), on code refactoring Gao and Constantinides (2015), as well as some of our most recent work on machine learning (I will blog separately about this latter topic over the next couple of months.)

The CSE conference is very large – with 30-40 small parallel sessions happening at any given moment – so I cannot begin to summarise the conference. However, I include some notes below on other talks I found particularly interesting.

Plenary Sessions

I very much enjoyed the plenary presentation by Rachel Ward on Stochastic Gradient Descent (SGD) in Theory and Practice. She introduced the SGD method very nicely, and looked at various assumptions for convergence. She took a particularly illuminating approach, by looking at applying SGD to the simple special case of solving a system of linear equations by minimising in the case where . She showed that if the system is under-determined, then SGD converges to the solution of minimum 2-norm, and therefore has an inherent regularising effect. I was surprised by some of the results on overparameterised neural networks, showing that SGD finds global minimisers and that there really doesn’t tend to be much overfitting despite the huge number of parameters, pointing to the implicit regularisation caused by the SGD algorithm itself. I learnt a lot from this talk, and have several papers on my “to read” list as a result, in particular:

• Needell, Srebro and Ward (2013) on convergence of SGD
• Soudry, Carmon (2016) and Du, Zhai, Poczos, Singh (2019) on the absence of poor local minima

There was also an interesting plenary from Anima Anandkumar on the role of tensors in machine learning. The mathematical structure of tensors and multi-linear algebra are topics I’ve not explored before – mainly because I’ve not seen the need to spend time on them. Anandkumar certainly provided me with motivation to do that!

Floating-Point Error Analysis

Theo Mary from the University of Manchester gave a very good presentation of his work with Nick Higham on probabilistic rounding error analysis, treating numerical roundoff errors as zero-mean independent random variables of arbitrary distribution, making use of Hoeffding’s inequality to a produce a backward error analysis. Their work is described in more detail on their own blog post and – in more depth – in their their very interesting paper. It’s a really exciting and useful direction, I think, given the greater emphasis on average-case performance from modern applications, together with both very large data sets and very low precision computation, the combination of which renders many worst-case analyses meaningless. In a similar vein, Ilse Ipsen also presented a very interesting approach: a forward error analysis, more specialised in that she only looked at inner products, but also without the assumption of independence, making use of Azuma’s inequality. The paper on this topic has not yet been finished, but I certainly look forward to reading it in due course!

Reducing Communication Costs

There were a number of interesting talks on mitigating communication costs. Lawrence Livermore National Labs presented several papers relating to the ZFP format they’ve recently proposed for (lossily) compressed floating-point vectors, at a mini-symposium organised by Alyson Fox, Jeffrey Hittinger, and James Diffenderfer. Diffenderfer’s talk developed a bound on the norm-wise relative error of vectors reconstructed from ZFP; Alyson Fox’s talk then extended this to the setting of iterative methods, noting as future work their interest in probabilistic analyses. In the same session, Nick Higham gave a crystal clear and well-motivated talk on his recent work with Srikara Pranesh and Mawussi Zunon – slides and paper are available. This work extends the applicability of Nick’s earlier work with Erin Carson to cases that would have over- or under-flowed, or led to subnormal numbers, without the scaling technique developed and analysed here. They use matrix equilibration – this reminded me of some work I did with my former PhD student Juan Jerez and colleague Eric Kerrigan, but in our case for a different algorithm kernel and targeting fixed-point arithmetic, where making use of the full dynamic range is particularly important. The Higham, Pranesh and Zunon results are both interesting and practically very useful.

In a different session, Hartwig Anzt spoke about the work he and others have been doing to explicitly decouple storage precision from compute precision in sparse linear algebra. The idea is simple but effective: take the high-order bits of the mantissa (and the sign / exponent) and store them in one chunk of data and – separately – store the low-order bits in another chunk. Perform all arithmetic in high precision (because it’s not the computation that’s the bottleneck), but convert low-precision stored data to high precision on the fly at data load (e.g. by packing low-order bits with zeros.) Then, at run-time, decide whether to load the full-precision data or only the low-precision data, based on current estimates of convergence. This approach could also make a good case study application for the run-time adaptation methodology we developed with U. Southampton in the PRiME project.

A Reflection

Beyond the technical talks, there were two things that stood out for me since I’m new to the conference. Firstly, there were many more women than in the typical engineering conferences I attend. I don’t know whether the statistics on maths versus engineering are in line with this observation, but clearly maths is doing something right from which we could learn. Secondly, there were clear sessions devoted to community building: mentoring sessions, tutorials for new research students, SIAM student chapter presentations, early career panels, presentations on funding programmes, diversity and inclusion sessions, a session on helping people improve their CV, an explicit careers fair, etc. Partly this may simply reflect the size of the conference, but even so, this seems to be something SIAM does particularly well.