Leslie G. Valiant

Over a lifetime the brain performs hundreds of thousands of individual cognitive acts of a variety of kinds, including the formation of new associations and other kinds of learning. Each such act depends on past experience, and, in turn, can have long lasting effects on future behavior. It is difficult to reconcile such large scale capabilities quantitatively with the known resource constraints on cortex, such as low connectivity. Here we shall describe an approach to this problem, in terms of concrete functions, representations, and algorithms, that seeks to explain these phenomena in terms that are faithful to the basic quantitative resources available. Until recently an algorithmic understanding of cognition has been regarded as an overambitious goal for experimental neuroscience. As we shall explain, with current experimental techniques this view is no longer justified, and we should expect algorithmic theories to be experimentally testable, and tested.

Download link to the slides of Valiant's lecture

(12:00-12:15) - Andreas Matt of IMAGINARY introduces the "La La Lab - The Mathematics of Music" exhibition running parallel to this year's program.

In mammals, space is mapped by specialized position-coding cell types in entorhinal cortex and hippocampus, including entorhinal grid cells, which are active only when animals are at locations that tile environments in a periodic hexagonal pattern. I will first show how space-coding neurons in the medial entorhinal cortex (MEC) collectively form a low-dimensional representation that persists across behavioral tasks and activity states. This low-dimensionality points to network architecture as a determinant of firing patterns and continuous attractor models have been proposed to account for the dynamics. Current models do not easily account for the representation of the unidirectional flow of experience, however. In the second part of my talk, I will thus ask how entorhinal networks are organized in time. Which trajectories in high-dimensional state space do cell ensembles take during experience? To determine how activity is self-organized in the MEC network, we tested mice in a spontaneous locomotion task under sensory-deprived conditions, when activity is determined primarily by the intrinsic structure of the network. Mice were head-fixed and ran on a spherical cylinder in darkness. Using 2-photon calcium imaging, we monitored the activity of several hundreds of MEC layer-2 neurons. Both linear and non-linear dimensionality reduction techniques were applied to the spike matrix of each individual session. When the cells were sorted according to their contribution to one of the first principal components of a principal components analysis, stereotyped motifs appeared, involving the sequential activation of neurons over epochs of tens of seconds to minutes. Transitions between cells that were close in principal-component space were favored, while transitions between clusters farther apart happened with a lower frequency than chance. Such stereotyped sequence elements may be recruited during encoding of space, and more widely experience, in the entorhinal-hippocampal network. Deficiencies in these mechanisms may be at the core of neurological diseases characterized by early entorhinal cell death, spatial disorientation and memory dysfunction, such as Alzheimer’s disease.

Scientific publishing is facing a number of challenging issues, the increasing demand for open access journals being the most prominent one. Other topics include: The different models of peer review; novel publication models such as „registered reports“; interactive journals; specific aspects of publications in computational sciences (data sets, software platforms, hardware platforms, licenses, etc.); publications and reproducibility; publication of negative results. The panel will address these and potentially other issues, primarily from the perspectives of the two disciplines represented at the HLF.

Gerard Meijer
Director at the Fritz Haber Institute of the Max Planck Society, Berlin

Joseph Konstan
University of Minnesota, Co-Chair of the Publications Board of the Association of Computing Machinery

Julie Williamson
University of Glasgow

Gabriele von Voigt
University of Hannover, Chair of the European e-Infrastructure Reflection Group (e-IRG)
            
Klaus Hulek
University of Hannover, Editor-in-Chief of the „Zentralblatt für Mathematik“

Efim Zelmanov
University of California in San Diego, Fields Medal 1994

This lecture will look back at some of the principles behind the recent successes of deep learning as well as acknowledge current limitations, and finally propose research directions to build on top of this progress and towards human-level AI. Notions of distributed representations, the curse of dimensionality, and compositionality with neural networks will be discussed, along with the fairly recent advances changing neural networks from pattern recognition devices to systems that can process any data structure thanks to attention mechanisms, and that can imagine novel but  plausible configurations of random variables through deep generative networks.  At the same time, analyzing the mistakes made by these systems suggests that the dream of learning a hierarchy of representations which disentangle the underlying high-level concepts (of the kind we communicate with language) is far from achieved. This suggests new research directions for deep learning, in particular from the agent perspective, with grounded language learning, discovering causal variables and causal structure, and the ability to explore in an unsupervised way to understand the world and quickly adapt to changes in it.

Download link to the slides of Bengio's lecture

WS 1: “Mathematics and Climate”
Makrina Agaoglou
Room H13 (New University, Second Floor)

WS 2: “Polymath and the future of collaborations in mathematics”
Đorđe Baralić
Room HS1 (Historical Seminar room 1, on the opposite site of the inner courtyard)

WS 4: “Neural Computing and Deep Learning”
Ramanarayan Mohanty
Room P18 (on the left side of the Triplex Mensa)

WS 5: “Ethics in AI”
Jesmin Jahan Tithi
Room HS4 (Historical Seminar room 4, on the opposite site of the inner courtyard)

WS 6: “Concurrency - Theory and Practice”
Yatin Avdhut Manerkar
Room HS3 (Historical Seminar room 3, on the opposite site of the inner courtyard)

WS 7: “Misinformation and Social Bots”
Onur Varol
Room H12 (New University, Second Floor)

Can we really predict next century’s climate, if we can hardly predict this weekend’s weather? Is the latest flooding or heatwave due to climate change, or not? Why is it so hard to take action on this problem? Climate change is likely the most complex crisis humanity has ever faced. It is a convoluted scientific problem. And it involves complicated social, economical and psychological dynamics. In this Hot Topic Session, we will try to pin down the hard facts on climate change and what scientific questions are still open. In the first part of the session, we will discuss the fundamental laws underlying climate change; how mathematics, data, and computation allow to make predictions; and what are the big open questions in research. In the second part, we will discuss what citizens – and especially scientists – can do to make things change. This includes a range of lessons from psychology, communication, and history, that scholars can use to play an important role.

Chris Budd
“The mathematics of climate change”
Gresham College, director of the Center of Nonlinear Mechanics (University of Bath)

Sonia I. Seneviratne
“The frontiers of climate change research”
ETH Zurich, IPCC co-author, Thomson Reuters list of highly cited scientists

Opha Pauline Dube
“The science of impacts, vulnerabilities, adaptation, and mitigation”
University of Botswana, IPCC lead author, University of Queensland alumna

Timothy Palmer
“Climate change and supercomputation”
Co-director of the Oxford Martin Programme on Modelling and Predicting Climate

Can we really predict next century’s climate, if we can hardly predict this weekend’s weather? Is the latest flooding or heatwave due to climate change, or not? Why is it so hard to take action on this problem? Climate change is likely the most complex crisis humanity has ever faced. It is a convoluted scientific problem. And it involves complicated social, economical and psychological dynamics. In this Hot Topic Session, we will try to pin down the hard facts on climate change and what scientific questions are still open. In the first part of the session, we will discuss the fundamental laws underlying climate change; how mathematics, data, and computation allow to make predictions; and what are the big open questions in research. In the second part, we will discuss what citizens – and especially scientists – can do to make things change. This includes a range of lessons from psychology, communication, and history, that scholars can use to play an important role. 

Paul Edwards
“The history of climate change modelling”
Center for International Security and Cooperation (Stanford University), University of Michigan, author of “A Vast Machine: Computer Models, Climate Data, and the Politics of Global Warming” (MIT Press, 2010)

Manfred Milinski
“The psychology of climate change”
Director of the Max Planck Institute for Evolutionary Biology

Jennifer Marlon
“The perception and communication of climate change”
Yale’s School of Forestry and Environmental Studies and the Yale Program on Climate Change Communication (YPCCC)

Can we trust autonomous systems? This question arises urgently with the perspective of massive use of AI-enabled techniques in autonomous systems, critical systems intended to replace humans in complex organizations.

We propose a framework for tackling this question and bringing reasoned and principled answers. First, we discuss a classification of different types of knowledge according to their truthfulness and generality. We show basic differences and similarities between knowledge produced and managed by humans and computers, respectively. In particular, we discuss how differences in the system development process of knowledge affect its truthfulness.

To determine whether we can trust a system to perform a given task, we study the interplay between two main factors: 1) the degree of trustworthiness achievable by a system performing the task; and 2) the degree of criticality of the task. Simple automated systems can be trusted if their trustworthiness can match the desired degree of criticality. Nonetheless, the acceptance of autonomous systems to perform complex critical tasks will additionally depend on their ability to exhibit symbiotic behavior and allow harmonious collaboration with human operators. We discuss how objective and subjective factors determine the balance in the division of work between autonomous systems and human operators.

We conclude emphasizing that the role of autonomous systems will depend on decisions about when we can trust them and when we cannot. Making these choices wisely, goes hand in hand with compliance with principles promulgated by policy-makers and regulators rooted both in ethical and technical criteria.

The problem of finding the connected components of an undirected graph is one of the most basic in graph algorithms. It can be solved sequentially in linear time using graph search or in almost-linear time using a disjoint-set data structure. The latter solves the incremental version of the problem, in which edges are added singly or in batches on-line.

With the growth of the internet, computing connected components on huge graphs has become important, and both experimentalists and theoreticians have explored the use of concurrency in speeding up the computation. We shall survey recent work. Even simple concurrent algorithms are hard to analyze, as we discuss. This work is joint with Sixue Liu of Princeton.

Download link to the slides of Tarjan's lecture

Karen Uhlenbeck was awarded the Abel Prize 2019 “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Unfortunately, Karen Uhlenbeck is unable to attend the 7th HLF. Therefore, Elena Mäder-Baumdicker, who is a mathematics professor at TU Darmstadt, will give a short introduction and overview of Karen Uhlenbeck’s work.

Boarding: 13:30-14:00

Boat Trip: 14:00-18:00

Laureates: Visit to Local Schools 

YR: Visit to the following local institutions

• BioQuant
• European Molecular Biology Laboratory (EMBL)
• European Media Laboratory (EML)
• German Cancer Research Center (DKFZ)
• Heidelberg Institute for Theoretical Studies (HITS)
• Interdisciplinary Center for Scientific Computing (IWR)
• Mathematics Center of University of Heidelberg and the Mathematics Center Heidelberg (MATCH)
• Max Planck Institute for Astronomy (MPIA)
• NEC
• SAP
• SAS

Almost overnight, the Manhattan Project transformed ethical decision making from a purely moral concern into one that is essential for human survival. Recent technological advances, including genetic engineering, AI, and cyber-technology, reinforce that imperative. This talk explores how to accelerate our ethical progress and thereby increase our odds of not only surviving, but also thriving. It uses several personal lessons that I learned the hard way. In 1976, when confronted with a decision that NSA told me could cause “grave harm to national security,” I thought I made my decision ethically, but later realized I had fooled myself and how easily we all can make that mistake. The talk then explores several other lessons including how to use the evolution of ethical standards over time to accelerate that process.

Download link to the slides of Hellman's lecture

Download links to two additional documents:

Hellman's Federation of American Scientists report on “Rethinking National Security”

Book Dorothie and Martin Hellman wrote in PDF “A New Map for Relationships: Creating True Love at Home & Peace on the Planet"

Deep learning has been applied in many domains and is very effective. Much of the research is on applications and is experimental. This talk will suggest an approach to developing a theory of deep learning that can be taught in university courses.

Download link to the slides of Hopcroft's lecture

The "Training" of "Deep Learning" for "Artificial Intelligence" is a process that minimizes a "Loss Function" f(w) subject to memory constraints that allow the computation of Gradients G(w) := df(w)/dw` but not the Hessian  d2f(w)/dw2 nor estimates of it from many stored pairs {G(w), w}. Therefore the process is iterative using "Gradient Descent" or an accelerated modification of it like "Gradient Descent Plus Momentum". These iterations require choices of one or two scalar "Hyper-Parameters" which cause divergence if chosen badly. Fastest convergence requires choices derived from the Hessian's two attributes, its "Norm" and "Condition Number", that can almost never be known in advance. This retards Training, severely if the Condition Number is big. A new scheme chooses Gradient Descent's Hyper-Parameter, a step-size called "the Learning Rate", automatically without any prior information about the Hessian; and yet that scheme has been observed always to converge ultimately almost as fast as could any acceleration of Gradient Descent with optimally chosen Hyper-Parameters. Alas, a mathematical proof of that scheme's efficacy has not been found yet.

Details, a work in progress continually evolving, are posted on:
https://people.eecs.berkeley.edu/~wkahan/STEPSIZE.pdf

Download link to the slides of Kahan's lecture

Much of the fundamental research in computer science has been driven by the needs of those attempting to utilize computing for various applications, such as health. Dr. Patel will describe a collection of research projects conducted with his clinical collaborators that leverage the sensors on mobile devices (e.g., microphones, cameras, accelerometers, etc) in new ways to enable the screening, self-management and longitudinal study of diseases. These projects follow the theme of finding unique signals and biomarkers in order to enable access and scale by leveraging existing hardware. His remarks will underscore the potential advances in health and clinical science through the convergence of sensing, machine learning, and human-computer interaction.

Download link to the slides of Patel's lecture

Myocites, a class of heart cells, when put into a petri dish will oscillate independently, but after some time, nearby cells will have similar oscillatory behavior. Our goal is to give a mathematical model of synchronization to help understand this phenomenon.
Important work on this subject goes back to Huygens more than 350 years ago (pre-Newton). More recently, Turing (morphogenesis), Winfree, and Strogatz, (a one-time post-doc of my student Nancy Kopell) made contributions to these studies.
Here we focus especially on the work of Kuramoto on the collective behavior of phases. We will give a geometric analysis of Kuramoto's ordinary differential equations. Starting from the graph Laplacian of the cellular architecture of the heart, and a "hard-wiring" hypothesis of the associated genome dynamics, we obtain a phase setting of Kuramoto equations to obtain a "beating in unison" result.

In this talk I will talk about my personal story with an emphasis on mathematical education and research. In particular I will talk about the challenges I faced and the factors that shaped my academic life.

Download link to the slides of Birkar's lecture

In this talk I will discuss some Grand Challenges of AI, successes of the past 30 years, and the unfinished agenda for the 21st century. In 1988, I presented a list of unsolved open Grand Challenge Problems in AI, as part of the Presidential Address of American Association for AI (https://www.aaai.org/ojs/index.php/aimagazine/article/view/950). Since then some of the problems have been solved. The World Champion Chess Machine challenge was settled in 1996 when IBM Deep Blue (developed by Hsu, Anantharaman, Campbell, Hoane et al) defeated the then reigning World Champion of Chess, Boris Kasparov (https://en.wikipedia.org/wiki/Deep_Blue_(chess_computer). The Accident Avoiding Car (Driverless Car) challenge was decided in 2005 when Stanford’s Stanley headed by Sebastian Thrun and CMU’s Sandstorm headed by Red Whittaker were among the five cars to successfully complete the challenge (https://en.wikipedia.org/wiki/DARPA_Grand_Challenge_(2005). The Challenge to demonstrate Understanding of Science Textbooks by taking an Exam was successfully demonstrated recently in 2019. https://www.wired.com/2016/02/the-best-ai-still-flunks-8th-grade-science/ and http://bit.ly/aristo90. Starting from a failing performance in 2016, Peter Clark, Oren Etzioni and team at Allen Institute for AI developed a system that answered over 90% of the questions correctly in the NY Regents Science Exams.

The Unfinished Agenda for 21st Century includes: Discovery of a Major Mathematical Result by AI; Summarization of Media (Books, Talks, Music and Movies); Remote Repair in Space; Encyclopedia on Demand; Provide Right Information to the Right People at the Right Time in the Right Language; Self-Reproducing Robots; and AI that can See, Hear, Talk and Walk as well as a Human. Each of the above seemingly reasonable problems would require significant breakthroughs and fundamental advances in AI and all other subfields of Computer Science and Technology.

Download link to the slides of Reddy's lecture

Mathematical and natural sciences have long and honorable traditions of participation by highly creative women contributors. However, the percentages of women scientists remain shockingly low and there is a significant gender gap at all levels between women and men. Barriers to achievement by women persist, especially in developing countries.
The international and interedisciplinary project “A Global Approach to the Gender Gap in Mathematical, Computing, and Natural Sciences: How to Measure It, How to Reduce It?”(2017-2019) is producing sound data to support the analysis of the gender gap and the choices of interventions that ICS  and its member unions can feasibly undertake.
Moreover, the project aims to provide easy access to materials proven to be useful in encouraging girls and young women to study and pursue education in mathematics and natural sciences.
The panel will discuss the various aspects of the gender gap, the progress of the project and the agenda for the near future.

Ragni Piene
University of Oslo

Marie-Francoise Roy
Institut de recherche mathématique de Rennes, Chair of the Executive Committee oft he Gender Gap Project

Margo Seltzer
University of British Columbia

Jessica Carter
University of Southern Denmark

Anna Wienhard (via Skype)
Heidelberg University

Anna Vasilchenko
Young researcher, Newcastle University

Fernando Seabra Chirigati
Young researcher, New York University

Over two thirds of the funds that Germany invests in research and development are covered by industry. It’s no wonder as the combination of business knowledge with fundamental and industrial research is a competitive advantage in a rapidly changing economy where innovation is a necessity. In addition, it is a win-win situation. Research focused professionals can benefit from relevant research topics that translates directly into commercial outcomes. Business on the other hand gets the most up to date knowledge from the academic community and wins over highly skilled professionals. In this session, we will discuss different scenarios on how to build a bridge between research and industry innovation and how researchers can find new opportunities in the business world.

In this scientific interaction, participants will get an overview of career paths in the academic as well as in the corporate environment. In the plenary session, the speakers introduce themselves and give a brief insight into what is being exchanged with the participants in the three parallel sessions.

2:00 p.m.        Plenary:

Christine Regitz
SAP

Jana Koehler
German Research Center for Artificial Intelligence

Efim Zelmanov
Fields Medal 1994

Moderated by: Peter Mirski
Management Center Innsbruck

2:30 p.m.        Sessions – Different perspectives

Table 1: “Career Paths in Business“
Christine Regitz
Moderated by: Dietmar Kilian (Management Center Innsbruck)

Table 2: “Career Paths in Academia“
Jana Koehler
Moderated by: Peter Mirski

Table 3: “Career Paths in Academia“
Efim Zelmanov
Moderated by: Helge Holden (Norwegian University of Science and Technology)