Cynthia is well known, among other things, for her work on non-malleability (about which she spoke in the historical papers seminar series) and for her work on differential privacy.

The interview is about concerns about *fairness*, and you can read about the concept of fairness through awareness here.

The Computing Community Consortium, which has been recently very active in promoting the emerging research interface between Computation and Brain Science, see cra.org/ccc/events/brain-workshop, generously agreed to fund this CS component of the summer course.

We advertised the course to CS departments, and from a field of about a dozen applications we selected four CS graduate students, who ended up attending the course: Chihua Ma (UI Chicago), Yunjie Liu (UC Davis and Lawrence Berkeley Labs), Yu Liu (UC Davis), and Antonio Moretti (Columbia). Below are their contributions about highlights of the summer course.

**Chihua Ma:**

I am a computer science PhD student in the electronic visualization lab at University of Illinois at Chicago. My research interests mainly focus on data visualization and human computer interaction. I am currently collaborating with neuroscientists to work on the visualization of dynamic mouse brain networks. Therefore, I am interested in knowing more about the neuroscience data and methods of analyzing the data. I learnt a lot from the neuroscience summer school in Berkeley. From my point of view, I was most impressed by the evening talk given by Prof. Jack Gallant and the lectures taught by Prof. Sonja Gruen.

Prof. Gallant gave a talk on modeling fMRI data to discover how the brain represents information about the world, as well as about its own mental states. We know that each cortical area represents information implicit in the input. Neuroscientists should identify cortical areas of interest first, and then determine what specific information is mapped across each area. Prof. Gallant indicated the biggest challenge to understand brain computation is not finding a more effective encoding model, or apply more powerful computations, but data measurement — and that is something that I hadn’t realized before. Once the data are collected, they use some statistical tools and machine learning approaches to fit computational models to the brain data. Prof. Gallant showed us his amazing results, including his technique for re-constructing the images seen by an animal. In addition, they also developed a web-based interactive visualization called brain viewer. I am quite interested in this visualization since it is relevant to my current visualization project that combines spatial and non-spatial structures. After his talk, Prof. Gallant told me he thought visualization would be a very important field in the future of Neuroscience.

Prof. Gruen lectured about correlation analysis of parallel spike trains. From her class, I had a general idea why analysis of parallel spike trains is important, and learnt some basic concepts about spike train statistics, pairwise comparison of spike trains, and multiple-neuro spike patterns. Now, I understand that neuroscientists need to collect and analyze the activity of multiple neurons simultaneously to understand how concerted activity of ensembles of neurons is related to behavior and cognition. I was especially impressed by a representation of intersection matrix designed by her team to visualize the detected spatio-temporal patterns. I had a discussion with Prof. Gruen after class about how important computer science is in studying parallel spike trains. She pointed out that identifying spatio-temporal patterns is very hard since what to search for finding such a pattern, and where to search for it, are both far from obvious. Prof. Gruen thought this is a great challenge for both neuroscientists and computer scientists, and she hopes computer scientists will help in addressing it.

**Yunjie Liu:**

Intelligence is a computational problem as Jeff Hawkins said in his book “On Intelligence”. Neuroscientists are interested in experimenting and collecting data from areas of the brain analyzing individual neuron spiking, hoping that neuron behavior can guide us on how neuron circuit and the entire brain works. Despite many fruitful explorations of single and multiple neuron spike train analysis, linear/non-linear transformation functions of neuron as well as mountains of accessible neural science data nowadays, there is few productive theories of how brain function as a whole. Of course, brain is made of a network of neurons, but what makes a network of neurons brain-like? ‘Neurons that fire together wire together,’ is Hebb’s maxim. Perhaps capturing and modeling the behavior of a population of neurons could be the first step towards theories of whole brain function. The brain has roughly 85 billions of neurons, the connectivity between which are as complex as one could imagine. The dynamics of information propagation between them are quite a mystery — almost magic — and so is the spatial and temporal scales of neuron interconnections.

The Earth climate is another complicated system that scientists are still working hard to understand. But nowadays, researchers are relying more and more on climate modeling for understanding the complex feedback mechanism between individual components and behaviors of the whole system. One cannot perturb the real word climate system in order to test hypotheses, but it is comparatively easy and quick in climate modeling. Would a conceptual neuron circuit model be a helpful tool to understand how the brain works?

Prof. Shea-Brown’s lectures on population coding and neural circuit model were quite interesting to me. In the population coding model that he talked about, one of the key factors are the correlation between neurons, how and on what scale do they correlate. Such correlations are mostly stimulus driven: firing patterns and correlation variations depend on the dynamics of stimulus. But where do neurons group together and when do they react together and how strong their dependencies? From the information propagation perspective, the activation of downstream neuron depends on the correlation of upstream neurons, where low correlation usually cancels the fluctuation, which inhibits downstream neuron, but high correlation act as opposite. On the scale of entire network, the neurons are highly non-randomly connected, but rather can be thinking of as a stack of numerous small motifs (small connected units). This regular stacking pattern makes the whole network connections predictable. However, one should pay attention that connection is not the whole story, while connection strength also plays an important role of correlation between neurons and propagation of signal to downstream neuron. The connection and connection strength can change over response time to dynamic stimulus, which makes the neuron network even more magic. But what reasonable theory can model this or do we even understand what’s going on from experiments data? A computational model of neuron circuits definitely would help us, in my opinion, understanding the complexity of the network, which would, hopefully, stimulate a series of theories on how brain computes.

If asked what is the most import challenge in neural science now, I would vote for the need of a neuron circuit models that are able to reasonably capture the connectivity, correlation among a population of neurons! If evolution is an optimization process, the brain must be a very fine tuned model, and the model must start from somewhere simple.

**Yu Liu:**

I am currently a last year Ph.D. candidate at the Networks Lab, Department of Computer Science, UC Davis. I was motivated to learn the key techniques and methods used in modern brain science and neural networks, and apply them in my field for designing our next generation wireless networks. I am very happy with what i got out of this summer program and here is what impressed me most in the lecture of “Image statistics” given by Professor Odelia Schwartz.

Sensory systems aim to form an efficient code by reducing the redundancies and statistical dependencies of the input. Starting with this argument, Dr. Schwartz started by discussing the problem of fitting a receptive field model to experimental data. When estimating a statistical model, one needs to go back and check that model estimates match statistical assumptions. She first discussed bottom-up scene statistics, efficient coding scheme and relation of linear transforms to visual filters. One could do PCA on visual scene data, but ICA (independent component analysis) gives much better sparse representations, where the components resemble features detected by neurons of the retina. She showed us how Information Theory informs the study of visual images. Then she discussed generative models, which are applied largely to understand more complex visual representations, contextual effects, and she address nonlinearities such as complex cells and divisive normalization in a richer way. It is quite impressive how Dr. Schwartz uses a broad range of tools to study sensory systems at the neural level and ultimately understand visual perception.

**Antonio Moretti:**

]]>I’m a first year PhD student in the Computer Science department at Columbia University, interested in Machine Learning. I’m also affiliated with the Neural Engineering lab at the City College of New York (CCNY). As someone without much neuroscience background, my time at the Redwood Center at Berkeley was a good introduction to some of the challenges of analyzing spike trains and techniques used to study how neurons represent information. I appreciated how both presenters and students drew on expertise from many different disciplines.

I think of the quote (by Dijkstra?) that ‘computer science has no more to do with computers than astronomy has to do with telescopes or surgery has to do with knives.’ My time at the Redwood Center has given me a deeper appreciation for neuroscience as a field that both drives and is driven by the study of computation, and which naturally has many parallels with other disciplines. I was particularly excited by Professor Jose Carmena’s talk on neuroprosthetics and sensorimotor learning. This is one of the coolest and most substantive applications of statistical machine learning and something I hope to explore in depth during my time as a graduate student.

Coincidentally, Don Knuth has just posted online a draft of Section 7.2.2.2 of The Art of Computer Programming, which will be part of Volume 4B.

Chapter 7 deals with combinatorial searching; Section 7.2, titled “Generating all possibilities” is about enumeration and exhaustive search; Subsection 7.2.2 is about basic backtracking algorithms; and Sub-subsection 7.2.2.2 is about SAT.

Even people who are familiar with Don’s famously comprehensive approach to exposition might be surprised to see that this sub-subsection runs to 317 pages, 106 of which are devoted to solutions of exercises. Unfortunately, there was no space to provide the solution to Exercise 516.

]]>A bunch of us hapless cryptographers got the following boilerplate comment from the FOCS’15 PC:

Overall, submissions related to multi-linear maps and indistinguishability obfuscation were held to a somewhat higher standard. The PC expressed some concern with the recent flurry of activities pertaining to multi-linear maps and indistinguishability obfuscation, given how little we understand and can say and *prove* about the underlying hardness assumptions.

This comment was clearly written with the best of intentions, to explain views expressed at the PC deliberations. And I’m thankful to it – mainly since it made the underlying misconceptions so explicit that it mandated a response. So, after discussing and commiserating with colleagues here at Simons, and after amusing ourselves with some analogues of above statement (e.g., “results on NP completeness are held to a higher standard given how little we understand and can say and *prove* about the hardness solving SAT in polynomial time”), I decided to try to write an – obviously subjective – account for the recent developments in multilinear maps and indistinguishability obfuscation (IO) and why this exciting research should be embraced and highlighted rather than “held to a somewhat higher standard” — in spite of how little we understand about the underlying assumptions. The account is aimed at the general CS-theorist.

Let me start by giving rough definitions of the concepts involved. An Indistinguishability Obfuscator (IO) is a randomized algorithm O that takes as input a circuit C and outputs a (distribution over) circuits O(C) with the properties that:

- C and O(C) have the same functionality,
- O(C) is only polynomially larger than C,
- for any two same-size, functionally equivalent circuits C and C’ we have that O(C) ~ O(C’) (i.e., the distributions over strings representing O(C) and O(C’) are computationally indistinguishable).

IO has been proposed as a notion of obfuscation in 2000 (Hada, Barak-Goldreich-Impagliazzo-Sahai-Vadhan-Yang). Indeed, it is arguably a clean and appealing notion – in some sense the natural extension of semantic security of standard encryption to “functionality-preserving encryption of programs”. However, it has been largely viewed as too weak to be of real applicability or interest. (There were also no candidate polytime IO schemes, but this in my eyes is a secondary point, see below.)

Things changed dramatically in 2013 when Sahai and Waters demonstrated how IO schemes can be ingeniously combined with other rather “mundane” cryptographic constructs to do some amazing things. Since then dozens of papers came about that extend the SW techniques and apply them to obtain even more amazing things – that by now have transcended crypto and spilled over to other areas. (e.g.: deniable encryption, succinct delegation, succinct multi-party computation with hardly any interaction, one message succinct witness hiding and witness indistinguishable proofs, hash functions with random-oracle-like properties, hardness results for PPAD, and many more). In fact, think about a result in your area that assumes that some computation is done inside a black box – most probably IO can replace that assumption in one way or another…

Still, my (subjective but distinct) feeling is that we are far from understanding the limits and full power of IO. Furthermore, the study of IO has brought with it a whole new toolbox of techniques that are intriguing in their own right, and teach us about the power and limitations of working with “encrypted computations”.

So far I have not mentioned any candidate constructions of IO – and indeed the above study is arguably valuable as a pure study of this amazing concept, even without any candidate constructions. (Paraphrasing Levin on quantum computers, one can take the viewpoint that the above is the study of impossibility results for IO…)

However, unlike quantum computers, here we also have candidate constructions. This is where multilinear maps come to play.

Multi-linear maps are this cool new technical tool (or set of tools) that was recently put forth. (The general concept was proposed by Boneh and Silverberg around 2000, and the first candidate construction of one of the current variants was presented in 2012 by Garg, Gentry and Halevi.) Essentially, a multilinear map scheme is a fully homomorphic encryption scheme where the public key provides, in addition to the ability to encrypt elements and perform homomorphic operations on ciphertexts, also the ability to partially decrypt ciphertexts under certain restrictions. There are many incomparable variants of this general paradigm, which differ both in the functionality provided and in the security guarantees. Indeed, variants appear to be closely tied to candidate constructions. Furthermore, our understanding of what’s possible here has been evolving considerably, with multiple new constructions, attacks, and fixes reported.

Still, the number and variety of applications of multi-linear maps makes it clear that this “family of primitives” is extremely powerful and well worth studying – both at the level of candidate constructions, at the level of finding the “right” computational abstractions, and at the level of applications. In a sense, we are here back to the 70’s: we are faced with this new set of algebraic and number theoretic tools, and are struggling to find good ways to use them and abstract them.

Indeed, some of the most powerful applications of multilinear maps are candidate constructions of IO schemes. The first such candidate construction (by Garg, Gentry, Halevi, Raykova, Sahai and Waters in 2013) came with only heuristic arguments for security; However more rigorous analyses of this and other constructions, based on well-defined formulations of multi-linear map variants, soon followed suite. Some of these analyses have eventually been “broken” in the sense that we currently don’t have candidate constructions that satisfy the properties they assume. Still, other analyses do remain valid. Indeed, there are no attacks against the actual basic IO scheme of Garg etal.

The fact that the only current candidate constructions of IO need to assume existence of some variant of multi-linear maps at some point or another may make it seem as it the two concepts are somehow tied together. However, there is no reason to believe that this is the case. For all we know, multi-linear maps are just the path first uncovered to IO, and other paths may well be found. Similarly, even if IO turns out to be unobtainable for some reason, the study of multilinear maps and their power will still remain very relevant.

So, to sum up this long-winded account:

- IO is a natural and fascinating computational concept. Studying its consequences (both within and outside cryptography) is a well worth endeavor.
- Studying new candidate constructions of IO and/or new analyses of their security is another well worth endeavor.
- Multilinear maps are an intriguing and powerful set of techniques and tools. Finding better candidate constructions and abstractions is of central importance to cryptography. Finding new cool uses of these maps is another intriguing challenge.
- The three should be treated as separate (although touching and potentially interleaving) research efforts.

———–

I’d like to thank Guy Rothblum and Vinod Vaikuntanathan for great comments that significantly improved this post.

All talks are recorded, and the recordings are available here.

Tomorrow afternoon, Daniele Micciancio will speak at 3pm on lattice-based cryptography.

Tomorrow is also the first day of the Workshop on the mathematics of modern cryptography. The program starts at 9:30am Pacific time, and all talk are broadcast live, as usual.

]]>The program started with week-long series of lectures, all available here, which covered tools such as lattice problems, multilinear maps, oblivious RAMs, scrambled circuits, and differential privacy, and their applications to homomorphic encryption, obfuscation, delegated computations, and multiparty computations.

This week there is a workshop on secure computations, all whose talks are livestreamed, which starts today at 9:30 Pacific Time with a talk by Amit Sahai on obfuscation.

]]>On October 14, 2013, Emmanuel Candès gave this wonderful lecture on the effectiveness of convex programming in data science and in the physical sciences. Slides are here.

]]>