Tag Archives: Michael W. Reimann

Brain stuff: quantum entanglement and a multi-dimensional universe

I have two brain news bits, one about neural networks and quantum entanglement and another about how the brain operates on more than three dimensions.

Quantum entanglement and neural networks

A June 13, 2017 news item on phys.org describes how machine learning can be used to solve problems in physics (Note: Links have been removed),

Machine learning, the field that’s driving a revolution in artificial intelligence, has cemented its role in modern technology. Its tools and techniques have led to rapid improvements in everything from self-driving cars and speech recognition to the digital mastery of an ancient board game.

Now, physicists are beginning to use machine learning tools to tackle a different kind of problem, one at the heart of quantum physics. In a paper published recently in Physical Review X, researchers from JQI [Joint Quantum Institute] and the Condensed Matter Theory Center (CMTC) at the University of Maryland showed that certain neural networks—abstract webs that pass information from node to node like neurons in the brain—can succinctly describe wide swathes of quantum systems.

An artist’s rendering of a neural network with two layers. At the top is a real quantum system, like atoms in an optical lattice. Below is a network of hidden neurons that capture their interactions (Credit: E. Edwards/JQI)

A June 12, 2017 JQI news release by Chris Cesare, which originated the news item, describes how neural networks can represent quantum entanglement,

Dongling Deng, a JQI Postdoctoral Fellow who is a member of CMTC and the paper’s first author, says that researchers who use computers to study quantum systems might benefit from the simple descriptions that neural networks provide. “If we want to numerically tackle some quantum problem,” Deng says, “we first need to find an efficient representation.”

On paper and, more importantly, on computers, physicists have many ways of representing quantum systems. Typically these representations comprise lists of numbers describing the likelihood that a system will be found in different quantum states. But it becomes difficult to extract properties or predictions from a digital description as the number of quantum particles grows, and the prevailing wisdom has been that entanglement—an exotic quantum connection between particles—plays a key role in thwarting simple representations.

The neural networks used by Deng and his collaborators—CMTC Director and JQI Fellow Sankar Das Sarma and Fudan University physicist and former JQI Postdoctoral Fellow Xiaopeng Li—can efficiently represent quantum systems that harbor lots of entanglement, a surprising improvement over prior methods.

What’s more, the new results go beyond mere representation. “This research is unique in that it does not just provide an efficient representation of highly entangled quantum states,” Das Sarma says. “It is a new way of solving intractable, interacting quantum many-body problems that uses machine learning tools to find exact solutions.”

Neural networks and their accompanying learning techniques powered AlphaGo, the computer program that beat some of the world’s best Go players last year (link is external) (and the top player this year (link is external)). The news excited Deng, an avid fan of the board game. Last year, around the same time as AlphaGo’s triumphs, a paper appeared that introduced the idea of using neural networks to represent quantum states (link is external), although it gave no indication of exactly how wide the tool’s reach might be. “We immediately recognized that this should be a very important paper,” Deng says, “so we put all our energy and time into studying the problem more.”

The result was a more complete account of the capabilities of certain neural networks to represent quantum states. In particular, the team studied neural networks that use two distinct groups of neurons. The first group, called the visible neurons, represents real quantum particles, like atoms in an optical lattice or ions in a chain. To account for interactions between particles, the researchers employed a second group of neurons—the hidden neurons—which link up with visible neurons. These links capture the physical interactions between real particles, and as long as the number of connections stays relatively small, the neural network description remains simple.

Specifying a number for each connection and mathematically forgetting the hidden neurons can produce a compact representation of many interesting quantum states, including states with topological characteristics and some with surprising amounts of entanglement.

Beyond its potential as a tool in numerical simulations, the new framework allowed Deng and collaborators to prove some mathematical facts about the families of quantum states represented by neural networks. For instance, neural networks with only short-range interactions—those in which each hidden neuron is only connected to a small cluster of visible neurons—have a strict limit on their total entanglement. This technical result, known as an area law, is a research pursuit of many condensed matter physicists.

These neural networks can’t capture everything, though. “They are a very restricted regime,” Deng says, adding that they don’t offer an efficient universal representation. If they did, they could be used to simulate a quantum computer with an ordinary computer, something physicists and computer scientists think is very unlikely. Still, the collection of states that they do represent efficiently, and the overlap of that collection with other representation methods, is an open problem that Deng says is ripe for further exploration.

Here’s a link to and a citation for the paper,

Quantum Entanglement in Neural Network States by Dong-Ling Deng, Xiaopeng Li, and S. Das Sarma. Phys. Rev. X 7, 021021 – Published 11 May 2017

This paper is open access.

Blue Brain and the multidimensional universe

Blue Brain is a Swiss government brain research initiative which officially came to life in 2006 although the initial agreement between the École Politechnique Fédérale de Lausanne (EPFL) and IBM was signed in 2005 (according to the project’s Timeline page). Moving on, the project’s latest research reveals something astounding (from a June 12, 2017 Frontiers Publishing press release on EurekAlert),

For most people, it is a stretch of the imagination to understand the world in four dimensions but a new study has discovered structures in the brain with up to eleven dimensions – ground-breaking work that is beginning to reveal the brain’s deepest architectural secrets.

Using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain.

The research, published today in Frontiers in Computational Neuroscience, shows that these structures arise when a group of neurons forms a clique: each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object.

“We found a world that we had never imagined,” says neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland, “there are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to eleven dimensions.”

Markram suggests this may explain why it has been so hard to understand the brain. “The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly.”

If 4D worlds stretch our imagination, worlds with 5, 6 or more dimensions are too complex for most of us to comprehend. This is where algebraic topology comes in: a branch of mathematics that can describe systems with any number of dimensions. The mathematicians who brought algebraic topology to the study of brain networks in the Blue Brain Project were Kathryn Hess from EPFL and Ran Levi from Aberdeen University.

“Algebraic topology is like a telescope and microscope at the same time. It can zoom into networks to find hidden structures – the trees in the forest – and see the empty spaces – the clearings – all at the same time,” explains Hess.

In 2015, Blue Brain published the first digital copy of a piece of the neocortex – the most evolved part of the brain and the seat of our sensations, actions, and consciousness. In this latest research, using algebraic topology, multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance. Experiments were then performed on real brain tissue in the Blue Brain’s wet lab in Lausanne confirming that the earlier discoveries in the virtual tissue are biologically relevant and also suggesting that the brain constantly rewires during development to build a network with as many high-dimensional structures as possible.

When the researchers presented the virtual brain tissue with a stimulus, cliques of progressively higher dimensions assembled momentarily to enclose high-dimensional holes, that the researchers refer to as cavities. “The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner,” says Levi. “It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates.”

The big question these researchers are asking now is whether the intricacy of tasks we can perform depends on the complexity of the multi-dimensional “sandcastles” the brain can build. Neuroscience has also been struggling to find where the brain stores its memories. “They may be ‘hiding’ in high-dimensional cavities,” Markram speculates.

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About Blue Brain

The aim of the Blue Brain Project, a Swiss brain initiative founded and directed by Professor Henry Markram, is to build accurate, biologically detailed digital reconstructions and simulations of the rodent brain, and ultimately, the human brain. The supercomputer-based reconstructions and simulations built by Blue Brain offer a radically new approach for understanding the multilevel structure and function of the brain. http://bluebrain.epfl.ch

About Frontiers

Frontiers is a leading community-driven open-access publisher. By taking publishing entirely online, we drive innovation with new technologies to make peer review more efficient and transparent. We provide impact metrics for articles and researchers, and merge open access publishing with a research network platform – Loop – to catalyse research dissemination, and popularize research to the public, including children. Our goal is to increase the reach and impact of research articles and their authors. Frontiers has received the ALPSP Gold Award for Innovation in Publishing in 2014. http://www.frontiersin.org.

Here’s a link to and a citation for the paper,

Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function by Michael W. Reimann, Max Nolte, Martina Scolamiero, Katharine Turner, Rodrigo Perin, Giuseppe Chindemi, Paweł Dłotko, Ran Levi, Kathryn Hess, and Henry Markram. Front. Comput. Neurosci., 12 June 2017 | https://doi.org/10.3389/fncom.2017.00048

This paper is open access.

Blue Brain Project builds a digital piece of brain

Caption: This is a photo of a virtual brain slice. Credit: Makram et al./Cell 2015

Caption: This is a photo of a virtual brain slice. Credit: Makram et al./Cell 2015

Here’s more *about this virtual brain slice* from an Oct. 8, 2015 Cell (magazine) news release on EurekAlert,

If you want to learn how something works, one strategy is to take it apart and put it back together again [also known as reverse engineering]. For 10 years, a global initiative called the Blue Brain Project–hosted at the Ecole Polytechnique Federale de Lausanne (EPFL)–has been attempting to do this digitally with a section of juvenile rat brain. The project presents a first draft of this reconstruction, which contains over 31,000 neurons, 55 layers of cells, and 207 different neuron subtypes, on October 8 [2015] in Cell.

Heroic efforts are currently being made to define all the different types of neurons in the brain, to measure their electrical firing properties, and to map out the circuits that connect them to one another. These painstaking efforts are giving us a glimpse into the building blocks and logic of brain wiring. However, getting a full, high-resolution picture of all the features and activity of the neurons within a brain region and the circuit-level behaviors of these neurons is a major challenge.

Henry Markram and colleagues have taken an engineering approach to this question by digitally reconstructing a slice of the neocortex, an area of the brain that has benefitted from extensive characterization. Using this wealth of data, they built a virtual brain slice representing the different neuron types present in this region and the key features controlling their firing and, most notably, modeling their connectivity, including nearly 40 million synapses and 2,000 connections between each brain cell type.

“The reconstruction required an enormous number of experiments,” says Markram, of the EPFL. “It paves the way for predicting the location, numbers, and even the amount of ion currents flowing through all 40 million synapses.”

Once the reconstruction was complete, the investigators used powerful supercomputers to simulate the behavior of neurons under different conditions. Remarkably, the researchers found that, by slightly adjusting just one parameter, the level of calcium ions, they could produce broader patterns of circuit-level activity that could not be predicted based on features of the individual neurons. For instance, slow synchronous waves of neuronal activity, which have been observed in the brain during sleep, were triggered in their simulations, suggesting that neural circuits may be able to switch into different “states” that could underlie important behaviors.

“An analogy would be a computer processor that can reconfigure to focus on certain tasks,” Markram says. “The experiments suggest the existence of a spectrum of states, so this raises new types of questions, such as ‘what if you’re stuck in the wrong state?'” For instance, Markram suggests that the findings may open up new avenues for explaining how initiating the fight-or-flight response through the adrenocorticotropic hormone yields tunnel vision and aggression.

The Blue Brain Project researchers plan to continue exploring the state-dependent computational theory while improving the model they’ve built. All of the results to date are now freely available to the scientific community at https://bbp.epfl.ch/nmc-portal.

An Oct. 8, 2015 Hebrew University of Jerusalem press release on the Canadian Friends of the Hebrew University of Jerusalem website provides more detail,

Published by the renowned journal Cell, the paper is the result of a massive effort by 82 scientists and engineers at EPFL and at institutions in Israel, Spain, Hungary, USA, China, Sweden, and the UK. It represents the culmination of 20 years of biological experimentation that generated the core dataset, and 10 years of computational science work that developed the algorithms and built the software ecosystem required to digitally reconstruct and simulate the tissue.

The Hebrew University of Jerusalem’s Prof. Idan Segev, a senior author of the research paper, said: “With the Blue Brain Project, we are creating a digital reconstruction of the brain and using supercomputer simulations of its electrical behavior to reveal a variety of brain states. This allows us to examine brain phenomena within a purely digital environment and conduct experiments previously only possible using biological tissue. The insights we gather from these experiments will help us to understand normal and abnormal brain states, and in the future may have the potential to help us develop new avenues for treating brain disorders.”

Segev, a member of the Hebrew University’s Edmond and Lily Safra Center for Brain Sciences and director of the university’s Department of Neurobiology, sees the paper as building on the pioneering work of the Spanish anatomist Ramon y Cajal from more than 100 years ago: “Ramon y Cajal began drawing every type of neuron in the brain by hand. He even drew in arrows to describe how he thought the information was flowing from one neuron to the next. Today, we are doing what Cajal would be doing with the tools of the day: building a digital representation of the neurons and synapses, and simulating the flow of information between neurons on supercomputers. Furthermore, the digitization of the tissue is open to the community and allows the data and the models to be preserved and reused for future generations.”

While a long way from digitizing the whole brain, the study demonstrates that it is feasible to digitally reconstruct and simulate brain tissue, and most importantly, to reveal novel insights into the brain’s functioning. Simulating the emergent electrical behavior of this virtual tissue on supercomputers reproduced a range of previous observations made in experiments on the brain, validating its biological accuracy and providing new insights into the functioning of the neocortex. This is a first step and a significant contribution to Europe’s Human Brain Project, which Henry Markram founded, and where EPFL is the coordinating partner.

Cell has made a video abstract available (it can be found with the Hebrew University of Jerusalem press release)

Here’s a link to and a citation for the paper,

Reconstruction and Simulation of Neocortical Microcircuitry by Henry Markram, Eilif Muller, Srikanth Ramaswamy, Michael W. Reimann, Marwan Abdellah, Carlos Aguado Sanchez, Anastasia Ailamaki, Lidia Alonso-Nanclares, Nicolas Antille, Selim Arsever, Guy Antoine Atenekeng Kahou, Thomas K. Berger, Ahmet Bilgili, Nenad Buncic, Athanassia Chalimourda, Giuseppe Chindemi, Jean-Denis Courcol, Fabien Delalondre, Vincent Delattre, Shaul Druckmann, Raphael Dumusc, James Dynes, Stefan Eilemann, Eyal Gal, Michael Emiel Gevaert, Jean-Pierre Ghobril, Albert Gidon, Joe W. Graham, Anirudh Gupta, Valentin Haenel, Etay Hay, Thomas Heinis, Juan B. Hernando, Michael Hines, Lida Kanari, Daniel Keller, John Kenyon, Georges Khazen, Yihwa Kim, James G. King, Zoltan Kisvarday, Pramod Kumbhar, Sébastien Lasserre, Jean-Vincent Le Bé, Bruno R.C. Magalhães, Angel Merchán-Pérez, Julie Meystre, Benjamin Roy Morrice, Jeffrey Muller, Alberto Muñoz-Céspedes, Shruti Muralidhar, Keerthan Muthurasa, Daniel Nachbaur, Taylor H. Newton, Max Nolte, Aleksandr Ovcharenko, Juan Palacios, Luis Pastor, Rodrigo Perin, Rajnish Ranjan, Imad Riachi, José-Rodrigo Rodríguez, Juan Luis Riquelme, Christian Rössert, Konstantinos Sfyrakis, Ying Shi, Julian C. Shillcock, Gilad Silberberg, Ricardo Silva, Farhan Tauheed, Martin Telefont, Maria Toledo-Rodriguez, Thomas Tränkler, Werner Van Geit, Jafet Villafranca Díaz, Richard Walker, Yun Wang, Stefano M. Zaninetta, Javier DeFelipe, Sean L. Hill, Idan Segev, Felix Schürmann. Cell, Volume 163, Issue 2, p456–492, 8 October 2015 DOI: http://dx.doi.org/10.1016/j.cell.2015.09.029

This paper appears to be open access.

My most substantive description of the Blue Brain Project , previous to this, was in a Jan. 29, 2013 posting featuring the European Union’s (EU) Human Brain project and involvement from countries that are not members.

* I edited a redundant lede (That’s a virtual slice of a rat brain.), moved the second sentence to the lede while adding this:  *about this virtual brain slice* on Oct. 16, 2015 at 0955 hours PST.