Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session F66: Inference, Information, and Learning in Biophysics IFocus
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Sponsoring Units: DBIO GSNP Chair: David Schwab, Princeton Univ Room: BCEC 261 |
Tuesday, March 5, 2019 11:15AM - 11:51AM |
F66.00001: Bounding Information flow in E. Coli chemotaxis Invited Speaker: Benjamin Machta
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Tuesday, March 5, 2019 11:51AM - 12:03PM |
F66.00002: Towards a New Theory of Biological Information Daniel Inafuku, Kay Kirkpatrick Many attempts have been made to understand biomolecular machines, such as the ribosome, from a computational and information-theoretic perspective. However, it is well-understood that current information theory is limited to symbolic (i.e., syntactic) manipulations only and is not equipped to deal with objects that possess functions beyond such manipulations. In this study, we present a quantitative analysis of the information-processing abilities of several classes of biomolecular machines that demonstrates their capacities for biological information. Furthermore, we argue that such machines possess functions that lie beyond the scope of traditional Shannon information theory and require a new description to completely characterize them. Finally, we propose new ways to extend current models by rigorously abstracting the structure and dynamics of these machines. |
Tuesday, March 5, 2019 12:03PM - 12:15PM |
F66.00003: Information transmission and evolution of crosstalk in noisy signal transduction networks Ammar Tareen, Ned Wingreen, Ranjan Mukhopadhyay Reliable transmission of information about the environment along cellular signaling pathways is crucial for accurate regulation of cellular function. However, signaling pathways are often highly interconnected, creating signal transduction networks consisting of multiple pathways. How did such complex, interconnected networks evolve and what constraints did the dynamics of evolution place on their architecture? Does crosstalk between pathways necessarily lead to reduction in the amount of information that can be reliably transmitted? In this talk, we will study information transmission and the evolution of cross-talk between noisy signaling pathways with the aim of addressing these and related questions. For this purpose, we develop a sequence-based evolutionary algorithm and evolve networks consisting of more than one pathway based on physically motivated fitness functions. We show how two fitness functions, both related to measures of information transmission, lead to very different evolutionary outcomes, one with a high degree of crosstalk and the other without. We relate the evolutionary outcomes to the fitness landscapes, and discuss the biological implications of our results. |
Tuesday, March 5, 2019 12:15PM - 12:27PM |
F66.00004: Information loss under coarse graining: A geometric approach Archishman Raju, James Patarasp Sethna, Benjamin Machta We use information geometry, in which the local distance between models measures their distinguishability from data, to quantify the flow of information under the renormalization group. We show that information about relevant parameters is preserved, with distances along relevant directions maintained under flow. By contrast, irrelevant parameters become less distinguishable under the flow, with distances along irrelevant directions contracting according to renormalization group exponents. We develop a covariant formalism to understand the contraction of the model manifold. We then apply our tools to understand the emergence of the diffusion equation and more general statistical systems described by a free energy. Our results give an information-theoretic justification of universality in terms of the flow of the model manifold under coarse-graining. |
Tuesday, March 5, 2019 12:27PM - 12:39PM |
F66.00005: The strength of protein-protein interactions controls the information capacity and dynamical response of signaling networks Ching-Hao Wang, Caleb Bashor, Pankaj Mehta Eukaryotic cells transmit information by signaling through complex networks of interacting proteins. Here we develop a theoretical and computational framework that relates the biophysics of protein-protein interactions (PPIs) within a signaling network to its information processing properties. We formulate a statistical physics-inspired model and combine it with information-theoretic methods to find that PPIs are a key determinant of information transmission within a signaling network, with weak interactions giving rise to “noise” that diminishes information transmission. While noise can be mitigated by increasing interaction strength, the accompanying increase in transmission comes at the expense of a slower dynamical response. This suggests that the biophysics of signaling protein interactions give rise to a fundamental “speed-information” trade-off. We further use this framework to interrogate the relationship between pathway cross-talks and information capacity, as well as its implications in synthetic biology. |
Tuesday, March 5, 2019 12:39PM - 12:51PM |
F66.00006: Random input expansion improves classifier accuracy Julia Steinberg, Madhu Advani, Haim Sompolinsky We have discovered a surprising phenomena in the problem of inference with noisy high dimensional data: that adding random input dimensions (completely uncorrelated to the data) can lead to lower generalization error when training max-margin classifiers. When applied appropriately, we prove that this expansion of the network can yield equivalent solutions to the addition of slack variables in support vector machine learning. We also consider two layer networks and demonstrate that this phenomena can allow wide random neural networks with sparse activity to handle output noise more effectively than networks exactly matched to the structure of the teacher network. This finding has implications for the design of neural networks and in understanding the role of neurogenesis and short-lived synapses in biological neural network structures. |
Tuesday, March 5, 2019 12:51PM - 1:03PM |
F66.00007: The renormalization group and information bottleneck: a unified framework Andrew Tan, Leenoy Meshulam, William Bialek, David Schwab Achieving useful simplified descriptions of high-dimensional systems is a fundamental problem in statistical physics. A central issue is formalizing which details should be retained and which discarded, such that we are left with only “relevant” information. In statistical physics, the outcome of the renormalization group is a reduced description where we are left with an accurate description of the macroscopic behavior of the system. In information theory, we use the information bottleneck to determine the optimal balance between features we accurately convey and those that are irrelevant complexity. Here we present an approach that unifies the concepts of the renormalization group and the information bottleneck. We achieve a coarse-graining procedure where we can control what “relevant” information we choose to keep, e.g. retaining information about long-distance features while removing local information. Studying the method in the information plane allows us to automatically select the best representation at each size. Variational approaches allow us to scale up our implementation, so that this approach can be successfully applied to large systems. We test our method on a variety of datasets from both physics and machine learning. |
Tuesday, March 5, 2019 1:03PM - 1:15PM |
F66.00008: Optimal visual motion estimation in a natural environment William Bialek, Shiva Sinha, Robert deRuyter van Steveninck Many organisms, from flies to humans, use visual signals to estimate their motion through the world. In flies we know that the precision of motion estimation is close to the limits set by photon shot noise and diffraction blur, yet the actual estimates suffer from systematic errors, some of which are shared by human perception. To explore the structure of the motion estimation problem, we have constructed a camera/gyroscope system that allows us to sample, at high temporal resolution, the joint distribution of input images and rotational motions during a long walk in the woods. From these data we construct the optimal estimator of velocity based on spatial and temporal derivatives of image intensity in small patches of the visual world. Over the bulk of the naturally occurring dynamic range, the optimal estimator exhibits the same systematic errors seen in neural and behavioral responses, including the confounding of velocity and contrast. These results suggest that apparent errors of sensory processing may reflect an optimal response to the physical signals in the environment. |
Tuesday, March 5, 2019 1:15PM - 1:27PM |
F66.00009: The Stochastic Complexity of Spin Models: Are Pairwise Models Really Simple? Alberto Beretta, Claudia Battistin, Clélia De Mulatier, Iacopo Mastromatteo Mastromatteo, Matteo Marsili Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a dataset (e.g. in terms of pairwise dependencies)--as in statistical learning--or because they capture the laws of a specific phenomenon--as in physics--leading to non-trivial falsifiable predictions. In information theory, the simplicity of a model is quantified by the stochastic complexity, which measures the number of bits needed to encode its parameters. In order to understand how simple models look like, we study the stochastic complexity of spin models with interactions of arbitrary order. We show that bijections within the space of possible interactions preserve the stochastic complexity, which allows to partition the space of all models into equivalence classes. We thus found that the simplicity of a model is not determined by the order of the interactions, but rather by their mutual arrangements. Models where statistical dependencies are localized on non-overlapping groups of few variables are simple, affording predictions on independencies that are easy to falsify. On the contrary, fully connected pairwise models, often used in statistical learning, appear to be highly complex, because of their extended set of interactions, and are hard to falsify. |
Tuesday, March 5, 2019 1:27PM - 1:39PM |
F66.00010: Who is your neighbor? Inferring locality from pairwise correlations Mahajabin Rahman, Ilya Nemenman Modeling multivariate biological systems, such as multielectrode neural recordings, genetic sequences, or gene expression patterns, requires identification of combinatorial interaction coefficients coupling the measured variables. This is impossible to do from data sets of realistic sizes. One could hope to regularize the inference by imposing the constraint that interactions must be local. However, whether two variables are neighbors and thus can interact is unknown for many biological data sets. Here we explore the possibility that neighborhood relations can be inferred from the pairwise correlation matrix, even in the undersampled data limit. Our toy model consists of a set of images whose pixels are shuffled randomly, but in the same way for all images, such that spatial information is lost, but pixel-to-pixel correlations are preserved. We use t-SNE, a dimensionality reduction and visualization technique, to embed the shuffled pixels in space, such that strongly correlated pixels end up next to each other. We observe that embedding the data in 2D space produces images nearly identical to the originals, save for global transformations. This shows that analysis of the covariance matrix correctly identifies local neighborhoods, as well as the global dimensionality of the data. |
Tuesday, March 5, 2019 1:39PM - 1:51PM |
F66.00011: Mean Field Analysis of Batch Normalization Mingwei Wei, James Stokes, David Schwab Batch Normalization (BatchNorm) is an extremely useful component of modern neural network architectures, enabling optimization using higher learning rates and achieving faster convergence. In this paper, we use mean-field theory to analytically quantify the impact of BatchNorm on the geometry of the loss landscape for multi-layer networks consisting of fully-connected and convolutional layers. We show that it has a flattening effect on the loss landscape, as quantified by the maximum eigenvalue of the Fisher Information Matrix. These findings are then used to justify the use of larger learning rates for networks that use BatchNorm, and we provide quantitative characterization of the maximal allowable learning rate to ensure convergence. Experiments support our theoretically predicted maximum learning rate, and furthermore suggest that networks with smaller values of the BatchNorm parameter achieve lower loss after the same number of epochs of training. |
Tuesday, March 5, 2019 1:51PM - 2:03PM |
F66.00012: Nonequilibrium cooperative sensing Vudtiwat Ngampruetikorn, David J. Schwab, Greg Stephens While cellular sensing relies on both cooperation between receptors and energy consumption to suppress noise, their combined effect is not well understood. Here we introduce a minimal model of interacting sensors which allows for the detailed exploration of signal statistics and cooperation strategies in the context of optimal sensing. For two sensors we show that the sensing strategy which maximizes the mutual information between the signal and the sensors depends both on the noise level and the statistics of the signals. For signals on a single sensor, nonequilibrium, asymmetric couplings result in maximum information gain in the noise-dominated limit while for joint, correlated signals, the improvement is greatest in the low-noise limit. In particular we show that optimal sensing does not always require energy consumption. We detail the difference in mechanism behind nonequilibrium improvement for univariate and correlated signals and our results provide insight into the principles of optimal sensor design. |
Tuesday, March 5, 2019 2:03PM - 2:15PM |
F66.00013: A Novel Algorithm for Unsupervised Behavioral Classification Adam Fine, Nirag Kadakia, Thierry Emonet I present a novel software package used for extraction of behavioral patterns from a data matrix with no a priori assumptions about the form of the data. The underlying algorithm transforms a data matrix into the time-frequency domain using a wavelet transform, which is analogous to taking a Fourier transform at each time step. This equalizes the power between frequency components, to ensure repeated high frequency motions do not dominate. The transformed matrix is then decomposed into behavioral patterns and their relative activity over time using an algorithm called seqNMF [1]. Though the algorithm was originally developed for positional data from an assay of Drosophila, it has been used to extract behavioral patterns from other organisms (e.g. E. coli) as well. The algorithm is robust with respect to both the number of underlying patterns in the data as well as the length of the patterns. In addition, the lack of any input other than the data itself makes the software package a powerful unsupervised classification tool with broad potential applications. |
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