arXiv subjects

Kameron Decker Harris

Publications and source records attributed to Kameron Decker Harris.

At least 19 recordsLinked to original sources

arXiv2026

Neural Variability Enhances Artificial Network Robustness

Neural responses in cortex exhibit substantial trial-to-trial variability in response to repeated stimuli, while peripheral sensory neurons respond far more consistently, leading many to wonder whether stochasticity may carry meaning. Existing work has argued that noise and signal correlations may be optimized for discrimination in animals, whereas artificial neural network (ANN) studies have shown similar benefits of noise in machine learning tasks, although most ANN work has neglected the effects of correlations. Here we investigate whether correlated noise improves the robustness of artificial neural networks to adversarial attacks and naturalistic image modifications. Using the covariance of activations under modified versus clean inputs, we find that structured noise may significantly improve network robustness. Robustness to naturalistic image modifications benefits most from structure, but this structure transfers poorly across modification types. In contrast, noise structure from adversarial attacks can generalize to other kinds of attacks. These results suggest that structured noise in ANN activations generally improves robustness, establishing a biologically plausible strategy for creating robust artificial neural networks that only relies on local information.

cs.LG↗

arXiv2023

Spectral gap-based deterministic tensor completion

Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the sampling patterns are deterministic. Here we bound the generalization error of the solutions of two tensor completion methods, Poisson loss and atomic norm minimization, providing tighter bounds in terms of the target tensor rank. If the ground-truth tensor is order $t$ with CP-rank $r$, the dependence on $r$ is improved from $r^{2(t-1)(t^2-t-1)}$ in arXiv:1910.10692 to $r^{2(t-1)(3t-5)}$. The error in our bounds is deterministically controlled by the spectral gap of the sampling sparsity pattern. We also prove several new properties for the atomic tensor norm, reducing the rank dependence from $r^{3t-3}$ in arXiv:1711.04965 to $r^{3t-5}$ under random sampling schemes. A limitation is that atomic norm minimization, while theoretically interesting, leads to inefficient algorithms. However, numerical experiments illustrate the dependence of the reconstruction error on the spectral gap for the practical max-quasinorm, ridge penalty, and Poisson loss minimization algorithms. This view through the spectral gap is a promising window for further study of tensor algorithms.

stat.ML↗

arXiv2022

BrainViewer: interacting with spatial connectome data at the mesoscale

Scientists construct connectomes, comprehensive descriptions of neuronal connections across a brain, in order to better understand and model brain function. Interactive visualizations of these pathways would enable exploratory analysis of such information flows. Current tools can be used to see individual tracing experiments which are used to build mesoscale connectomes of the mouse brain, but not the brain network itself. We present a connectivity visualization program called BrainViewer, which we use with a high-resolution mouse cortical connectome. This has the ability to display connectomes from other datasets when they become available and compare spatial connectivity across multiple brain structures. Our tool, optimized for speed and portability, presents a GUI visualization in 2-D top view and flatmap projections, allowing users to select and explore the connections of every source voxel to everywhere else in the cortex. Anatomists and other neuroscientists will find BrainViewer useful for building understanding beyond the known topography of cortical connectivity.

q-bio.NC↗

arXiv2021

Deterministic tensor completion with hypergraph expanders

We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows that the number of samples required to approximately recover an order-$t$ tensor with at most $n$ entries per dimension is linear in $n$, under the assumption that the rank and order of the tensor are $O(1)$. As steps in our proof, we find a new expander mixing lemma for a $t$-partite, $t$-uniform regular hypergraph model, and prove several new properties about tensor max-quasinorm. To the best of our knowledge, this is the first deterministic analysis of tensor completion. We develop a practical algorithm that solves a relaxed version of the max-quasinorm minimization problem, and we demonstrate its efficacy with numerical experiments.

stat.ML↗

arXiv2021

Spectral gap in random bipartite biregular graphs and applications

We prove an analogue of Alon's spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara-Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A byproduct of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full-rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

math.PR↗

arXiv2020

Time-varying Autoregression with Low Rank Tensors

We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex optimization. In each time window, we assume the data follow a linear model parameterized by a system matrix, and we model this stack of potentially different system matrices as a low rank tensor. Because of its structure, the model is scalable to high-dimensional data and can easily incorporate priors such as smoothness over time. We find the components of the tensor using alternating minimization and prove that any stationary point of this algorithm is a local minimum. We demonstrate on a synthetic example that our method identifies the true rank of a switching linear system in the presence of noise. We illustrate our model's utility and superior scalability over extant methods when applied to several synthetic and real-world example: two types of time-varying linear systems, worm behavior, sea surface temperature, and monkey brain datasets.

stat.ML↗

arXiv2019

Greedy low-rank algorithm for spatial connectome regression

Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regression problem (Harris et al., 2016), but existing techniques do not scale to the whole-brain setting. The corresponding matrix equation is challenging to solve due to large scale, ill-conditioning, and a general form that lacks a convergent splitting. We propose a greedy low-rank algorithm for connectome reconstruction problem in very high dimensions. The algorithm approximates the solution by a sequence of rank-one updates which exploit the sparse and positive definite problem structure. This algorithm was described previously (Kressner and Sirković, 2015) but never implemented for this connectome problem, leading to a number of challenges. We have had to design judicious stopping criteria and employ efficient solvers for the three main sub-problems of the algorithm, including an efficient GPU implementation that alleviates the main bottleneck for large datasets. The performance of the method is evaluated on three examples: an artificial "toy" dataset and two whole-cortex instances using data from the Allen Mouse Brain Connectivity Atlas. We find that the method is significantly faster than previous methods and that moderate ranks offer good approximation. This speedup allows for the estimation of increasingly large-scale connectomes across taxa as these data become available from tracing experiments. The data and code are available online.

math.NA↗

arXiv2019

Additive function approximation in the brain

Many biological learning systems such as the mushroom body, hippocampus, and cerebellum are built from sparsely connected networks of neurons. For a new understanding of such networks, we study the function spaces induced by sparse random features and characterize what functions may and may not be learned. A network with $d$ inputs per neuron is found to be equivalent to an additive model of order $d$, whereas with a degree distribution the network combines additive terms of different orders. We identify three specific advantages of sparsity: additive function approximation is a powerful inductive bias that limits the curse of dimensionality, sparse networks are stable to outlier noise in the inputs, and sparse random features are scalable. Thus, even simple brain architectures can be powerful function approximators. Finally, we hope that this work helps popularize kernel theories of networks among computational neuroscientists.

cs.NE↗

arXiv2019

Centering Data Improves the Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by linear dynamics. For nonlinear dynamical systems exhibiting strongly coherent structures, DMD can be a useful approximation to extract dominant, interpretable modes. In many domains with large spatiotemporal data---including fluid dynamics, video processing, and finance---the dynamics of interest are often perturbations about fixed points or equilibria, which motivates the application of DMD to centered (i.e. mean-subtracted) data. In this work, we show that DMD with centered data is equivalent to incorporating an affine term in the dynamic model and is not equivalent to computing a discrete Fourier transform. Importantly, DMD with centering can always be used to compute eigenvalue spectra of the dynamics. However, in many cases DMD without centering cannot model the corresponding dynamics, most notably if the dynamics have full effective rank. Additionally, we generalize the notion of centering to extracting arbitrary, but known, fixed frequencies from the data. We corroborate these theoretical results numerically on three nonlinear examples: the Lorenz system, a surveillance video, and brain recordings. Since centering the data is simple and computationally efficient, we recommend it as a preprocessing step before DMD; furthermore, we suggest that it can be readily used in conjunction with many other popular implementations of the DMD algorithm.

math.DS↗

arXiv2017

Different roles for inhibition in the rhythm-generating respiratory network

Unraveling the interplay of excitation and inhibition within rhythm-generating networks remains a fundamental issue in neuroscience. We use a biophysical model to investigate the different roles of local and long-range inhibition in the respiratory network, a key component of which is the pre-Bötzinger complex inspiratory microcircuit. Increasing inhibition within the microcircuit results in a limited number of out-of-phase neurons before rhythmicity and synchrony degenerate. Thus, unstructured local inhibition is destabilizing and cannot support the generation of more than one rhythm. A two-phase rhythm requires restructuring the network into two microcircuits coupled by long-range inhibition in the manner of a half-center. In this context, inhibition leads to greater stability of the two out-of-phase rhythms. We support our computational results with in vitro recordings from mouse pre-Bötzinger complex. Partial excitation block leads to increased rhythmic variability, but this recovers following blockade of inhibition. Our results support the idea that local inhibition in the pre-Bötzinger complex is present to allow for descending control of synchrony or robustness to adverse conditions like hypoxia. We conclude that the balance of inhibition and excitation determines the stability of rhythmogenesis, but with opposite roles within and between areas. These different inhibitory roles may apply to a variety of rhythmic behaviors that emerge in widespread pattern generating circuits of the nervous system.

q-bio.NC↗

arXiv2016

High resolution neural connectivity from incomplete tracing data using nonnegative spline regression

Whole-brain neural connectivity data are now available from viral tracing experiments, which reveal the connections between a source injection site and elsewhere in the brain. These hold the promise of revealing spatial patterns of connectivity throughout the mammalian brain. To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 $μ$m brain "voxels" using viral tracer data. Despite a multi-year experimental effort, injections provide incomplete coverage, and the number of voxels in our data is orders of magnitude larger than the number of injections, making the problem severely underdetermined. Furthermore, projection data are missing within the injection site because local connections there are not separable from the injection signal. We use a novel machine-learning algorithm to meet these challenges and develop a spatially explicit, voxel-scale connectivity map of the mouse visual system. Our method combines three features: a matrix completion loss for missing data, a smoothing spline penalty to regularize the problem, and (optionally) a low rank factorization. We demonstrate the consistency of our estimator using synthetic data and then apply it to newly available Allen Mouse Brain Connectivity Atlas data for the visual system. Our algorithm is significantly more predictive than current state of the art approaches which assume regions to be homogeneous. We demonstrate the efficacy of a low rank version on visual cortex data and discuss the possibility of extending this to a whole-brain connectivity matrix at the voxel scale.

q-bio.NC↗

arXiv2015

Direct, physically motivated derivation of triggering probabilities for spreading processes on generalized random networks

We derive a general expression for the probability of global spreading starting from a single infected seed for contagion processes acting on generalized, correlated random networks. We employ a simple probabilistic argument that encodes the spreading mechanism in an intuitive, physical fashion. We use our approach to directly and systematically obtain triggering probabilities for contagion processes acting on a collection of random network families including bipartite random networks. We find the contagion condition, the location of the phase transition into an endemic state, from an expansion about the disease-free state.

cond-mat.dis-nn↗

arXiv2014

Dynamical influence processes on networks: General theory and applications to social contagion

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. We construct a general mean field theory for random networks and show this predicts that the dynamics on the network are a smoothed version of the average response function dynamics. Thus, the behavior of the system can range from steady state to chaotic depending on the response functions, network connectivity, and update synchronicity. As a specific example, we model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into standard threshold models of social contagion. In this way we attempt to capture important aspects of fashions and societal trends. We compare our theory to extensive simulations of this "limited imitation contagion" model on Poisson random graphs, finding agreement between the mean-field theory and stochastic simulations.

physics.soc-ph↗

arXiv2014

Human language reveals a universal positivity bias

Using human evaluation of 100,000 words spread across 24 corpora in 10 languages diverse in origin and culture, we present evidence of a deep imprint of human sociality in language, observing that (1) the words of natural human language possess a universal positivity bias; (2) the estimated emotional content of words is consistent between languages under translation; and (3) this positivity bias is strongly independent of frequency of word usage. Alongside these general regularities, we describe inter-language variations in the emotional spectrum of languages which allow us to rank corpora. We also show how our word evaluations can be used to construct physical-like instruments for both real-time and offline measurement of the emotional content of large-scale texts.

physics.soc-ph↗

arXiv2013

The Geography of Happiness: Connecting Twitter sentiment and expression, demographics, and objective characteristics of place

We conduct a detailed investigation of correlations between real-time expressions of individuals made across the United States and a wide range of emotional, geographic, demographic, and health characteristics. We do so by combining (1) a massive, geo-tagged data set comprising over 80 million words generated over the course of several recent years on the social network service Twitter and (2) annually-surveyed characteristics of all 50 states and close to 400 urban populations. Among many results, we generate taxonomies of states and cities based on their similarities in word use; estimate the happiness levels of states and cities; correlate highly-resolved demographic characteristics with happiness levels; and connect word choice and message length with urban characteristics such as education levels and obesity rates. Our results show how social media may potentially be used to estimate real-time levels and changes in population-level measures such as obesity rates.

physics.soc-ph↗

arXiv2013

Limited Imitation Contagion on Random Networks: Chaos, Universality, and Unpredictability

We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or deterministic individual response functions on both dynamic and fixed random networks. In particular, we find significant variation in the limiting behavior of a population's infected fraction, ranging from steady-state to chaotic. We show that period doubling arises as we increase the average node degree, and that the universality class of this well known route to chaos depends on the interaction structure of random networks rather than the microscopic behavior of individual nodes. We find that increasing the fixedness of the system tends to stabilize the infected fraction, yet disjoint, multiple equilibria are possible depending solely on the choice of the initially infected node.

nlin.CD↗

arXiv2012

On-off Threshold Models of Social Contagion

We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into standard threshold models of behavior. In this way, we attempt to capture important aspects of fashions and general societal trends. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in the random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. The dynamical behavior of the system ranges from steady state to chaotic depending on network connectivity and update synchronicity. We construct a mean field theory for general random networks. In the undirected case, the mean field theory predicts that the dynamics on the network are a smoothed version of the average node response dynamics. We compare our theory to extensive simulations on Poisson random graphs with node responses that average to the chaotic tent map.

physics.soc-ph↗

arXiv2012

Twitter reciprocal reply networks exhibit assortativity with respect to happiness

The advent of social media has provided an extraordinary, if imperfect, 'big data' window into the form and evolution of social networks. Based on nearly 40 million message pairs posted to Twitter between September 2008 and February 2009, we construct and examine the revealed social network structure and dynamics over the time scales of days, weeks, and months. At the level of user behavior, we employ our recently developed hedonometric analysis methods to investigate patterns of sentiment expression. We find users' average happiness scores to be positively and significantly correlated with those of users one, two, and three links away. We strengthen our analysis by proposing and using a null model to test the effect of network topology on the assortativity of happiness. We also find evidence that more well connected users write happier status updates, with a transition occurring around Dunbar's number. More generally, our work provides evidence of a social sub-network structure within Twitter and raises several methodological points of interest with regard to social network reconstructions.

cs.SI↗