arXiv subjects

Jason Z. Kim

Publications and source records attributed to Jason Z. Kim.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying the cost of network computations to unpack structure-function relationships in the brain

The brain supports computations through coordinated patterns of activity on an underlying network. These networks---from microscale navigational circuits in insects to macroscale brain areas in humans---are organized in structured ways that are thought to support their function. We seek a unifying quantitative framework to understand how network structure shapes the computations a network can readily support. To do so, we frame computation as a goal-directed transition of activity and quantify its cost on a given network using control theory. We then define the distribution of costs across all possible transitions as a $\textit{computational affordance landscape}$ that encodes which computations a network structure readily supports. We apply this framework to a circuit model for how insects maintain a sense of direction and show that updating orientation is the least costly computation, with predicted inputs consistent with known circuitry. In the human brain, we find that the affordance landscape varies systematically with the functional role of each network. Sensory networks display more heterogeneous landscapes (reflecting their role in specialized information processing), whereas association networks display more homogeneous landscapes (reflecting their role in generalized information processing). In recurrent neural networks trained on cognitive tasks, we show that learning progressively increases landscape heterogeneity, reshaping the distribution of affordable computations. Generally, we establish a quantitative framework for studying relationships between structure and computation in neural circuits, with future applications extending to other biological and physical networks.

q-bio.NC↗

arXiv2026

Charting the emergent low-dimensional manifold of quantum materials

The periodic table of elements transformed chemistry by revealing simple organizing principles underlying atomic behavior. Despite decades of effort, no analogous framework has emerged for crystalline materials -- their microscopic complexity and vast configurational space have defied reduction to fundamental organizing principles. Current databases catalog thousands of synthesized materials, but extracting predictive, interpretable models from this wealth of data remains a formidable challenge. Here we demonstrate that the materials landscape possesses a hidden geometric organization that can be unveiled through unsupervised nonlinear dimensionality reduction. Applying differential geometry techniques to the Inorganic Crystal Structure Database (ICSD), we reveal that just a few combinations of microscopic descriptors capture the vast majority of variance in material properties. This low-dimensional embedding autonomously segregates superconductors from ordinary materials and further distinguishes superconducting families in ways that transcend chemical similarity alone. Remarkably, the discovered geometric organization directly governs critical temperatures ($T_c$) across diverse superconducting families, enabling accurate $T_c$ predictions without any knowledge of the pairing mechanism. Our approach uncovers emergent organizing principles that control macroscopic quantum behavior, offering a new paradigm in how we build models of complex quantum materials directly from experimental data.

cond-mat.supr-con↗

arXiv2026

Multistable energy landscapes for adaptive microscopic machines

The past few years have seen great strides in our ability to build synthetic microscopic machines. However, the function of such machines is often controlled directly by externally applied fields that deterministically specify the instantaneous machine dynamics. A crucial step towards machines that can respond adaptively to changes in their environment is the ability to program multiple functions that actuate under the same external driving field, so that their internal state dictates which function is executed. Here, we demonstrate that energy landscapes with designed multistability enable the same externally applied field to drive multiple configurations and dynamic responses in microscopic machines, enabling increasing levels of autonomy. We show three examples. First, we write a bistable energy landscape into a microscopic device, enabling the device to exhibit two stable mechanical configurations under the same external magnetic field. Next, adding a second degree of freedom enables differing dynamic responses to the same external magnetic field, which we direct into net displacement of the environment. Finally, we demonstrate how a microscopic machine with a continuous symmetry autonomously channels a single degree-of-freedom magnetic actuation into locomotion and adaptively responds to forces induced by other machines.

cond-mat.soft↗

arXiv2026

Dicovering the emergent nonlinear dynamics of acoustically levitated cube clusters

The complex behavior of many natural and engineered systems emerges from the interaction of a small number of effective degrees of freedom. Discovering the physical basis of the interactions between these degrees of freedom directly from experimental observations has been a longstanding challenge, particularly with respect to predicting the long-time dynamics of dynamical systems with unknown equations of motion. Here, we introduce a data-driven approach that is able to produce a generative model for the long-time dynamical behavior of systems with a weakly attracting manifold. We apply this method to an experimental dynamical system with two degrees of freedom: acoustically levitated pairs of cube-shaped particles, which cluster by sharing a single edge. In the acoustic trap, the center-of-mass of the cube cluster oscillates vertically about the levitation plane, while also oscillating about their flexible hinge-like connection. Depending on their initial condition, the hinge dynamics evolve about three distinct nonlinear dynamical attractors persisting for hundreds of cycles. In order to capture the underlying physics, we develop a numerical fitting procedure and extract a minimal nonlinear dynamical model that captures both the long-time dynamics of the cluster as well as the convergence onto the dynamical steady state. This dynamical model uncovers the nonlinear, non-reciprocal coupling between the center-of-mass motion and the hinge degree of freedom that stabilizes the dynamical attractors, which we subsequently confirm by independent finite-element methods. Our results demonstrate a novel data-driven method for the discovery of nonlinear models with long-timescale stable predictions.

nlin.CD↗

arXiv2026

Linear control theory for jammed particle systems

Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not yet fully understood, with profound consequences for phenomena ranging from landscape evolution to cellular unjamming during tumor metastasis. With this paper, we introduce tools from linear control theory that quantify system response to external input, and demonstrate their utility in elucidating the dynamics of jammed amorphous materials under stress. Our results indicate that average controllability, the response of a system to perturbation, strongly correlates with particle rearrangement in systems subject to quasistatic shear, implying that average controllability is an accurate predictor of rearrangement dynamics in certain contexts. Moreover, we show that the time scale over which average controllability is calculated can be tuned to optimize its predictive capacity for particle rearrangement. Values of the optimal time scale provide physical insight into the system; namely, that multiple rearranging particles participate on average in vibrational eigenmodes of lower and lower energy as the system is sheared until the rearrangement event. Broadly, our study demonstrates that linear control theory is a promising mathematical framework for predicting and designing mechanical response in disordered media.

cond-mat.soft↗

arXiv2025

Habit learning is associated with efficiently controlled network dynamics in naive macaque monkeys

Primates utilize distributed neural circuits to learn habits in uncertain environments, but the underlying mechanisms remain poorly understood. We propose a formal theory of network energetics explaining how brain states influence sequential behavior. We test our theory on multi-unit recordings from the caudate nucleus and cortical regions of macaques performing a motor habit task. The theory predicts the energy required to transition between brain states represented by trial-specific firing rates across channels, assuming activity spreads through effective connections. We hypothesized that habit formation would correlate with lower control energy. Consistent with this, we observed smaller energy requirements for transitions between similar saccade patterns and those of intermediate complexity, and sessions exploiting fewer patterns. Simulations ruled out confounds from neurons' directional tuning. Finally, virtual lesioning demonstrated robustness of observed relationships between control energy and behavior. This work paves the way for examining how behavior arises from changing activity in distributed circuitry.

q-bio.NC↗

arXiv2025

Excitation and inhibition imbalance affects dynamical complexity through symmetries

From the perfect radial symmetries of radiolarian mineral skeletons to the broken symmetry of homochirality, the logic of Nature's regularities has fascinated scientists for centuries. Some of Nature's symmetries are clearly visible in morphology and physical structure, whereas others are hidden in the network of interactions among system components. Just as visible symmetries and asymmetries contribute to the system's beauty, might hidden symmetries contribute to the system's functional harmony? And if so, how? Here we demonstrate that the interaction networks of biological systems from cell signaling to cancer display a form of dynamical reflection symmetry that serves to expand their dynamical complexity. The expansion proceeds according to precise rules regarding the lengths of dynamical cycles, made possible by a peculiar imbalance between excitation and inhibition. To probe the conditions under which this reflection symmetry evolves, we use a multi-objective genetic algorithm to produce networks with long dynamical cycles. We find that local structural motifs that break the reflection symmetry are deleted in the evolutionary process, providing evidence for symmetry's causal role in dynamical complexity. Finally, we identify symmetries in real continuous-valued scRNA-seq data of gene expression in drug-resistant cancer cells. Broadly, our work reveals a class of hidden symmetries in biology, present in the network of interactions among system components, and it underscores their functional importance. Mathematically simple and computational inexpensive, our approach is applicable to the types of biological data commonly acquired in modern experiments.

physics.bio-ph↗

arXiv2024

$Γ$-VAE: Curvature regularized variational autoencoders for uncovering emergent low dimensional geometric structure in high dimensional data

Natural systems with emergent behaviors often organize along low-dimensional subsets of high-dimensional spaces. For example, despite the tens of thousands of genes in the human genome, the principled study of genomics is fruitful because biological processes rely on coordinated organization that results in lower dimensional phenotypes. To uncover this organization, many nonlinear dimensionality reduction techniques have successfully embedded high-dimensional data into low-dimensional spaces by preserving local similarities between data points. However, the nonlinearities in these methods allow for too much curvature to preserve general trends across multiple non-neighboring data clusters, thereby limiting their interpretability and generalizability to out-of-distribution data. Here, we address both of these limitations by regularizing the curvature of manifolds generated by variational autoencoders, a process we coin ``$Γ$-VAE''. We demonstrate its utility using two example data sets: bulk RNA-seq from the The Cancer Genome Atlas (TCGA) and the Genotype Tissue Expression (GTEx); and single cell RNA-seq from a lineage tracing experiment in hematopoietic stem cell differentiation. We find that the resulting regularized manifolds identify mesoscale structure associated with different cancer cell types, and accurately re-embed tissues from completely unseen, out-of distribution cancers as if they were originally trained on them. Finally, we show that preserving long-range relationships to differentiated cells separates undifferentiated cells -- which have not yet specialized -- according to their eventual fate. Broadly, we anticipate that regularizing the curvature of generative models will enable more consistent, predictive, and generalizable models in any high-dimensional system with emergent low-dimensional behavior.

cs.LG↗

arXiv2023

Shaping dynamical neural computations using spatiotemporal constraints

Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant multidisciplinary progress has been made in bridging the gap between how we understand biological versus artificial computation, including how insights gained from one can translate to the other. Research has revealed that neurobiology is a key determinant of brain network architecture, which gives rise to spatiotemporally constrained patterns of activity that underlie computation. Here, we discuss how neural systems use dynamics for computation, and claim that the biological constraints that shape brain networks may be leveraged to improve the implementation of artificial neural networks. To formalize this discussion, we consider a natural artificial analog of the brain that has been used extensively to model neural computation: the recurrent neural network (RNN). In both the brain and the RNN, we emphasize the common computational substrate atop which dynamics occur -- the connectivity between neurons -- and we explore the unique computational advantages offered by biophysical constraints such as resource efficiency, spatial embedding, and neurodevelopment.

q-bio.NC↗

arXiv2023

The information content of brain states is explained by structural constraints on state energetics

Signal propagation along the structural connectome of the brain induces changes in the patterns of activity. These activity patterns define global brain states and contain information in accordance with their expected probability of occurrence. The structural connectome, in conjunction with the dynamics, determines the set of possible brain states and constrains the transition between accessible states. Yet, precisely how these structural constraints on state-transitions relate to their information content remains unexplored. To address this gap in knowledge, we defined the information content as a function of the activation distribution, where statistically rare values of activation correspond to high information content. With this numerical definition in hand, we studied the spatiotemporal distribution of information content in fMRI data from the Human Connectome Project during different tasks, and report four key findings. First, information content strongly depends on the cognitive task. Second, while information content shows similarities to other measures of brain activity, it is distinct from both Neurosynth maps and task contrast maps generated by a general linear model applied to the fMRI data. Third, the brain's structural wiring constrains the cost to control its state, where the cost to transition into high information content states is larger than that to transition into low information content states. Finally, all state transitions - especially those to high information content states - are less costly than expected from random network null models, thereby indicating the brain's marked efficiency. Taken together, our findings establish an explanatory link between the information contained in a brain state and the energetic cost of attaining that state, thereby laying important groundwork for our understanding of large-scale cognitive computations.

q-bio.NC↗

arXiv2022

Compression supports low-dimensional representations of behavior across neural circuits

Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity. Hence, the brain may benefit from generating both compressed and uncompressed activity, and may do so in a heterogeneous manner across diverse neural circuits that represent low-level (sensory) or high-level (cognitive) stimuli. However, precisely how compression and representational capacity differ across the cortex remains unknown. Here we predict different levels of compression across regional circuits by using random walks on networks to model activity flow and to formulate rate-distortion functions, which are the basis of lossy compression. Using a large sample of youth ($n=1,040$), we test predictions in two ways: by measuring the dimensionality of spontaneous activity from sensorimotor to association cortex, and by assessing the representational capacity for 24 behaviors in neural circuits and 20 cognitive variables in recurrent neural networks. Our network theory of compression predicts the dimensionality of activity ($t=12.13, p<0.001$) and the representational capacity of biological ($r=0.53, p=0.016$) and artificial ($r=0.61, p<0.001$) networks. The model suggests how a basic form of compression is an emergent property of activity flow between distributed circuits that communicate with the rest of the network.

q-bio.NC↗

arXiv2022

Curiosity as filling, compressing, and reconfiguring knowledge networks

Due to the significant role that curiosity plays in our lives, several theoretical constructs, such as the information gap theory and compression progress theory, have sought to explain how we engage in its practice. According to the former, curiosity is the drive to acquire information that is missing from our understanding of the world. According to the latter, curiosity is the drive to construct an increasingly parsimonious mental model of the world. To complement the densification processes inherent to these theories, we propose the conformational change theory, wherein we posit that curiosity results in mental models with marked conceptual flexibility. We formalize curiosity as the process of building a growing knowledge network to quantitatively investigate information gap theory, compression progress theory, and the conformational change theory of curiosity. In knowledge networks, gaps can be identified as topological cavities, compression progress can be quantified using network compressibility, and flexibility can be measured as the number of conformational degrees of freedom. We leverage data acquired from the online encyclopedia Wikipedia to determine the degree to which each theory explains the growth of knowledge networks built by individuals and by collectives. Our findings lend support to a pluralistic view of curiosity, wherein intrinsically motivated information acquisition fills knowledge gaps and simultaneously leads to increasingly compressible and flexible knowledge networks. Across individuals and collectives, we determine the contexts in which each theoretical account may be explanatory, thereby clarifying their complementary and distinct explanations of curiosity. Our findings offer a novel network theoretical perspective on intrinsically motivated information acquisition that may harmonize with or compel an expansion of the traditional taxonomy of curiosity.

q-bio.NC↗

arXiv2022

A Neural Programming Language for the Reservoir Computer

From logical reasoning to mental simulation, biological and artificial neural systems possess an incredible capacity for computation. Such neural computers offer a fundamentally novel computing paradigm by representing data continuously and processing information in a natively parallel and distributed manner. To harness this computation, prior work has developed extensive training techniques to understand existing neural networks. However, the lack of a concrete and low-level programming language for neural networks precludes us from taking full advantage of a neural computing framework. Here, we provide such a programming language using reservoir computing -- a simple recurrent neural network -- and close the gap between how we conceptualize and implement neural computers and silicon computers. By decomposing the reservoir's internal representation and dynamics into a symbolic basis of its inputs, we define a low-level neural machine code that we use to program the reservoir to solve complex equations and store chaotic dynamical systems as random access memory (dRAM). Using this representation, we provide a fully distributed neural implementation of software virtualization and logical circuits, and even program a playable game of pong inside of a reservoir computer. Taken together, we define a concrete, practical, and fully generalizable implementation of neural computation.

cond-mat.dis-nn↗

arXiv2021

Citation inequity and gendered citation practices in contemporary physics

The historical and contemporary under-attribution of women's contributions to scientific scholarship is well-known and well-studied, with effects that are felt today in myriad ways by women scientists. One measure of this under-attribution is the so-called citation gap between men and women: the under-citation of papers authored by women relative to expected rates coupled with a corresponding over-citation of papers authored by men relative to expected rates. We explore the citation gap in contemporary physics, analyzing over one million articles published over the last 25 years in 35 physics journals that span a wide range of subfields. Using a model that predicts papers' expected citation rates according to a set of characteristics separate from author gender, we find a global bias wherein papers authored by women are significantly under-cited, and papers authored by men are significantly over-cited. Moreover, we find that citation behavior varies along several dimensions, such that imbalances differ according to who is citing, where they are citing, and how they are citing. Specifically, citation imbalance in favor of man-authored papers is highest for papers authored by men, papers published in general physics journals, and papers likely to be less familiar to citing authors. Our results suggest that, although deciding which papers to cite is an individual choice, the cumulative effects of these choices needlessly harm a subset of scholars. We discuss several strategies for the mitigation of these effects, including conscious behavioral changes at the individual, journal, and community levels.

physics.soc-ph↗

arXiv2021

Learning Continuous Chaotic Attractors with a Reservoir Computer

Neural systems are well known for their ability to learn and store information as memories. Even more impressive is their ability to abstract these memories to create complex internal representations, enabling advanced functions such as the spatial manipulation of mental representations. While recurrent neural networks (RNNs) are capable of representing complex information, the exact mechanisms of how dynamical neural systems perform abstraction are still not well-understood, thereby hindering the development of more advanced functions. Here, we train a 1000-neuron RNN -- a reservoir computer (RC) -- to abstract a continuous dynamical attractor memory from isolated examples of dynamical attractor memories. Further, we explain the abstraction mechanism with new theory. By training the RC on isolated and shifted examples of either stable limit cycles or chaotic Lorenz attractors, the RC learns a continuum of attractors, as quantified by an extra Lyapunov exponent equal to zero. We propose a theoretical mechanism of this abstraction by combining ideas from differentiable generalized synchronization and feedback dynamics. Our results quantify abstraction in simple neural systems, enabling us to design artificial RNNs for abstraction, and leading us towards a neural basis of abstraction.

cs.NE↗

arXiv2021

Variability in higher order structure of noise added to weighted networks

From spiking activity in neuronal networks to force chains in granular materials, the behavior of many real-world systems depends on a network of both strong and weak interactions. These interactions give rise to complex and higher-order system behaviors, and are encoded using data as the network's edges. However, distinguishing between true weak edges and low-weight edges caused by noise remains a challenge. We address this problem by examining the higher-order structure of noisy, weak edges added to model networks. We find that the structure of low-weight, noisy edges varies according to the topology of the model network to which it is added. By investigating this variation more closely, we see that at least three qualitative classes of noise structure emerge. Furthermore, we observe that the structure of noisy edges contains enough model-specific information to classify the model networks with moderate accuracy. Finally, we offer network generation rules that can drive different types of structure in added noisy edges. Our results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topology-dependent, and even useful entity in characterizing higher-order network interactions. Hence, we provide an alternate approach to noise management by embracing its role in such interactions.

q-bio.QM↗

arXiv2020

Path-dependent connectivity, not modularity, consistently predicts controllability of structural brain networks

The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the communication dynamics that can emerge therefrom is not well-understood. In addition to offering insight into the structure-function relationship of networked systems, such an understanding is a critical step towards the ability to manipulate the brain's large-scale dynamical activity in a targeted manner. We investigate the role of community structure in the controllability of structural brain networks. At the region level, we find that certain network measures of community structure are sometimes statistically correlated with measures of linear controllability. However, we then demonstrate that this relationship depends on the distribution of network edge weights. We highlight the complexity of the relationship between community structure and controllability by performing numerical simulations using canonical graph models with varying mesoscale architectures and edge weight distributions. Finally, we demonstrate that weighted subgraph centrality, a measure rooted in the graph spectrum, and which captures higher-order graph architecture, is a stronger and more consistent predictor of controllability. Our study contributes to an understanding of how the brain's diverse mesoscale structure supports transient communication dynamics.

q-bio.NC↗

arXiv2020

Teaching Recurrent Neural Networks to Modify Chaotic Memories by Example

The ability to store and manipulate information is a hallmark of computational systems. Whereas computers are carefully engineered to represent and perform mathematical operations on structured data, neurobiological systems perform analogous functions despite flexible organization and unstructured sensory input. Recent efforts have made progress in modeling the representation and recall of information in neural systems. However, precisely how neural systems learn to modify these representations remains far from understood. Here we demonstrate that a recurrent neural network (RNN) can learn to modify its representation of complex information using only examples, and we explain the associated learning mechanism with new theory. Specifically, we drive an RNN with examples of translated, linearly transformed, or pre-bifurcated time series from a chaotic Lorenz system, alongside an additional control signal that changes value for each example. By training the network to replicate the Lorenz inputs, it learns to autonomously evolve about a Lorenz-shaped manifold. Additionally, it learns to continuously interpolate and extrapolate the translation, transformation, and bifurcation of this representation far beyond the training data by changing the control signal. Finally, we provide a mechanism for how these computations are learned, and demonstrate that a single network can simultaneously learn multiple computations. Together, our results provide a simple but powerful mechanism by which an RNN can learn to manipulate internal representations of complex information, allowing for the principled study and precise design of RNNs.

cond-mat.dis-nn↗