arXiv subjects

James P. Crutchfield

Publications and source records attributed to James P. Crutchfield.

At least 55 records · Page 3Linked to original sources

arXiv2021

Topology, Convergence, and Reconstruction of Predictive States

Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models. We examine the conditions under which they can be reliably reconstructed from time-series data, showing that convergence of predictive states can be achieved from empirical samples in the weak topology of measures. Moreover, predictive states may be represented in Hilbert spaces that replicate the weak topology. We mathematically explain how these representations are particularly beneficial when reconstructing high-memory processes and connect them to reproducing kernel Hilbert spaces.

cond-mat.stat-mech↗

arXiv2021

Ambiguity Rate of Hidden Markov Processes

The $ε$-machine is a stochastic process' optimal model -- maximally predictive and minimal in size. It often happens that to optimally predict even simply-defined processes, probabilistic models -- including the $ε$-machine -- must employ an uncountably-infinite set of features. To constructively work with these infinite sets we map the $ε$-machine to a place-dependent iterated function system (IFS) -- a stochastic dynamical system. We then introduce the ambiguity rate that, in conjunction with a process' Shannon entropy rate, determines the rate at which this set of predictive features must grow to maintain maximal predictive power. We demonstrate, as an ancillary technical result which stands on its own, that the ambiguity rate is the (until now missing) correction to the Lyapunov dimension of an IFS's attractor. For a broad class of complex processes and for the first time, this then allows calculating their statistical complexity dimension -- the information dimension of the minimal set of predictive features.

cond-mat.stat-mech↗

arXiv2021

Time Symmetries of Memory Determine Thermodynamic Efficiency

While Landauer's Principle sets a lower bound for the work required for a computation, that work is recoverable for efficient computations. However, practical physical computers, such as modern digital computers or biochemical systems, are subject to constraints that make them inefficient -- irreversibly dissipating significant energy. Recent results show that the dissipation in such systems is bounded by the nonreciprocity of the embedded computation. We investigate the consequences of this bound for different types of memory, showing that different memory devices are better suited for different computations. This correspondence comes from the time-reversal symmetries of the memory, which depend on whether information is stored positionally or magnetically. This establishes that the time symmetries of the memory device play an essential roll in determining energetics. The energetic consequences of time symmetries are particularly pronounced in nearly deterministic computations, where the cost of computing diverges as minus log of the error rate. We identify the coefficient of that divergence as the dissipation divergence. We find that the dissipation divergence may be zero for a computation when implemented in one type of memory while it's maximal when implemented with another. Given flexibility in the type of memory, the dissipation divergence is bounded below by the average state compression of the computation. Moreover, we show how to explicitly construct the memory to achieve this minimal dissipation. As a result, we find that logically reversible computations are indeed thermodynamically efficient, but logical irreversibility comes at a much higher cost than previously anticipated.

cond-mat.stat-mech↗

arXiv2021

Modes of Information Flow in Collective Cohesion

Pairwise interactions between individuals are taken as fundamental drivers of collective behavior responsible for group cohesion and decision-making. While an individual directly influences only a few neighbors, over time indirect influences penetrate a much larger group. The abiding question is how this spread of influence comes to affect the collective. One or a few individuals are often identified as leaders, being more influential than others. Transfer entropy and time-delayed mutual information are used to identify underlying asymmetric interactions, such as leader-follower classification in aggregated individuals--cells, birds, fish, and animals. However, these conflate distinct functional modes of information flow between individuals. Computing information measures conditioning on multiple agents requires the proper sampling of a probability distribution whose dimension grows exponentially with the number of agents being conditioned on. Employing simple models of interacting self-propelled particles, we examine the pitfalls of using time-delayed mutual information and transfer entropy to quantify the strength of influence from a leader to a follower. Surprisingly, one must be wary of these pitfalls even for two interacting particles. As an alternative we decompose transfer entropy and time-delayed mutual information into intrinsic, shared, and synergistic modes of information flow. The result not only properly reveals the underlying effective interactions, but also facilitates a more detailed diagnosis of how individual interactions lead to collective behavior. This exposes the role of individual and group memory in collective behaviors. In addition, we demonstrate in a multi-agent system how knowledge of the decomposed information modes between a single pair of agents reveals the nature of many-body interactions without conditioning on additional agents.

nlin.AO↗

arXiv2021

Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are dramatic. Their predictive models are generically infinite-state. And, until recently, one could determine neither their intrinsic randomness nor structural complexity. The prequel, though, introduced methods to accurately calculate the Shannon entropy rate (randomness) and to constructively determine their minimal (though, infinite) set of predictive features. Leveraging this, we address the complementary challenge of determining how structured hidden Markov processes are by calculating their statistical complexity dimension -- the information dimension of the minimal set of predictive features. This tracks the divergence rate of the minimal memory resources required to optimally predict a broad class of truly complex processes.

cond-mat.stat-mech↗

arXiv2020

Refining Landauer's Stack: Balancing Error and Dissipation When Erasing Information

Nonequilibrium information thermodynamics determines the minimum energy dissipation to reliably erase memory under time-symmetric control protocols. We demonstrate that its bounds are tight and so show that the costs overwhelm those implied by Landauer's energy bound on information erasure. Moreover, in the limit of perfect computation, the costs diverge. The conclusion is that time-asymmetric protocols should be developed for efficient, accurate thermodynamic computing. And, that Landauer's Stack -- the full suite of theoretically-predicted thermodynamic costs -- is ready for experimental test and calibration.

cond-mat.stat-mech↗

arXiv2020

Spacetime Autoencoders Using Local Causal States

Local causal states are latent representations that capture organized pattern and structure in complex spatiotemporal systems. We expand their functionality, framing them as spacetime autoencoders. Previously, they were only considered as maps from observable spacetime fields to latent local causal state fields. Here, we show that there is a stochastic decoding that maps back from the latent fields to observable fields. Furthermore, their Markovian properties define a stochastic dynamic in the latent space. Combined with stochastic decoding, this gives a new method for forecasting spacetime fields.

cs.LG↗

arXiv2020

Non-Markovian Momentum Computing: Universal and Efficient

All computation is physically embedded. Reflecting this, a growing body of results embraces rate equations as the underlying mechanics of thermodynamic computation and biological information processing. Strictly applying the implied continuous-time Markov chains, however, excludes a universe of natural computing. We show that expanding the toolset to continuous-time hidden Markov chains substantially removes the constraints. The general point is made concrete by our analyzing two eminently-useful computations that are impossible to describe with a set of rate equations over the memory states. We design and analyze a thermodynamically-costless bit flip, providing a first counterexample to rate-equation modeling. We generalize this to a costless Fredkin gate---a key operation in reversible computing that is computation universal. Going beyond rate-equation dynamics is not only possible, but necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.

cond-mat.stat-mech↗

arXiv2020

Shannon Entropy Rate of Hidden Markov Processes

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge's second part on structure.

nlin.CD↗

arXiv2020

Beyond Density Matrices: Geometric Quantum States

A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical realization. Conveniently, when working only with the statistical outcomes of projective and positive operator-valued measurements this is not a hindrance. To track ensemble realizations and so remove the shortcoming, we explore geometric quantum states and explain their physical significance. We emphasize two main consequences: one in quantum state manipulation and one in quantum thermodynamics.

quant-ph↗

arXiv2020

Functional Thermodynamics of Maxwellian Ratchets: Constructing and Deconstructing Patterns, Randomizing and Derandomizing Behaviors

Maxwellian ratchets are autonomous, finite-state thermodynamic engines that implement input-output informational transformations. Previous studies of these "demons" focused on how they exploit environmental resources to generate work: They randomize ordered inputs, leveraging increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir while respecting both Liouvillian state-space dynamics and the Second Law. However, to date, correctly determining such functional thermodynamic operating regimes was restricted to a very few engines for which correlations among their information-bearing degrees of freedom could be calculated exactly and in closed form---a highly restricted set. Additionally, a key second dimension of ratchet behavior was largely ignored---ratchets do not merely change the randomness of environmental inputs, their operation constructs and deconstructs patterns. To address both dimensions, we adapt recent results from dynamical-systems and ergodic theories that efficiently and accurately calculate the entropy rates and the rate of statistical complexity divergence of general hidden Markov processes. In concert with the Information Processing Second Law, these methods accurately determine thermodynamic operating regimes for finite-state Maxwellian demons with arbitrary numbers of states and transitions. In addition, they facilitate analyzing structure versus randomness trade-offs that a given engine makes. The result is a greatly enhanced perspective on the information processing capabilities of information engines. As an application, we give a thorough-going analysis of the Mandal-Jarzynski ratchet, demonstrating that it has an uncountably-infinite effective state space.

cond-mat.stat-mech↗

arXiv2020

Correlated structural evolution within multiplex networks

Many natural, engineered, and social systems can be represented using the framework of a layered network, where each layer captures a different type of interaction between the same set of nodes. The study of such multiplex networks is a vibrant area of research. Yet, understanding how to quantify the correlations present between pairs of layers, and more so present in their co-evolution, is lacking. Such methods would enable us to address fundamental questions involving issues such as function, redundancy and potential disruptions. Here we show first how the edge-set of a multiplex network can be used to construct an estimator of a joint probability distribution describing edge existence over all layers. We then adapt an information-theoretic measure of general correlation called the conditional mutual information, which uses the estimated joint probability distribution, to quantify the pairwise correlations present between layers. The pairwise comparisons can also be temporal, allowing us to identify if knowledge of a certain layer can provide additional information about the evolution of another layer. We analyze datasets from three distinct domains---economic, political, and airline networks---to demonstrate how pairwise correlation in structure and dynamical evolution between layers can be identified and show that anomalies can serve as potential indicators of major events such as shocks.

physics.soc-ph↗

arXiv2020

The Hidden Fragility of Complex Systems -- Consequences of Change, Changing Consequences

Short-term survival and an exuberant plunge into building our future are generating a new kind of unintended consequence -- hidden fragility. This is a direct effect of the sophistication and structural complexity of the socio-technical systems humans create. It is inevitable. And so the challenge is, How much can we understand and predict about these systems and about the social dynamics that lead to their construction?

physics.soc-ph↗

arXiv2020

Variations on a Demonic Theme: Szilard's Other Engines

Szilard's now-famous single-molecule engine was only the first of three constructions he introduced in 1929 to resolve several paradoxes arising from Maxwell's demon. We analyze Szilard's remaining two demon models. We show that the second one, though a markedly different implementation employing a population of distinct molecular species and semi-permeable membranes, is informationally and thermodynamically equivalent to an ideal gas of the single-molecule engines. Since it is a gas of noninteracting particles one concludes, following Boyd and Crutchfield, that (i) it reduces to a chaotic dynamical system---called the Szilard Map, a composite of three piecewise linear maps that implement the thermodynamic transformations of measurement, control, and erasure; (ii) its transitory functioning as an engine that converts disorganized heat energy to work is governed by the Kolmogorov-Sinai entropy rate; (iii) the demon's minimum necessary "intelligence" for optimal functioning is given by the engine's statistical complexity, and (iv) its functioning saturates thermodynamic bounds and so it is a minimal, optimal implementation. We show that Szilard's third model is rather different and addresses the fundamental issue, raised by the first two, of measurement in and by thermodynamic systems and entropy generation. Taken together, Szilard's suite of constructions lays out a range of possible realizations of Maxwellian demons that anticipated by almost two decades Shannon's and Wiener's concept of information as surprise and cybernetics' notion of functional information. This, in turn, gives new insight into engineering implementations of novel nanoscale information engines that leverage microscopic fluctuations and into the diversity of thermodynamic mechanisms and intrinsic computation harnessed in physical, molecular, biochemical, and biological systems.

cond-mat.stat-mech↗

arXiv2020

Thermal Efficiency of Quantum Memory Compression

Quantum coherence allows for reduced-memory simulators of classical processes. Using recent results in single-shot quantum thermodynamics, we derive a minimal work cost rate for quantum simulators that is quasistatically attainable in the limit of asymptotically-infinite parallel simulation. Comparing this cost with the classical regime reveals that quantizing classical simulators not only results in memory compression but also in reduced dissipation. We explore this advantage across a suite of representative examples.

quant-ph↗

arXiv2020

Thermodynamically-Efficient Local Computation and the Inefficiency of Quantum Memory Compression

Modularity dissipation identifies how locally-implemented computation entails costs beyond those required by Landauer's bound on thermodynamic computing. We establish a general theorem for efficient local computation, giving the necessary and sufficient conditions for a local operation to have zero modularity cost. Applied to thermodynamically-generating stochastic processes it confirms a conjecture that classical generators are efficient if and only if they satisfy retrodiction, which places minimal memory requirements on the generator. This extends immediately to quantum computation: Any quantum simulator that employs quantum memory compression cannot be thermodynamically efficient.

quant-ph↗

arXiv2019

Nonequilibrium thermodynamics of erasure with superconducting flux logic

We implement a thermal-fluctuation driven logical bit reset on a superconducting flux logic cell. We show that the logical state of the system can be continuously monitored with only a small perturbation to the thermally activated dynamics at 500 mK. We use the trajectory information to derive a single-shot estimate of the work performed on the system per logical cycle. We acquire a sample of $10^5$ erasure trajectories per protocol, and show that the work histograms agree with both microscopic theory and global fluctuation theorems. The results demonstrate how to design and diagnose complex, high-speed, and thermodynamically efficient computing using superconducting technology.

cond-mat.mes-hall↗

arXiv2019

DisCo: Physics-Based Unsupervised Discovery of Coherent Structures in Spatiotemporal Systems

Extracting actionable insight from complex unlabeled scientific data is an open challenge and key to unlocking data-driven discovery in science. Complementary and alternative to supervised machine learning approaches, unsupervised physics-based methods based on behavior-driven theories hold great promise. Due to computational limitations, practical application on real-world domain science problems has lagged far behind theoretical development. We present our first step towards bridging this divide - DisCo - a high-performance distributed workflow for the behavior-driven local causal state theory. DisCo provides a scalable unsupervised physics-based representation learning method that decomposes spatiotemporal systems into their structurally relevant components, which are captured by the latent local causal state variables. Complex spatiotemporal systems are generally highly structured and organize around a lower-dimensional skeleton of coherent structures, and in several firsts we demonstrate the efficacy of DisCo in capturing such structures from observational and simulated scientific data. To the best of our knowledge, DisCo is also the first application software developed entirely in Python to scale to over 1000 machine nodes, providing good performance along with ensuring domain scientists' productivity. We developed scalable, performant methods optimized for Intel many-core processors that will be upstreamed to open-source Python library packages. Our capstone experiment, using newly developed DisCo workflow and libraries, performs unsupervised spacetime segmentation analysis of CAM5.1 climate simulation data, processing an unprecedented 89.5 TB in 6.6 minutes end-to-end using 1024 Intel Haswell nodes on the Cori supercomputer obtaining 91% weak-scaling and 64% strong-scaling efficiency.

physics.comp-ph↗