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Abstract The backpropagation method has enabled transformative uses of neural networks. Alternatively, for energy-based models, local learning methods involving only nearby neurons offer benefits in terms of decentralized training, and allow for the possibility of learning in computationally-constrained substrates. One class of local learning methodscontraststhe desired, clamped behavior with spontaneous, free behavior. However, directly contrasting free and clamped behaviors requires explicit memory. Here, we introduce ‘Temporal Contrastive Learning’, an approach that uses integral feedback in each learning degree of freedom to provide a simple form of implicit non-equilibrium memory. During training, free and clamped behaviors are shown in a sawtooth-like protocol over time. When combined with integral feedback dynamics, these alternating temporal protocols generate an implicit memory necessary for comparing free and clamped behaviors, broadening the range of physical and biological systems capable of contrastive learning. Finally, we show that non-equilibrium dissipation improves learning quality and determine a Landauer-like energy cost of contrastive learning through physical dynamics. 

Abstract The moth fly,Clogmia albipunctata, is a common synanthropic insect with a worldwide range that lives in nearly any area with moist, decaying organic matter. These habitats comprise both smooth, slippery substrates (e.g., bathroom drains) and heterogeneous, bumpy ground (e.g., soil in plant pots). By using terrain of varying levels of roughness, we focus specifically on how substrate roughness at the approximate size scale of the organism affects kinematics and coordination in adult moth flies. Finally, we compare and contrast our characterizations of locomotion inC. albipunctatawith previous work of insect walking in naturalistic environments. 

Abstract Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation^1–6. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state⁷. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems^8–12. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales⁴. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows^13–19, stellar plasma such as the solar wind^20–22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades^23–25. 

All biological systems are subject to perturbations arising from thermal fluctuations, external environments, or mutations. Yet, while biological systems consist of thousands of interacting components, recent high-throughput experiments have shown that their response to perturbations is surprisingly low dimensional: confined to only a few stereotyped changes out of the many possible. In this review, we explore a unifying dynamical systems framework—soft modes—to explain and analyze low dimensionality in biology, from molecules to ecosystems. We argue that this soft mode framework makes nontrivial predictions that generalize classic ideas from developmental biology to disparate systems, namely phenocopying, dual buffering, and global epistasis. While some of these predictions have been borne out in experiments, we discuss how soft modes allow for a surprisingly far-reaching and unifying framework in which to analyze data from protein biophysics to microbial ecology. 

Microbial ecosystems are commonly modeled by fixed interactions between species in steady exponential growth states. However, microbes in exponential growth often modify their environments so strongly that they are forced out of the growth state into stressed, nongrowing states. Such dynamics are typical of ecological succession in nature and serial-dilution cycles in the laboratory. Here, we introduce a phenomenological model, the Community State Model, to gain insight into the dynamic coexistence of microbes due to changes in their physiological states during cyclic succession. Our model specifies the growth preference of each species along a global ecological coordinate, taken to be the biomass density of the community, but is otherwise agnostic to specific interactions (e.g., nutrient starvation, stress, aggregation), in order to focus on self-consistency conditions on combinations of physiological states, “community states,” in a stable ecosystem. We identify three key features of such dynamical communities that contrast starkly with steady-state communities: enhanced community stability through staggered dominance of different species in different community states, increased tolerance of community diversity to fast growing species dominating distinct community states, and increased requirement of growth dominance by late-growing species. These features, derived explicitly for simplified models, are proposed here as principles aiding the understanding of complex dynamical communities. Our model shifts the focus of ecosystem dynamics from bottom–up studies based on fixed, idealized interspecies interaction to top–down studies based on accessible macroscopic observables such as growth rates and total biomass density, enabling quantitative examination of community-wide characteristics. 

Information is an important resource. Storing and retrieving information faithfully are huge challenges and many methods have been developed to understand the principles behind robust information processing. In this review, we focus on information storage and retrieval from the perspective of energetics, dynamics, and statistical mechanics. We first review the Hopfield model of associative memory, the classic energy-based model of memory. We then discuss generalizations and physical realizations of the Hopfield model. Finally, we highlight connections to energy-based neural networks used in deep learning. We hope this review inspires new directions along the lines of information storage and retrieval in physical systems. 

A core problem in systems and circuits neuroscience is deciphering the origin of shared dynamics in neuronal activity: Do they emerge through local network interactions, or are they inherited from external sources? We explore this question with large-scale networks of spatially ordered spiking neuron models where a downstream network receives input from an upstream sender network. We show that linear measures of the communication between the sender and receiver networks can discriminate between emergent or inherited population dynamics. A match in the dimensionality of the sender and receiver population activities promotes faithful communication. In contrast, a nonlinear mapping between the sender to receiver activity, for example, through downstream emergent population-wide fluctuations, can impair linear communication. Our work exposes the benefits and limitations of linear measures when analyzing between-area communication in circuits with rich population-wide neuronal dynamics.