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The sudden arrest of flow by formation of a stable arch over an outlet is a unique and characteristic feature of granular materials. Previous work suggests that grains near the outlet randomly sample configurational flow microstates until a clog-causing flow microstate is reached. However, factors that lead to clogging remain elusive. Here we experimentally observe over 50,000 clogging events for a tridisperse mixture of quasi-2D circular grains, and utilize a variety of machine learning (ML) methods to search for predictive signatures of clogging microstates. This approach fares just modestly better than chance. Nevertheless, our analysis using linear Support Vector Machines (SVMs) highlights the position of potential arch cornerstones as a key factor in clogging likelihood. We verify this experimentally by varying the position of a fixed (cornerstone) grain, and show that such a grain dictates the size of feasible flow-ending arches, and thus the time and mass of each flow. Positioning this grain correctly can even increase the ejected mass by over 50%. Our findings demonstrate that interpretable ML algorithms like SVMs can uncover meaningful physics even when their predictive power is below the standards of conventional ML practice., Comment: 16 pages, 11 figures

Probabilistic representation spaces convey information about a dataset, and to understand the effects of factors such as training loss and network architecture, we seek to compare the information content of such spaces. However, most existing methods to compare representation spaces assume representations are points, and neglect the distributional nature of probabilistic representations. Here, instead of building upon point-based measures of comparison, we build upon classic methods from literature on hard clustering. We generalize two information-theoretic methods of comparing hard clustering assignments to be applicable to general probabilistic representation spaces. We then propose a practical method of estimation that is based on fingerprinting a representation space with a sample of the dataset and is applicable when the communicated information is only a handful of bits. With unsupervised disentanglement as a motivating problem, we find information fragments that are repeatedly contained in individual latent dimensions in VAE and InfoGAN ensembles. Then, by comparing the full latent spaces of models, we find highly consistent information content across datasets, methods, and hyperparameters, even though there is often a point during training with substantial variety across repeat runs. Finally, we leverage the differentiability of the proposed method and perform model fusion by synthesizing the information content of multiple weak learners, each incapable of representing the global structure of a dataset. Across the case studies, the direct comparison of information content provides a natural basis for understanding the processing of information., Comment: Code: https://github.com/murphyka/representation-space-info-comparison

Equations of motion are developed for the oscillatory rotation of a disk suspended between twisted strings kept under tension by a hanging mass, to which additional forces may be applied. In the absence of forcing, damped harmonic oscillations are observed to decay with an exponential time envelope for two different string types. This is consistent with damping caused by string viscosity, rather than air turbulence, and may be quantified in terms of a quality factor. To test the proposed equation of motion and model for viscous damping within the string, we measure both the natural oscillation frequency and the quality factor for widely varied values of string length, string radius, disk moment of inertia, and hanging mass. The data are found to scale in good accord with predictions. A variation where rotational kinetic energy is converted back and forth to spring potential energy is also discussed., Comment: 7 pages, 3 figures, 1 table

Granular flows in small-outlet hoppers exhibit several characteristic but poorly understood behaviors: temporary clogs (pauses) that last for an extended period before flow spontaneously restarts, permanent clogs that last indefinitely, and non-Gaussian, non-monotonic flow-rate statistics. These aspects have been extensively studied independently, but a model of hopper flow that includes all three has not been formulated. Here, we introduce such a phenomenological model that provides a unifying dynamical explanation of all three behaviors: a coupling between the flow rate and a hidden configurational mode that controls the stability of clogs. In the theory, flow rate evolves according to Langevin dynamics with multiplicative noise and an absorbing state at zero flow, conditional on the hidden mode. The model fully reproduces the statistics of pause and clog events taken from a large ($>40,000$ flows) experimental dataset, including non-exponentially distributed clogging times and non-Gaussian flow rate distribution, and explains the stretched-exponential growth of the average clogging time with outlet size. Further, we highlight several microscopic configurational features of this hidden mode, including size and smoothness of the static arch structure formed during pauses and clogs. Our work provides a unifying framework for several poorly understood granular phenomena, and suggests numerous new paths toward further understanding of this complex system., Comment: 7 pages, 4 figures; SM included as an ancillary PDF file

Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic learning metamaterials offer potentially fast, efficient, and fault-tolerant hardware for analog machine learning, but existing implementations are linear, severely limiting their capabilities. These systems differ significantly from artificial neural networks as well as the brain, so the feasibility and utility of incorporating nonlinear elements have not been explored. Here we introduce a nonlinear learning metamaterial -- an analog electronic network made of self-adjusting nonlinear resistive elements based on transistors. We demonstrate that the system learns tasks unachievable in linear systems, including XOR and nonlinear regression, without a computer. We find our nonlinear learning metamaterial reduces modes of training error in order (mean, slope, curvature), similar to spectral bias in artificial neural networks. The circuitry is robust to damage, retrainable in seconds, and performs learned tasks in microseconds while dissipating only picojoules of energy across each transistor. This suggests enormous potential for fast, low-power computing in edge systems like sensors, robotic controllers, and medical devices, as well as manufacturability at scale for performing and studying emergent learning., Comment: 11 pages 8 figures

As the size and ubiquity of artificial intelligence and computational machine learning (ML) models grow, their energy consumption for training and use is rapidly becoming economically and environmentally unsustainable. Neuromorphic computing, or the implementation of ML in hardware, has the potential to reduce this cost. In particular, recent laboratory prototypes of self-learning electronic circuits, examples of ``physical learning machines," open the door to analog hardware that directly employs physics to learn desired functions from examples. In this work, we show that this hardware platform allows for even further reduction of energy consumption by using good initial conditions as well as a new learning algorithm. Using analytical calculations, simulation and experiment, we show that a trade-off emerges when learning dynamics attempt to minimize both the error and the power consumption of the solution--greater power reductions can be achieved at the cost of decreasing solution accuracy. Finally, we demonstrate a practical procedure to weigh the relative importance of error and power minimization, improving power efficiency given a specific tolerance to error., Comment: 15 pages, 7 figures

The conversion of raw images into quantifiable data can be a major hurdle in experimental research, and typically involves identifying region(s) of interest, a process known as segmentation. Machine learning tools for image segmentation are often specific to a set of tasks, such as tracking cells, or require substantial compute or coding knowledge to train and use. Here we introduce an easy-to-use (no coding required), image segmentation method, using a 15-layer convolutional neural network that can be trained on a laptop: Bellybutton. The algorithm trains on user-provided segmentation of example images, but, as we show, just one or even a portion of one training image can be sufficient in some cases. We detail the machine learning method and give three use cases where Bellybutton correctly segments images despite substantial lighting, shape, size, focus, and/or structure variation across the regions(s) of interest. Instructions for easy download and use, with further details and the datasets used in this paper are available at pypi.org/project/Bellybuttonseg., Comment: 6 Pages 3 Figures

The paper describes a study of wet foams in microgravity whose bubble size distribution evolves due to diffusive gas exchange. We focus on the comparison between the size of bubbles determined from images of the foam surface and the size of bubbles in the bulk foam, determined from Diffuse Transmission Spectroscopy (DTS). Extracting the bubble size distribution from images of a foam surface is difficult so we have used three different procedures : manual analysis, automatic analysis with a customized Python script and machine learning analysis. Once various pitfalls were identified and taken into account, all the three procedures yield identical results within error bars. DTS only allows the determination of an average bubble radius which is proportional to the photon transport mean free path $\ell^*$. The relation between the measured diffuse transmitted light intensity and {$\ell^*$} previously derived for slab-shaped samples of infinite lateral extent does not apply to the cuboid geometry of the cells used in the microgravity experiment. A new more general expression of the diffuse intensity transmitted with specific optical boundary conditions has been derived and applied to determine the average bubble radius. The temporal evolution of the average bubble radii deduced from DTS and of the same average radii of the bubbles measured at the sample surface are in very good agreement throughout the coarsening. Finally, ground experiments were performed to compare bubble size distributions in a bulk wet foam and at its surface at times so short that diffusive gas exchange is insignificant. They were found to be similar, confirming that bubbles seen at the surface are representative of the bulk foam bubbles.

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting., Comment: 27 pages, 17 figures + references and appendices, repo: https://github.com/google/BIG-bench

In a neuron network, synapses update individually using local information, allowing for entirely decentralized learning. In contrast, elements in an artificial neural network (ANN) are typically updated simultaneously using a central processor. Here we investigate the feasibility and effect of desynchronous learning in a recently introduced decentralized, physics-driven learning network. We show that desynchronizing the learning process does not degrade performance for a variety of tasks in an idealized simulation. In experiment, desynchronization actually improves performance by allowing the system to better explore the discretized state space of solutions. We draw an analogy between desynchronization and mini-batching in stochastic gradient descent, and show that they have similar effects on the learning process. Desynchronizing the learning process establishes physics-driven learning networks as truly fully distributed learning machines, promoting better performance and scalability in deployment., Comment: 6 pages 4 figures

Physical networks, such as biological neural networks, can learn desired functions without a central processor, using local learning rules in space and time to learn in a fully distributed manner. Learning approaches such as equilibrium propagation, directed aging, and coupled learning similarly exploit local rules to accomplish learning in physical networks such as mechanical, flow, or electrical networks. In contrast to certain natural neural networks, however, such approaches have so far been restricted to the quasistatic limit, where they learn on time scales slow compared to their physical relaxation. This quasistatic constraint slows down learning, limiting the use of these methods as machine learning algorithms, and potentially restricting physical networks that could be used as learning platforms. Here we explore learning in an electrical resistor network that implements coupled learning, both in the lab and on the computer, at rates that range from slow to far above the quasistatic limit. We find that up to a critical threshold in the ratio of the learning rate to the physical rate of relaxation, learning speeds up without much change of behavior or error. Beyond the critical threshold, the error exhibits oscillatory dynamics but the networks still learn successfully., Comment: 26 pages, 5 figures

We present a solvable model inspired by dimensional analysis for the time-dependent spreading of droplets that partially wet a substrate, where the spreading eventually stops and the contact angle reaches a nonzero equilibrium value. We separately consider small droplets driven by capillarity and large droplets driven by gravity. To explore both regimes, we first measure the equilibrium radius versus a comprehensive range of droplet volumes for four household fluids, and we compare the results with predictions based on minimizing the sum of gravitational and interfacial energies. The agreement is good, and gives a reliable measurement of an equilibrium contact angle that is consistent in both small and large droplet regimes. Next we use energy considerations to develop equations of motion for the time dependence of the spreading, in both regimes, where the driving forces are balanced against viscous drag in the bulk of the droplet and by friction at the moving contact line. Our approach leads to explicit prediction of the functional form of the spreading dynamics. It successfully describes prior data for a small capillary-driven droplet, and it fits well to new data we obtain for large gravity-driven droplets with a wide range of volumes.

In typical artificial neural networks, neurons adjust according to global calculations of a central processor, but in the brain neurons and synapses self-adjust based on local information. Contrastive learning algorithms have recently been proposed to train physical systems, such as fluidic, mechanical, or electrical networks, to perform machine learning tasks from local evolution rules. However, to date such systems have only been implemented in silico due to the engineering challenge of creating elements that autonomously evolve based on their own response to two sets of global boundary conditions. Here we introduce and implement a physics-driven contrastive learning scheme for a network of variable resistors, using circuitry to locally compare the response of two identical networks subjected to the two different sets of boundary conditions. Using this innovation, our system effectively trains itself, optimizing its resistance values without use of a central processor or external information storage. Once the system is trained for a specified allostery, regression, or classification task, the task is subsequently performed rapidly and automatically by the physical imperative to minimize power dissipation in response to the given voltage inputs. We demonstrate that, unlike typical computers, such learning systems are robust to extreme damage (and thus manufacturing defects) due to their decentralized learning. Our twin-network approach is therefore readily scalable to extremely large or nonlinear networks where its distributed nature will be an enormous advantage; a laboratory network of only 500 edges will already outpace its in silico counterpart., Comment: 11 pages 7 figures

Classically, the quantity of contact area $A_R$ between two bodies is considered a proxy for the force of friction. However, bond density across the interface - quality of contact - is also relevant, and contemporary debate often centers around the relative importance of these two factors. In this work, we demonstrate that a third factor, often overlooked, plays a significant role in static frictional strength: the distribution of contact. We perform static friction measurements, $\mu$, on three pairs of solid blocks while imaging the contact plane. By using linear regression on hundreds of image-$\mu$ pairs, we are able to predict future friction measurements with 3 to 7 times better accuracy than existing benchmarks, including total quantity of contact area. Our model has no access to quality of contact, and we therefore conclude that a large portion of the interfacial state is encoded in the spatial distribution of contact, rather than its quality or quantity., Comment: 6 pages 4 figures

The real area of contact of a frictional interface changes rapidly when the normal load is altered, and evolves slowly when normal load is held constant, aging over time. Traditionally, the total area of contact is considered a proxy for the frictional strength of the interface. Here we show that the state of a frictional interface is not entirely defined by the total real area of contact but depends on the geometrical nature of that contact as well. We directly visualize an interface between rough elastomers and smooth glass and identify that normal loading and frictional aging evolve the interface differently, even at a single contact level. We introduce a protocol wherein the real area of contact is held constant in time. Under these conditions, the interface is continually evolving; small contacts shrink and large contacts coarsen., Comment: 5 pages, 4 figures

We simultaneously measure the static friction and the real area of contact between two solid bodies. Under static conditions both quantities increase logarithmically in time, a phenomenon coined aging. Indeed, frictional strength is traditionally considered equivalent to the real area of contact. Here we show that this equivalence breaks down when a static shear load is applied during aging. The addition of such a shear load accelerates frictional aging while the aging rate of the real area of contact is unaffected. Moreover, a negative static shear - pulling instead of pushing - slows frictional aging, but similarly does not affect the aging of contacts. The origin of this shear effect on aging is geometrical. When shear load is increased, minute relative tilts between the two blocks prematurely erase interfacial memory prior to sliding, negating the effect of aging. Modifying the loading point of the interface eliminates these tilts and as a result frictional aging rate becomes insensitive to shear. We also identify a secondary memory-erasure effect that remains even when all tilts are eliminated and show that this effect can be leveraged to accelerate aging by cycling between two static shear loads., Comment: 5 pages, 3 figures

Many phenomena of interest in nature and industry occur rapidly and are difficult and cost-prohibitive to visualize properly without specialized cameras. Here we describe in detail the Virtual Frame Technique (VFT), a simple, useful, and accessible form of compressed sensing that increases the frame acquisition rate of any camera by several orders of magnitude by leveraging its dynamic range. VFT is a powerful tool for capturing rapid phenomenon where the dynamics facilitate a transition between two states, and are thus binary. The advantages of VFT are demonstrated by examining such dynamics in five physical processes at unprecedented rates and spatial resolution: fracture of an elastic solid, wetting of a solid surface, rapid fingerprint reading, peeling of adhesive tape, and impact of an elastic hemisphere on a hard surface. We show that the performance of the VFT exceeds that of any commercial high speed camera not only in rate of imaging but also in field of view, achieving a 65MHz frame rate at 4MPx resolution. Finally, we discuss the performance of the VFT with several commercially available conventional and high-speed cameras. In principle, modern cell phones can achieve imaging rates of over a million frames per second using the VFT., Comment: 7 Pages, 4 Figures, 1 Supplementary Video

We measure the static frictional resistance and the real area of contact between two solid blocks subjected to a normal load. We show that following a two-step change in the normal load the system exhibits nonmonotonic aging and memory effects, two hallmarks of glassy dynamics. These dynamics are strongly influenced by the discrete geometry of the frictional interface, characterized by the attachment and detachment of unique microcontacts. The results are in good agreement with a theoretical model we propose that incorporates this geometry into the framework recently used to describe Kovacs-like relaxation in glasses as well as thermal disordered systems. These results indicate that a frictional interface is a glassy system and strengthen the notion that nonmonotonic relaxation behavior is generic in such systems., Comment: 5 pages, 4 figures