Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session D07: Learning in Physical Systems without NeuronsFocus
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Sponsoring Units: DSOFT GSNP Chair: Sam Dillavou; Menachem Stern Room: Room 130 |
Monday, March 6, 2023 3:00PM - 3:36PM |
D07.00001: Equilibrium Propagation: A Physics-Grounded Theory of Computation and Learning Invited Speaker: Benjamin Scellier We present a mathematical framework of computation and learning grounded in physical principles, called "equilibrium propagation" (Eqprop). This framework is compatible with gradient-descent optimization -- the workhorse of deep learning -- but in Eqprop, inference and gradient computation are achieved using the same physical laws, and the learning rule for each trainable parameter (or `weight') is local. We apply Eqprop to a class of physical systems dubbed "deep resistive networks" (DRNs), i.e. electrical circuits composed of resistors and diodes, in which the conductances of variables resistors play the role of trainable parameters, and diodes play the role of nonlinearities. We show that DRNs have another essential feature of deep learning: they are universal approximators (i.e. they can represent arbitrary input-output functions), like deep neural networks are. We also present a fast algorithm to simulate DRNs and Eqprop on digital computers, and we demonstrate the potential of the framework on standard machine learning benchmarks. Altogether, we contend that our framework can guide the development of fast, compact and low-power hardware for AI (i.e. "learning machines"), in which inference and learning are performed efficiently. Such hardware is expected to be several orders of magnitude faster and more energy-efficient than conventional neural networks run and trained on GPUs. |
Monday, March 6, 2023 3:36PM - 3:48PM |
D07.00002: Frequency propagation: Multi-mechanism learning in nonlinear physical networks Vidyesh Rao Anisetti We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency, and an error current is applied at a set of output nodes at another frequency. The voltage response of the circuit to these boundary currents is the superposition of an 'activation signal' and an 'error signal' whose coefficients can be read in different frequencies of the frequency domain. Each conductance is updated proportionally to the product of the two coefficients. The learning rule is local and proved to perform gradient descent on a loss function. We argue that frequency propagation is an instance of a multi-mechanism learning strategy for physical networks, be it resistive, elastic, or flow networks. Multi-mechanism learning strategies incorporate at least two physical quantities, potentially governed by independent physical mechanisms, to act as activation and error signals in the training process. Locally available information about these two signals is then used to update the trainable parameters to perform gradient descent. We demonstrate how earlier work implementing learning via chemical signaling in flow networks [1] also falls under the rubric of multi-mechanism learning. |
Monday, March 6, 2023 3:48PM - 4:00PM |
D07.00003: Physical learning of energy-efficient solutions Menachem Stern, Sam J Dillavou, Douglas J Durian, Andrea J Liu Unlike an artificial neural network, the brain does not need an accompanying processor in order to learn. The ability to learn via local rules instead of a processor endows the brain with a vast power efficiency advantage compared to artificial neural networks, whose high power consumption constitutes a large economic and environmental burden. Physical learning systems that use physics-enabled local rules to replace processors have a similar power advantage. Here we show that power consumption can be lowered even further in physical learning networks. We train both experimental and computational physical networks not only for good performance on desired tasks, but also for energy-efficient solutions. This goal is achieved through explicit regularization of the local learning rules, promoting the optimization of the dissipated power together with performance. We describe the regularized learning dynamics and discuss how regularization leads to a trade-off between task performance and energy efficiency. In realistic noisy situations, regularization may improve energy efficiency at no penalty to performance. Finally, we propose a simple and practical training method that yields energy-efficient solutions in systems ranging from electronic circuits to mechanical spring networks. |
Monday, March 6, 2023 4:00PM - 4:12PM |
D07.00004: Persistent Homology Analysis of Learned Tasks in Physical Learning Systems Felipe Martins, Andrea J Liu Recent work has shown that physical systems such as mechanical, flow and electrical networks |
Monday, March 6, 2023 4:12PM - 4:24PM |
D07.00005: The effect of learning on information content in learning machines Ben Pisanty, Menachem Stern, Andrea J Liu Recent work has demonstrated the ability to train mechanical, flow, and electrical networks to perform desired tasks using local learning rules. The ability to perform a task is a collective property of the network that arises from the interactions among the edges. Here we use information measures to study the learning process, starting with lossless compression of the network’s response. A flow network on a square lattice makes a perfect candidate for this study for its simplicity and trainability. We train ensembles of networks to deliver specified pressures at specified output nodes in response to specified pressures at input nodes, and observe the evolution of the information content during training, and its relation to system size and task complexity. |
Monday, March 6, 2023 4:24PM - 4:36PM |
D07.00006: Transistor-Based Self-Learning Networks Sam J Dillavou, Benjamin Beyer, Menachem Stern, Marc Z Miskin, Andrea J Liu, Douglas J Durian Artificial neural networks are powerful tools with an enormous breadth of uses, but their current implementation is reliant on a computational bottleneck - the processor. This restriction is costly both in speed and energy efficiency, and as a result there has been a push to develop distributed learning systems that do not require a processor or external memory. In previous work [1-3] we demonstrated the feasibility of a laboratory system that harnesses physics to perform the forward `computation’ and also exploits physics to enable local learning rules. When each edge of this system, an electrical network of variable resistors, follows these rules independently, the ensemble as a whole approximates gradient descent. Here we demonstrate the second generation implementation of such a system, which uses transistors as variable resistors. The laboratory network of 32 identical repeated edges is capable of performing non-trivial tasks, like data classification, and non-linear tasks, like XOR, without the aid of a processor. The new network is over 1000x faster than the first generation, and already outpaces its in silico counterpart. Furthermore, the new design lends itself easily to micro fabrication. This is important because the speed advantage is expected to grow with the size of the network. We observe the system's dynamics during learning and discuss its scalability, power consumption, and robustness. |
Monday, March 6, 2023 4:36PM - 4:48PM |
D07.00007: Physical learning at nonzero temperatures Jovana Andrejevic, Purba Chatterjee, Sidney R Nagel, Andrea J Liu Biological processes in nature are remarkably robust to noise. One such example is protein allostery, in which the binding of a molecule at one site of the protein induces a nonlocal response at a distant site. The long-ranged communication required for this interaction to occur persists despite thermal fluctuations. Although such communication pathways are not yet fully understood, allosteric mechanisms have been successfully encoded at effectively zero temperature in computational models as well as physical realizations. Here, by examining the role of temperature on physical learning, we investigate whether these long-ranged interactions are as robust to thermal fluctuations as their biological counterparts. We use elastic networks as simple, mechanical analogs of physical systems and examine the ability to retain allosteric and auxetic responses that were encoded at zero temperature. We observe that target responses trained using local learning rules are robust to thermal fluctuations up to a certain temperature. Finally, we explore the extent to which the learning itself can occur at nonzero temperature. |
Monday, March 6, 2023 4:48PM - 5:00PM |
D07.00008: Electrochemical potential enables dormant spores to integrate environmental signals Leticia Galera-Laporta, Kaito Kikuchi, Colleen Weatherwax, Jamie Y Lam, Eun Chae Moon, Emmanuel A Theodorakis, Jordi Garcia-Ojalvo, Gürol M Süel The dormant state of bacterial spores is generally thought to be devoid of biological activity. We show that despite continued dormancy, spores can integrate environmental signals over time through a pre-existing electrochemical potential. Specifically, we studied thousands of individual Bacillus subtilis spores that remain dormant when exposed to transient nutrient pulses. Guided by a mathematical model of bacterial electrophysiology, we modulated the decision to exit dormancy by genetically and chemically targeting potassium ion flux. We confirmed that short nutrient pulses result in step-like changes in the electrochemical potential of persistent spores. During dormancy, spores thus gradually release their stored electrochemical potential to integrate extracellular information over time. These findings reveal a decision-making mechanism that operates in physiologically inactive cells. |
Monday, March 6, 2023 5:00PM - 5:12PM |
D07.00009: Bounds on Predictive Capabilities of Driven Markov Systems Ugur Cetiner, Lisa Duan, Jeremy Gunawardena All living systems gather information about their environment but it remains an open question whether there are fundamental limits on this process. We used coupled Markov chains to quantify the predictive capabilities of a system that evolves under the influence of a stochastically changing environment. We assumed that the environmental states change according to a fixed transition matrix, while the single-step jump probabilities of the system depend on the state of the environment. Because of this coupling, the system’s states carry information about the future environmental states. Using the tools of information theory and chaotic dynamics, we prove that the predictive power of a system is bounded by the stored information, a dynamical invariant of the environment. Hence, there is a limit on how much systems can learn about a given environment regardless of the complexity of systems or the way that they are coupled to the environment. Interestingly, for certain detailed balanced environments, the stored information can be zero, indicating that no system can extract useful information about the future of these environments. Our results reveal a delicate interplay between energy expenditure and information-processing capabilities of coupled Markov systems. |
Monday, March 6, 2023 5:12PM - 5:24PM |
D07.00010: Driving the most marginally stable variables as a paradigm for learning, memory, and optimization Stefan Boettcher It is shown that an extremally driven dynamics, which selectively moves in each update only the most unstable variables without prescribing any specific target state, can achieve a highly correlated state with long-term memory that allows to accomplish complex artificial intelligence tasks such solving hard optimization problems, better than current machine learning methods [1]. As an example, we discuss the approximation of spin-glass ground states, an NP-hard combinatorial problem, with the Extremal Optimization heuristic (EO) [2]. Inspired by the extremally driven dynamics in the Bak-Sneppen model of Self-Organized Criticality, the individual spin variables are ordered according to their energetic cost to the overall Hamiltonian and selectively updated with a bias towards moving poorly adapted variables. Simulations of EO on spin glass instances show that such a ranking of variables achieves broadly distributed return times between activation of variables, thus, preserving a hierarchy of memories of well-adapted variables within a configuration, as well as an efficient exploration of complex ("glassy") energy landscapes, exemplified by a stretched-exponential autocorrelation function. |
Monday, March 6, 2023 5:24PM - 5:36PM |
D07.00011: A local learning rule for training precise stress patterns Daniel Hexner We develop a simple local learning rule that allows us to encode desired stress patterns in a disordered network of springs. Our goal is to control the stresses on a subset of the bonds, which we call targets. The remaining bonds are the learning degrees of freedom and each is assumed to be a spring and dashpot in series. By applying training stresses to the targets we cause the system to evolve until ultimately, in force balance, the system acquires the desired stresses. We show that the system is able to learn random stress patterns to computer precision. Training is successful for a large number of bonds, approaching the theoretical limit dictated by the Maxwell-Calladine theorem. We conclude by demonstrating that our training rule is robust and applicable to dashpots with a yielding stress. Our work is another example of ordinary matter whose properties can be precisely controlled through training rather than by design. |
Monday, March 6, 2023 5:36PM - 5:48PM |
D07.00012: Self-learning mechanical circuits Vishal P Patil, Ian Ho, Manu Prakash Mechanical adaptive matter is ubiquitous in biological systems, from cytoplasm and biofilms to tissues and flocks. Despite important progress in analyzing the complexity of such structures, understanding how adaptive materials can continually learn and respond to their environment without supervision remains a central challenge. Here, we first construct fundamental mechanical unit operators for adaptive elastic materials and implement one such operator in a physical system. Next, we combine dynamical systems theory with our experimental realizations of adaptive elasticity to understand how elastic objects can be used as computational substrates. In particular, we develop a theoretical framework for studying a class of adaptive elastic materials and demonstrate how directed information propagation within a network leads to learning behavior. By constructing physical realizations of learning adaptive networks, we exhibit the range of computational tasks that such a network can solve. Our results suggest possible routes towards embedding distributed computational power in soft, mechanical materials. |
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