21,601 research outputs found
Balancing Error and Dissipation in Computing
Modern digital electronics support remarkably reliable computing, especially
given the challenge of controlling nanoscale logical components that interact
in fluctuating environments. However, we demonstrate that the high-reliability
limit is subject to a fundamental error-energy-efficiency tradeoff that arises
from time-symmetric control: Requiring a low probability of error causes energy
consumption to diverge as logarithm of the inverse error rate for nonreciprocal
logical transitions. The reciprocity (self-invertibility) of a computation is a
stricter condition for thermodynamic efficiency than logical reversibility
(invertibility), the latter being the root of Landauer's work bound on erasing
information. Beyond engineered computation, the results identify a generic
error-dissipation tradeoff in steady-state transformations of genetic
information carried out by biological organisms. The lesson is that computation
under time-symmetric control cannot reach, and is often far above, the Landauer
limit. In this way, time-asymmetry becomes a design principle for
thermodynamically efficient computing.Comment: 19 pages, 8 figures; Supplementary material 7 pages, 1 figure;
http://csc.ucdavis.edu/~cmg/compmech/pubs/tsp.ht
Collective behaviours: from biochemical kinetics to electronic circuits
In this work we aim to highlight a close analogy between cooperative
behaviors in chemical kinetics and cybernetics; this is realized by using a
common language for their description, that is mean-field statistical
mechanics. First, we perform a one-to-one mapping between paradigmatic
behaviors in chemical kinetics (i.e., non-cooperative, cooperative,
ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics
(i.e., paramagnetic, high and low temperature ferromagnetic,
anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a
unified, broad theory for all scenarios and, in particular, Michaelis-Menten,
Hill and Adair equations are consistently recovered. This framework is then
tested against experimental biological data with an overall excellent
agreement. One step forward, we consistently read the whole mapping from a
cybernetic perspective, highlighting deep structural analogies between the
above-mentioned kinetics and fundamental bricks in electronics (i.e.
operational amplifiers, flashes, flip-flops), so to build a clear bridge
linking biochemical kinetics and cybernetics.Comment: 15 pages, 6 figures; to appear on Scientific Reports: Nature
Publishing Grou
Large-Scale Optical Neural Networks based on Photoelectric Multiplication
Recent success in deep neural networks has generated strong interest in
hardware accelerators to improve speed and energy consumption. This paper
presents a new type of photonic accelerator based on coherent detection that is
scalable to large () networks and can be operated at high (GHz)
speeds and very low (sub-aJ) energies per multiply-and-accumulate (MAC), using
the massive spatial multiplexing enabled by standard free-space optical
components. In contrast to previous approaches, both weights and inputs are
optically encoded so that the network can be reprogrammed and trained on the
fly. Simulations of the network using models for digit- and
image-classification reveal a "standard quantum limit" for optical neural
networks, set by photodetector shot noise. This bound, which can be as low as
50 zJ/MAC, suggests performance below the thermodynamic (Landauer) limit for
digital irreversible computation is theoretically possible in this device. The
proposed accelerator can implement both fully-connected and convolutional
networks. We also present a scheme for back-propagation and training that can
be performed in the same hardware. This architecture will enable a new class of
ultra-low-energy processors for deep learning.Comment: Text: 10 pages, 5 figures, 1 table. Supplementary: 8 pages, 5,
figures, 2 table
Complete integrability of information processing by biochemical reactions
Statistical mechanics provides an effective framework to investigate
information processing in biochemical reactions. Within such framework
far-reaching analogies are established among (anti-) cooperative collective
behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical
mechanics and operational amplifiers/flip-flops in cybernetics. The underlying
modeling -- based on spin systems -- has been proved to be accurate for a wide
class of systems matching classical (e.g. Michaelis--Menten, Hill, Adair)
scenarios in the infinite-size approximation. However, the current research in
biochemical information processing has been focusing on systems involving a
relatively small number of units, where this approximation is no longer valid.
Here we show that the whole statistical mechanical description of reaction
kinetics can be re-formulated via a mechanical analogy -- based on completely
integrable hydrodynamic-type systems of PDEs -- which provides explicit
finite-size solutions, matching recently investigated phenomena (e.g.
noise-induced cooperativity, stochastic bi-stability, quorum sensing). The
resulting picture, successfully tested against a broad spectrum of data,
constitutes a neat rationale for a numerically effective and theoretically
consistent description of collective behaviors in biochemical reactions.Comment: 24 pages, 10 figures; accepted for publication in Scientific Report
Beyond Moore's technologies: operation principles of a superconductor alternative
The predictions of Moore's law are considered by experts to be valid until
2020 giving rise to "post-Moore's" technologies afterwards. Energy efficiency
is one of the major challenges in high-performance computing that should be
answered. Superconductor digital technology is a promising post-Moore's
alternative for the development of supercomputers. In this paper, we consider
operation principles of an energy-efficient superconductor logic and memory
circuits with a short retrospective review of their evolution. We analyze their
shortcomings in respect to computer circuits design. Possible ways of further
research are outlined.Comment: OPEN ACCES
Ferromagnetic models for cooperative behavior: Revisiting Universality in complex phenomena
Ferromagnetic models are harmonic oscillators in statistical mechanics.
Beyond their original scope in tackling phase transition and symmetry breaking
in theoretical physics, they are nowadays experiencing a renewal applicative
interest as they capture the main features of disparate complex phenomena,
whose quantitative investigation in the past were forbidden due to data
lacking. After a streamlined introduction to these models, suitably embedded on
random graphs, aim of the present paper is to show their importance in a
plethora of widespread research fields, so to highlight the unifying framework
reached by using statistical mechanics as a tool for their investigation.
Specifically we will deal with examples stemmed from sociology, chemistry,
cybernetics (electronics) and biology (immunology).Comment: Contributing to the proceedings of the Conference "Mathematical
models and methods for Planet Heart", INdAM, Rome 201
Bi-stability resistant to fluctuations
We study a simple micro-mechanical device that does not lose its snap-through
behavior in an environment dominated by fluctuations. The main idea is to have
several degrees of freedom that can cooperatively resist the de-synchronizing
effect of random perturbations. As an inspiration we use the power stroke
machinery of skeletal muscles, which ensures at sub-micron scales and finite
temperatures a swift recovery of an abruptly applied slack. In addition to
hypersensitive response at finite temperatures, our prototypical Brownian snap
spring also exhibits criticality at special values of parameters which is
another potentially interesting property for micro-scale engineering
applications
A walk in the statistical mechanical formulation of neural networks
Neural networks are nowadays both powerful operational tools (e.g., for
pattern recognition, data mining, error correction codes) and complex
theoretical models on the focus of scientific investigation. As for the
research branch, neural networks are handled and studied by psychologists,
neurobiologists, engineers, mathematicians and theoretical physicists. In
particular, in theoretical physics, the key instrument for the quantitative
analysis of neural networks is statistical mechanics. From this perspective,
here, we first review attractor networks: starting from ferromagnets and
spin-glass models, we discuss the underlying philosophy and we recover the
strand paved by Hopfield, Amit-Gutfreund-Sompolinky. One step forward, we
highlight the structural equivalence between Hopfield networks (modeling
retrieval) and Boltzmann machines (modeling learning), hence realizing a deep
bridge linking two inseparable aspects of biological and robotic spontaneous
cognition. As a sideline, in this walk we derive two alternative (with respect
to the original Hebb proposal) ways to recover the Hebbian paradigm, stemming
from ferromagnets and from spin-glasses, respectively. Further, as these notes
are thought of for an Engineering audience, we highlight also the mappings
between ferromagnets and operational amplifiers and between antiferromagnets
and flip-flops (as neural networks -built by op-amp and flip-flops- are
particular spin-glasses and the latter are indeed combinations of ferromagnets
and antiferromagnets), hoping that such a bridge plays as a concrete
prescription to capture the beauty of robotics from the statistical mechanical
perspective.Comment: Contribute to the proceeding of the conference: NCTA 2014. Contains
12 pages,7 figure
- …