1,721,006 research outputs found
Chaos in temperature in the Sherrington-Kirkpatrick model
No full textWe prove the existence of chaos in temperature in the Sherrington-Kirkpatrick model. The effect is exceedingly small, namely, of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behavior of the overlap distribution function P_(T1,T2)(q) in finite-size systems
Analysis of the ∞-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
No full textIn this work we analyze the Parisi ∞-replica symmetry breaking solution of the Sherrington-Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the ∞-replica symmetry breaking equations, which are solved using a pseudospectral code that allows for very accurate results. With these methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end point x_max of the plateau of q(x) and find that limopT⃗0 x_max(T)>0.5
Complexity in mean-field spin-glass models: Ising p-spin
No full textThe complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising p-spin is investigated in the temperature regime where the equilibrium phase is one-step replica symmetry breaking. Two solutions of the resulting saddle point equations are found. One is supersymmetric (SUSY) and includes the equilibrium value of the free energy while the other is non-SUSY. The two solutions cross exactly at a value of the free energy where the replicon eigenvalue is zero; at low free energy the complexity is described by the SUSY solution while at high free energy it is described by the non-SUSY solution, the latter accounting for the total number of solutions. The relevant TAP solutions counted by the non-SUSY complexity share the same features of the corresponding solutions in the Sherrington-Kirkpatrick model; in particular their Hessian has a vanishing isolated eigenvalue. The TAP solutions corresponding to the SUSY complexity, instead, are well separated minima
Universality and deviations in disordered systems
No full textWe compute the probability of positive large deviations of the free energy per spin in mean-field spin-glass models. The probability vanishes in the thermodynamic limit as P (Delta f) proportional to exp[-N(2)L(2)(Delta f)]. For the Sherrington-Kirkpatrick model we find L(2)(Delta f)=O(Delta f)(12/5) in good agreement with numerical data and with the assumption that typical small deviations of the free energy scale as N(1/6). For the spherical model we find L(2)(Delta f) =O(Delta f)(3) in agreement with recent findings on the fluctuations of the largest eigenvalue of random Gaussian matrices. The computation is based on a loop expansion in replica space and the non-Gaussian behavior follows in both cases from the fact that the expansion is divergent at all orders. The factors of the leading order terms are obtained resumming appropriately the loop expansion and display universality, pointing to the existence of a single universal distribution describing the small deviations of any model in the full-replica-symmetry-breaking class
Bethe M-layer construction on the Ising model
Full text linkIn statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in disordered models, some important finite dimensional second-order phase transitions are qualitatively different or absent in the corresponding fully connected model: in such cases the standard expansion fails. Recently, a new method, the M-layer one, has been introduced that performs an expansion around a different soluble mean field model: the Bethe lattice one. This new method has been already used to compute the upper critical dimension Du of different disordered systems such as the Random Field Ising model or the Spin glass model with field. If then one wants to go beyond and construct an expansion around Du to understand how critical quantities get renormalized, the actual computation of all the numerical factors is needed. This next step has still not been performed, being technically more involved. In this paper we perform this computation for the ferromagnetic Ising model without quenched disorder, in finite dimensions: we show that, at one-loop order inside the M-layer approach, we recover the continuum quartic field theory and we are able to identify the coupling constant g and the other parameters of the theory, as a function of macroscopic and microscopic details of the model such as the lattice spacing, the physical lattice dimension and the temperature. This is a fundamental step that will help in applying in the future the same techniques to more complicated systems, for which the standard field theoretical approach is impracticable
Quenched computation of the dependence of complexity on the free energy in the Sherrington-Kirkpatrick model
No full textThe quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified full replica symmetry breaking ansatz is introduced in order to study the complexity dependence on the free energy. Such an ansatz corresponds to require Becchi-Rouet-Stora-Tyutin supersymmetry. The complexity computed this way is the Legendre transform of the free energy averaged over the quenched disorder. The stability analysis shows that this complexity is inconsistent at any free energy level but the equilibrium one. The further problem of building a physically well-defined solution not invariant under supersymmetry and predicting an extensive number of metastable states is also discussed
A 6.78 MHz Maximum Efficiency Tracking Active Rectifier with Load Modulation Control for Wireless Power Transfer to Implantable Medical Devices
No full textThis paper presents a novel integrated wireless power transfer receiver for implantable medical devices, including a load-modulation feedback loop and an active rectifier with maximum efficiency tracking technique. The feedback loop enables the control of the power delivered to the load by means of a frequency modulation of the receiver load, introducing an efficiency loss of only 1.64 %. The active rectifier maximizes the efficiency of the link through a second feedback calibration loop of the off-transition of the active diodes, showing a Voltage Conversion Ratio of 0.98 and a Power Conversion Efficiency between 0.86 and 0.91 for a wide range of load conditions. The chip was designed in the 180 nm BCD-on-SOI XFAB technology and evaluated with accurate electrical simulations and Monte Carlo runs
Temperature-Resilient Analog Neuromorphic Chip in Single-Polysilicon CMOS Technology
No full textIn analog neuromorphic chips, designers can embed computing primitives in the intrinsic physical properties of devices and circuits, heavily reducing device count and energy consumption, and enabling high parallelism, because all devices are computing simultaneously. Neural network parameters can be stored in local analog non-volatile memories (NVMs), saving the energy required to move data between memory and logic. However, the main drawback of analog sub-threshold electronic circuits is their dramatic temperature sensitivity. In this paper, we demonstrate that a temperature compensation mechanism can be devised to solve this problem. We have designed and fabricated a chip implementing a two-layer analog neural network trained to classify low-resolution images of handwritten digits with a low-cost single-poly complementary metal-oxide-semiconductor (CMOS) process, using unconventional analog NVMs for weight storage. We demonstrate a temperature-resilient analog neuromorphic chip for image recognition operating between 10°C and 60°C without loss of classification accuracy, within 2% of the corresponding software-based neural network in the whole temperature range
Time Domain Analog Neuromorphic Engine Based on High-Density Non-Volatile Memory in Single-Poly CMOS
No full textIncreasing the energy efficiency of deep learning systems is critical for improving the cognitive capability of edge devices, often battery operated, as well as for data centers, constrained by the total power envelope. Specialized architectures accelerated by analog vector-matrix multipliers (VMMs) can reduce by orders of magnitude the energy per operation, since the reduced precision of analog computation does not undermine the classification accuracy of the neural network. We show an analog vector-matrix multiplier fabricated with industry-standard 0.18 μm CMOS process, exploiting a single-transistor non-volatile analog memory cell and dedicated technology circuit co-design. The design is focused on implementation in neural networks performing offline training. The VMM performs the analog multiplication of a vector of inputs, encoded in the duration of time pulses, times a matrix of weights, encoded in the programmable currents of the memory cells. A 1.72 μm2 memory cell is realized with a single transistor with floating gate, which can be operated as a two-terminal analog memristive device with more than 64 programmable current levels and high Ihigh/Ilow ratio (> 10 3 ), tuned by the charge injected in the floating gate. A small-area charge amplifier is used to convert the multiply and accumulate operation result into a voltage. System-level projections based on our measurements and simulations provide a throughput of 333.17 GOps/s and an energy efficiency of 122.3 TOps/J, higher than comparable-precision VMMs reported in the literature, and an equivalent area per cell down to 2.15 μm2 , lower than any similar state-of-the-art solution. Of critical importance in view of translation to industry, our proposal uses in a new way an industry-standard low-cost single-poly CMOS process flow
- …
