arXiv subjects

Alessandro Betti

Publications and source records attributed to Alessandro Betti.

48 records · Page 3Linked to original sources

arXiv2018

Backpropagation and Biological Plausibility

By and large, Backpropagation (BP) is regarded as one of the most important neural computation algorithms at the basis of the progress in machine learning, including the recent advances in deep learning. However, its computational structure has been the source of many debates on its arguable biological plausibility. In this paper, it is shown that when framing supervised learning in the Lagrangian framework, while one can see a natural emergence of Backpropagation, biologically plausible local algorithms can also be devised that are based on the search for saddle points in the learning adjoint space composed of weights, neural outputs, and Lagrangian multipliers. This might open the doors to a truly novel class of learning algorithms where, because of the introduction of the notion of support neurons, the optimization scheme also plays a fundamental role in the construction of the architecture.

cs.AI↗

arXiv2018

Generalization in quasi-periodic environments

By and large the behavior of stochastic gradient is regarded as a challenging problem, and it is often presented in the framework of statistical machine learning. This paper offers a novel view on the analysis of on-line models of learning that arises when dealing with a generalized version of stochastic gradient that is based on dissipative dynamics. In order to face the complex evolution of these models, a systematic treatment is proposed which is based on energy balance equations that are derived by means of the Caldirola-Kanai (CK) Hamiltonian. According to these equations, learning can be regarded as an ordering process which corresponds with the decrement of the loss function. Finally, the main results established in this paper is that in the case of quasi-periodic environments, where the pattern novelty is progressively limited as time goes by, the system dynamics yields an asymptotically consistent solution in the weight space, that is the solution maps similar patterns to the same decision.

cs.LG↗

arXiv2018

Motion Invariance in Visual Environments

The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams, just as happens in nature. In this paper, we claim that their processing naturally leads to formulate the motion invariance principle, which enables the construction of a new theory of visual learning based on convolutional features. The theory addresses a number of intriguing questions that arise in natural vision, and offers a well-posed computational scheme for the discovery of convolutional filters over the retina. They are driven by the Euler-Lagrange differential equations derived from the principle of least cognitive action, that parallels laws of mechanics. Unlike traditional convolutional networks, which need massive supervision, the proposed theory offers a truly new scenario in which feature learning takes place by unsupervised processing of video signals. An experimental report of the theory is presented where we show that features extracted under motion invariance yield an improvement that can be assessed by measuring information-based indexes.

cs.CV↗

arXiv2018

Trees in the Real Field

This paper proposes an algebraic view of trees which opens the doors to an alternative computational scheme with respect to classic algorithms. In particular, it is shown that this view is very well-suited for machine learning and computational linguistics.

cs.DM↗

arXiv2018

Large-N CP(N-1) sigma model on a finite interval and the renormalized string energy

We continue the analysis started in a recent paper of the large-N two-dimensional CP(N-1) sigma model, defined on a finite space interval L with Dirichlet (or Neumann) boundary conditions. Here we focus our attention on the problem of the renormalized energy density $\mathcal{E}(x,Λ,L)$ which is found to be a sum of two terms, a constant term coming from the sum over modes, and a term proportional to the mass gap. The approach to $\mathcal{E}(x,Λ,L)\to\tfrac{N}{4π}Λ^2$ at large $LΛ$ is shown, both analytically and numerically, to be exponential: no power corrections are present and in particular no Lüscher term appears. This is consistent with the earlier result which states that the system has a unique massive phase, which interpolates smoothly between the classical weakly-coupled limit for $LΛ\to 0$ and the "confined" phase of the standard CP(N-1) model in two dimensions for $LΛ\to\infty$.

hep-th↗

arXiv2018

Convolutional Networks in Visual Environments

The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams. In this paper, we claim that their processing naturally leads to formulate the motion invariance principle, which enables the construction of a new theory of learning with convolutional networks. The theory addresses a number of intriguing questions that arise in natural vision, and offers a well-posed computational scheme for the discovery of convolutional filters over the retina. They are driven by differential equations derived from the principle of least cognitive action. Unlike traditional convolutional networks, which need massive supervision, the proposed theory offers a truly new scenario in which feature learning takes place by unsupervised processing of video signals. It is pointed out that an opportune blurring of the video, along the interleaving of segments of null signal, make it possible to conceive a novel learning mechanism that yields the minimum of the cognitive action. Basically, while the theory enables the implementation of novel computer vision systems, it is also provides an intriguing explanation of the solution that evolution has discovered for humans, where it looks like that the video blurring in newborns and the day-night rhythm seem to emerge in a general computational framework, regardless of biology.

cs.CV↗

arXiv2011

Drift velocity peak and negative differential mobility in high field transport in graphene nanoribbons explained by numerical simulations

We present numerical simulations of high field transport in both suspended and deposited armchair graphene nanoribbon (A-GNR) on HfO2 substrate. Drift velocity in suspended GNR does not saturate at high electric field (F), but rather decreases, showing a maximum for F=10 kV/cm. Deposition on HfO2 strongly degrades the drift velocity by up to a factor of 10 with respect to suspended GNRs in the low-field regime, whereas at high fields drift velocity approaches the intrinsic value expected in suspended GNRs. Even in the assumption of perfect edges, the obtained mobility is far behind what expected in two-dimensional graphene, and is further reduced by surface optical phonons.

cond-mat.mes-hall↗

arXiv2011

Strong mobility degradation in ideal graphene nanoribbons due to phonon scattering

We investigate the low-field phonon-limited mobility in armchair graphene nanoribbons (GNRs) using full-band electron and phonon dispersion relations. We show that lateral confinement suppresses the intrinsic mobility of GNRs to values typical of common bulk semiconductors, and very far from the impressive experiments on 2D graphene. Suspended GNRs with a width of 1 nm exhibit a mobility close to 500 cm^2/Vs at room temperature, whereas if the same GNRs are deposited on HfO2 mobility is further reduced to about 60 cm^2/Vs due to surface phonons. We also show the occurrence of polaron formation, leading to band gap renormalization of ~118 meV for 1 nm-wide armchair GNRs.

cond-mat.mes-hall↗

arXiv2011

Atomistic investigation of low-field mobility in graphene nanoribbons

We have investigated the main scattering mechanisms affecting mobility in graphene nanoribbons using detailed atomistic simulations. We have considered carrier scattering due to acoustic and optical phonons, edge roughness, single defects, and ionized impurities, and we have defined a methodology based on simulations of statistically meaningful ensembles of nanoribbon segments. Edge disorder heavily affects mobility at room temperature in narrower nanoribbons, whereas charged impurities and phonons are hardly the limiting factors. Results are favorably compared to the few experiments available in the literature.

cond-mat.mes-hall↗

arXiv2010

Enhanced shot noise in carbon nanotube field-effect transistors

We predict shot noise enhancement in defect-free carbon nanotube field-effect transistors through a numerical investigation based on the self-consistent solution of the Poisson and Schrodinger equations within the non-equilibrium Green functions formalism, and on a Monte Carlo approach to reproduce injection statistics. Noise enhancement is due to the correlation between trapping of holes from the drain into quasi-bound states in the channel and thermionic injection of electrons from the source, and can lead to an appreciable Fano factor of 1.22 at room temperature.

cond-mat.mes-hall↗

arXiv2010

Statistical theory of shot noise in quasi-1D Field Effect Transistors in the presence of electron-electron interaction

We present an expression for the shot noise power spectral density in quasi-one dimensional conductors electrostatically controlled by a gate electrode, that includes the effects of Coulomb interaction and of Pauli exclusion among charge carriers. In this sense, our expression extends the well known Landauer-Buttiker noise formula to include the effect of Coulomb interaction through induced fluctuations in the device potential. Our approach is based on the introduction of statistical properties of the scattering matrix and on a second-quantization many-body description. From a quantitative point of view, statistical properties are obtained by means of Monte Carlo simulations on a ensemble of different configurations of injected states, requiring the solution of the Poisson-Schrodinger equation on a three-dimensional grid, with the non-equilibrium Green functions formalism. In a series of example, we show that failure to consider the effects of Coulomb interaction on noise leads to a gross overestimation of the noise spectrum of quasi-one dimensional devices.

cond-mat.mes-hall↗

arXiv2010

Shot noise suppression in quasi one-dimensional Field Effect Transistors

We present a novel method for the evaluation of shot noise in quasi one-dimensional field-effect transistors, such as those based on carbon nanotubes and silicon nanowires. The method is derived by using a statistical approach within the second quantization formalism and allows to include both the effects of Pauli exclusion and Coulomb repulsion among charge carriers. In this way it extends Landauer-Buttiker approach by explicitly including the effect of Coulomb repulsion on noise. We implement the method through the self-consistent solution of the 3D Poisson and transport equations within the NEGF framework and a Monte Carlo procedure for populating injected electron states. We show that the combined effect of Pauli and Coulomb interactions reduces shot noise in strong inversion down to 23 % of the full shot noise for a gate overdrive of 0.4 V, and that neglecting the effect of Coulomb repulsion would lead to an overestimation of noise up to 180 %.

cond-mat.mes-hall↗