scholarly journals Learning Numerosity Representations with Transformers

2021 ◽  
Author(s):  
Tommaso Boccato ◽  
Alberto Testolin ◽  
Marco Zorzi
Keyword(s):  
Deep Learning ◽  
Numerical Cognition ◽  
Joint Probability ◽  
Latent Factors ◽  
Challenging Tasks ◽  
Probability Mass ◽  
Latent Representations ◽  
Mass Functions ◽  
Specific Number ◽  
Learning Architectures

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

scholarly journals Learning Numerosity Representations with Transformers: Number Generation Tasks and Out-of-Distribution Generalization

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 857
Author(s):  
Tommaso Boccato ◽  
Alberto Testolin ◽  
Marco Zorzi
Keyword(s):  
Deep Learning ◽  
Numerical Cognition ◽  
Joint Probability ◽  
Latent Factors ◽  
Challenging Tasks ◽  
Probability Mass ◽  
Latent Representations ◽  
Mass Functions ◽  
Specific Number ◽  
Learning Architectures

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here, we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

Joint distributions of successes, failures and patterns in enumeration problems

2000 ◽  
Vol 32 (3) ◽  
pp. 866-884 ◽  
Author(s):  
S Chadjiconstantinidis ◽  
D. L. Antzoulakos ◽  
M. V. Koutras
Keyword(s):  
Joint Distribution ◽  
Joint Probability ◽  
Fixed Number ◽  
Composite Pattern ◽  
Joint Distributions ◽  
Special Cases ◽  
Enumeration Problems ◽  
Binomial Type ◽  
Probability Mass ◽  
Mass Functions

Let ε be a (single or composite) pattern defined over a sequence of Bernoulli trials. This article presents a unified approach for the study of the joint distribution of the number Sn of successes (and Fn of failures) and the number Xn of occurrences of ε in a fixed number of trials as well as the joint distribution of the waiting time Tr till the rth occurrence of the pattern and the number STr of successes (and FTr of failures) observed at that time. General formulae are developed for the joint probability mass functions and generating functions of (Xn,Sn), (Tr,STr) (and (Xn,Sn,Fn),(Tr,STr,FTr)) when Xn belongs to the family of Markov chain imbeddable variables of binomial type. Specializing to certain success runs, scans and pattern problems several well-known results are delivered as special cases of the general theory along with some new results that have not appeared in the statistical literature before.

Joint distributions of successes, failures and patterns in enumeration problems

2000 ◽  
Vol 32 (03) ◽  
pp. 866-884 ◽  
Author(s):  
S Chadjiconstantinidis ◽  
D. L. Antzoulakos ◽  
M. V. Koutras
Keyword(s):  
Joint Distribution ◽  
Joint Probability ◽  
Fixed Number ◽  
Composite Pattern ◽  
Joint Distributions ◽  
Special Cases ◽  
Enumeration Problems ◽  
Binomial Type ◽  
Probability Mass ◽  
Mass Functions

Let ε be a (single or composite) pattern defined over a sequence of Bernoulli trials. This article presents a unified approach for the study of the joint distribution of the number S n of successes (and F n of failures) and the number X n of occurrences of ε in a fixed number of trials as well as the joint distribution of the waiting time T r till the rth occurrence of the pattern and the number S T r of successes (and F T r of failures) observed at that time. General formulae are developed for the joint probability mass functions and generating functions of (X n ,S n ), (T r ,S T r ) (and (X n ,S n ,F n ),(T r ,S T r ,F T r )) when X n belongs to the family of Markov chain imbeddable variables of binomial type. Specializing to certain success runs, scans and pattern problems several well-known results are delivered as special cases of the general theory along with some new results that have not appeared in the statistical literature before.

scholarly journals A Generalization Performance Study Using Deep Learning Networks in Embedded Systems

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1031
Author(s):  
Joseba Gorospe ◽  
Rubén Mulero ◽  
Olatz Arbelaitz ◽  
Javier Muguerza ◽  
Miguel Ángel Antón
Keyword(s):  
Deep Learning ◽  
Embedded Systems ◽  
Embedded System ◽  
General Purpose ◽  
Learning Networks ◽  
Performance Study ◽  
Learning Techniques ◽  
Wide Range ◽  
Learning Architectures

Deep learning techniques are being increasingly used in the scientific community as a consequence of the high computational capacity of current systems and the increase in the amount of data available as a result of the digitalisation of society in general and the industrial world in particular. In addition, the immersion of the field of edge computing, which focuses on integrating artificial intelligence as close as possible to the client, makes it possible to implement systems that act in real time without the need to transfer all of the data to centralised servers. The combination of these two concepts can lead to systems with the capacity to make correct decisions and act based on them immediately and in situ. Despite this, the low capacity of embedded systems greatly hinders this integration, so the possibility of being able to integrate them into a wide range of micro-controllers can be a great advantage. This paper contributes with the generation of an environment based on Mbed OS and TensorFlow Lite to be embedded in any general purpose embedded system, allowing the introduction of deep learning architectures. The experiments herein prove that the proposed system is competitive if compared to other commercial systems.

scholarly journals Multimodal Deep Learning and Visible-Light and Hyperspectral Imaging for Fruit Maturity Estimation

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1288
Author(s):  
Cinmayii A. Garillos-Manliguez ◽  
John Y. Chiang
Keyword(s):  
Deep Learning ◽  
Visible Light ◽  
Hyperspectral Imaging ◽  
Morphological Changes ◽  
Consumer Preference ◽  
Hyperspectral Data ◽  
Sensitivity Analyses ◽  
Deep Convolutional Neural Networks ◽  
Fruit Maturity ◽  
Learning Architectures

Fruit maturity is a critical factor in the supply chain, consumer preference, and agriculture industry. Most classification methods on fruit maturity identify only two classes: ripe and unripe, but this paper estimates six maturity stages of papaya fruit. Deep learning architectures have gained respect and brought breakthroughs in unimodal processing. This paper suggests a novel non-destructive and multimodal classification using deep convolutional neural networks that estimate fruit maturity by feature concatenation of data acquired from two imaging modes: visible-light and hyperspectral imaging systems. Morphological changes in the sample fruits can be easily measured with RGB images, while spectral signatures that provide high sensitivity and high correlation with the internal properties of fruits can be extracted from hyperspectral images with wavelength range in between 400 nm and 900 nm—factors that must be considered when building a model. This study further modified the architectures: AlexNet, VGG16, VGG19, ResNet50, ResNeXt50, MobileNet, and MobileNetV2 to utilize multimodal data cubes composed of RGB and hyperspectral data for sensitivity analyses. These multimodal variants can achieve up to 0.90 F1 scores and 1.45% top-2 error rate for the classification of six stages. Overall, taking advantage of multimodal input coupled with powerful deep convolutional neural network models can classify fruit maturity even at refined levels of six stages. This indicates that multimodal deep learning architectures and multimodal imaging have great potential for real-time in-field fruit maturity estimation that can help estimate optimal harvest time and other in-field industrial applications.

scholarly journals Stochastic methods defeat regular RSA exponentiation algorithms with combined blinding methods

2021 ◽  
Vol 15 (1) ◽  
pp. 408-433
Author(s):  
Margaux Dugardin ◽  
Werner Schindler ◽  
Sylvain Guilley
Keyword(s):  
State Of The Art ◽  
Stochastic Methods ◽  
Rsa Algorithm ◽  
Montgomery Ladder ◽  
Channel Information ◽  
Probability Mass ◽  
The Cost ◽  
Noisy Measurements ◽  
Mass Functions ◽  
Larger Sample

Abstract Extra-reductions occurring in Montgomery multiplications disclose side-channel information which can be exploited even in stringent contexts. In this article, we derive stochastic attacks to defeat Rivest-Shamir-Adleman (RSA) with Montgomery ladder regular exponentiation coupled with base blinding. Namely, we leverage on precharacterized multivariate probability mass functions of extra-reductions between pairs of (multiplication, square) in one iteration of the RSA algorithm and that of the next one(s) to build a maximum likelihood distinguisher. The efficiency of our attack (in terms of required traces) is more than double compared to the state-of-the-art. In addition to this result, we also apply our method to the case of regular exponentiation, base blinding, and modulus blinding. Quite surprisingly, modulus blinding does not make our attack impossible, and so even for large sizes of the modulus randomizing element. At the cost of larger sample sizes our attacks tolerate noisy measurements. Fortunately, effective countermeasures exist.

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