Learning Combinations of Activation Functions

In the last decade, an active area of research has been devoted to design novel activation functions that are able to help deep neural networks to converge, obtaining better performance. The training procedure of these architectures usually involves optimization of the weights of their layers only, while non-linearities are generally pre-specified and their (possible) parameters are usually considered as hyper-parameters to be tuned manually. In this paper, we introduce two approaches to automatically learn different combinations of base activation functions (such as the identity function, ReLU, and tanh) during the training phase. We present a thorough comparison of our novel approaches with well-known architectures (such as LeNet-5, AlexNet, and ResNet-56) on three standard datasets (Fashion-MNIST, CIFAR-10, and ILSVRC-2012), showing substantial improvements in the overall performance, such as an increase in the top-1 accuracy for AlexNet on ILSVRC-2012 of 3.01 percentage points.Comment: 6 pages, 3 figures. Published as a conference paper at ICPR 2018. Code: https://bitbucket.org/francux/learning_combinations_of_activation_function

The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory

The present paper is both a review on the Feynman problem, and an original research presentation on the relations between Fermionic theories and qubits theories, both regarded in the novel framework of operational probabilistic theories. The most relevant results about the Feynman problem of simulating Fermions with qubits are reviewed, and in the light of the new original results the problem is solved. The answer is twofold. On the computational side the two theories are equivalent, as shown by Bravyi and Kitaev (Ann. Phys. 298.1 (2002): 210-226). On the operational side the quantum theory of qubits and the quantum theory of Fermions are different, mostly in the notion of locality, with striking consequences on entanglement. Thus the emulation does not respect locality, as it was suspected by Feynman (Int. J. Theor. Phys. 21.6 (1982): 467-488).Comment: 46 pages, review about the "Feynman problem". Fixed many typo

Automated Pruning for Deep Neural Network Compression

In this work we present a method to improve the pruning step of the current state-of-the-art methodology to compress neural networks. The novelty of the proposed pruning technique is in its differentiability, which allows pruning to be performed during the backpropagation phase of the network training. This enables an end-to-end learning and strongly reduces the training time. The technique is based on a family of differentiable pruning functions and a new regularizer specifically designed to enforce pruning. The experimental results show that the joint optimization of both the thresholds and the network weights permits to reach a higher compression rate, reducing the number of weights of the pruned network by a further 14% to 33% compared to the current state-of-the-art. Furthermore, we believe that this is the first study where the generalization capabilities in transfer learning tasks of the features extracted by a pruned network are analyzed. To achieve this goal, we show that the representations learned using the proposed pruning methodology maintain the same effectiveness and generality of those learned by the corresponding non-compressed network on a set of different recognition tasks.Comment: 8 pages, 5 figures. Published as a conference paper at ICPR 201

Spooky action at a distance in general probabilistic theories

We call a probabilistic theory "complete" if it cannot be further refined by no-signaling hidden-variable models, and name a theory "spooky" if every equivalent hidden-variable model violates Shimony's Outcome Independence. We prove that a complete theory is spooky if and only if it admits a pure steering state in the sense of Schr\"odinger. Finally we show that steering of complementary states leads to a Schr\"odinger's cat-like paradox.Comment: 7 pages, 1 figure, elsart, significantly revised versio

Determinism without causality

Causality has often been confused with the notion of determinism. It is mandatory to separate the two notions in view of the debate about quantum foundations. Quantum theory provides an example of causal non-deterministic theory. Here we introduce a toy operational theory that is deterministic and non-causal, thus proving that the two notions of causality and determinism are totally independent