52 research outputs found

    OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training

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    In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability. We compare with the value derived by cross-validation for overfitting control and optimisation of the generalization performance. We test our method for both regression and classification tasks. The proposed method is quite effective in terms of predictivity, often with some improvement on performance with respect to the reference cases considered. This approach, due to analytical determination of the regularization parameter, dramatically reduces the computational load required by many other techniques.Comment: Published on Neural Network

    Tensor-Based Algorithms for Image Classification

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    Interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classification. One is a kernel-based reformulation of the previously introduced multidimensional approximation of nonlinear dynamics (MANDy), the other an alternating ridge regression in the tensor train format. We apply both methods to the MNIST and fashion MNIST data set and show that the approaches are competitive with state-of-the-art neural network-based classifiers

    Perception-motivated parallel algorithms for haptics

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    Negli ultimi anni l\u2019utilizzo di dispositivi aptici, atti cio\ue8 a riprodurre l\u2019interazione fisica con l\u2019ambiente remoto o virtuale, si sta diffondendo in vari ambiti della robotica e dell\u2019informatica, dai videogiochi alla chirurgia robotizzata eseguita in teleoperazione, dai cellulari alla riabilitazione. In questo lavoro di tesi abbiamo voluto considerare nuovi punti di vista sull\u2019argomento, allo scopo di comprendere meglio come riportare l\u2019essere umano, che \ue8 l\u2019unico fruitore del ritorno di forza, tattile e di telepresenza, al centro della ricerca sui dispositivi aptici. Allo scopo ci siamo focalizzati su due aspetti: una manipolazione del segnale di forza mutuata dalla percezione umana e l\u2019utilizzo di architetture multicore per l\u2019implementazione di algoritmi aptici e robotici. Con l\u2019aiuto di un setup sperimentale creato ad hoc e attraverso l\u2019utilizzo di un joystick con ritorno di forza a 6 gradi di libert\ue0, abbiamo progettato degli esperimenti psicofisici atti all\u2019identificazione di soglie differenziali di forze/coppie nel sistema mano-braccio. Sulla base dei risultati ottenuti abbiamo determinato una serie di funzioni di scalatura del segnale di forza, una per ogni grado di libert\ue0, che permettono di aumentare l\u2019abilit\ue0 umana nel discriminare stimoli differenti. L\u2019utilizzo di tali funzioni, ad esempio in teleoperazione, richiede la possibilit\ue0 di variare il segnale di feedback e il controllo del dispositivo sia in relazione al lavoro da svolgere, sia alle peculiari capacit\ue0 dell\u2019utilizzatore. La gestione del dispositivo deve quindi essere in grado di soddisfare due obbiettivi tendenzialmente in contrasto, e cio\ue8 il raggiungimento di alte prestazioni in termini di velocit\ue0, stabilit\ue0 e precisione, abbinato alla flessibilit\ue0 tipica del software. Una soluzione consiste nell\u2019affidare il controllo del dispositivo ai nuovi sistemi multicore che si stanno sempre pi\uf9 prepotentemente affacciando sul panorama informatico. Per far ci\uf2 una serie di algoritmi consolidati deve essere portata su sistemi paralleli. In questo lavoro abbiamo dimostrato che \ue8 possibile convertire facilmente vecchi algoritmi gi\ue0 implementati in hardware, e quindi intrinsecamente paralleli. Un punto da definire rimane per\uf2 quanto costa portare degli algoritmi solitamente descritti in VLSI e schemi in un linguaggio di programmazione ad alto livello. Focalizzando la nostra attenzione su un problema specifico, la pseudoinversione di matrici che \ue8 presente in molti algoritmi di dinamica e cinematica, abbiamo mostrato che un\u2019attenta progettazione e decomposizione del problema permette una mappatura diretta sulle unit\ue0 di calcolo disponibili. In aggiunta, l\u2019uso di parallelismo a livello di dati su macchine SIMD permette di ottenere buone prestazioni utilizzando semplici operazioni vettoriali come addizioni e shift. Dato che di solito tali istruzioni fanno parte delle implementazioni hardware la migrazione del codice risulta agevole. Abbiamo testato il nostro approccio su una Sony PlayStation 3 equipaggiata con un processore IBM Cell Broadband Engine.In the last years the use of haptic feedback has been used in several applications, from mobile phones to rehabilitation, from video games to robotic aided surgery. The haptic devices, that are the interfaces that create the stimulation and reproduce the physical interaction with virtual or remote environments, have been studied, analyzed and developed in many ways. Every innovation in the mechanics, electronics and technical design of the device it is valuable, however it is important to maintain the focus of the haptic interaction on the human being, who is the only user of force feedback. In this thesis we worked on two main topics that are relevant to this aim: a perception based force signal manipulation and the use of modern multicore architectures for the implementation of the haptic controller. With the help of a specific experimental setup and using a 6 dof haptic device we designed a psychophysical experiment aimed at identifying of the force/torque differential thresholds applied to the hand-arm system. On the basis of the results obtained we determined a set of task dependent scaling functions, one for each degree of freedom of the three-dimensional space, that can be used to enhance the human abilities in discriminating different stimuli. The perception based manipulation of the force feedback requires a fast, stable and configurable controller of the haptic interface. Thus a solution is to use new available multicore architectures for the implementation of the controller, but many consolidated algorithms have to be ported to these parallel systems. Focusing on specific problem, i.e. the matrix pseudoinversion, that is part of the robotics dynamic and kinematic computation, we showed that it is possible to migrate code that was already implemented in hardware, and in particular old algorithms that were inherently parallel and thus not competitive on sequential processors. The main question that still lies open is how much effort is required in order to write these algorithms, usually described in VLSI or schematics, in a modern programming language. We show that a careful task decomposition and design permit a mapping of the code on the available cores. In addition, the use of data parallelism on SIMD machines can give good performance when simple vector instructions such as add and shift operations are used. Since these instructions are present also in hardware implementations the migration can be easily performed. We tested our approach on a Sony PlayStation 3 game console equipped with IBM Cell Broadband Engine processor
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