Roger Penrose

Roger Penrose, né le à Colchester, est un mathématicien, cosmologiste et philosophe des sciences britannique. Il enseigne les mathématiques au Birkbeck College de Londres où il élabore la théorie décrivant l'effondrement des étoiles sur elles-mêmes, entre 1964 et 1973, et où il rencontre le célèbre physicien Stephen Hawking. Ils travaillent alors à une théorie de l'origine de l'univers, Penrose apportant sa contribution mathématique à la théorie de la relativité générale appliquée à la cosmologie et à l'étude des trous noirs. Il est actuellement professeur émérite à l'université d'Oxford. En 1974, il publie un article où il présente ses premiers pavages non périodiques : les pavages de Penrose. On lui doit quelques objets impossibles, tels le triangle de Penrose. Conjointement avec Andrea M. Ghez et Reinhard Genzel, il est lauréat du prix Nobel de physique 2020. Biographie Famille Né à Colchester, Essex, Roger Penrose est le fils de Margaret (Leathes) et du p

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.

EPFL2016

Magnons, worms and nanogratings in artificial magnetic quasicrystals

Sho Watanabe

Magnons (spin waves, SWs) are elementary spin excitations in magnetically ordered materials. They are the promising quanta for the transmission and processing of information. Magnons can be coupled to the electromagnetic waves utilized for the wireless communication technologies. A wavelength of magnons is orders of magnitude shorter than that of electromagnetic waves at the same frequency. Therefore, wave-based computing with magnons would be promising for the next generation information technology. For the optimized information processing, artificial magnetic media have the potential to offer advanced controls of SWs. A magnonic crystal, consisting of a periodically arranged nanomagnets, provides a tailored magnon band structure. Periodic magnonic grating couplers (MGCs) efficiently convert centimeter-scaled microwaves to sub-100 nm wavelength SWs. Artificial spin ices (ASIs) are expected to offer reprogrammable magnetization configurations. However, the studies on artificial magnetic materials based on the quasicrystalline and aperiodic arrangement are in their infancy. A quasicrystal, a long range ordered material with a lack of translational invariance, exhibits manifold rotational symmetry. The reciprocal vectors associated with the quasicrystal densely fill out all reciprocal space. These exotic properties would be advantageous for the control of SWs. During my PhD study, I explored SW properties in two dimensional (2D) artificial magnetic quasicrystals (AMQs) to understand the effect of aperiodicity on magnetic properties by means of broadband SW spectroscopy, inelastic light scattering spectroscopy, X-ray magnetic circular dichroism and micromagnetic simulation. By nanofabrication, AMQs made of different magnetic materials were created based on Penrose P2, P3 and Ammann tilings. First, we fabricated AMQs based on aperiodically arranged nanoholes etched into ferromagnetic thin films. Angular-dependent SW spectra exhibited tenfold rotational symmetry reflecting the lattice symmetry of the quasicrystalline nanohole arrangement. Intriguingly, worm-like nanochannels, each exhibiting different SW states, were generated in the AMQs. Our findings imply that the nanohole-based AMQ would become a new class of dense-wavelength division multiplexer. AMQs based on low damping Yttrium iron garnet (YIG) allowed for omnidirectional SW emission thanks to the unconventional rotational symmetry of the quasicrystal. Absorption spectra exhibited forbidden frequency gap openings and a corresponding modification of the magnon density of states, indicating the formation of a magnonic band structure. MGCs, prepared from aperiodically arranged ferromagnetic nanopillars on YIG thin films, allowed also for omnidirectional SW emission with a broad range of wave vectors. The constructive/destructive interference of SWs excited by two emitters allowed for a binary 1/0 output operation. ASIs composed of interconnected ferromagnetic nanobars were found to show non-stochastic switching relevant for reconfigurable functionalities. An ASI integrated on a YIG film showed MGC modes and SW channeling with the presence of an external field. The SW spectra at remnant state exhibited reprogrammable characteristics depending on the magnetic field history. Our study on AMQs is important for the fundamental understanding of quasicrystals as well as fabrication of future magnonic devices targeting at information processing by wave-based computing system on the nanoscale.

EPFL2021

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

EPFL2016

Magnons, worms and nanogratings in artificial magnetic quasicrystals

Sho Watanabe

EPFL2021

Theory of representation learning in cortical neural networks

Robust Prediction for Spatial Processes

Magnons, worms and nanogratings in artificial magnetic quasicrystals

Theory of representation learning in cortical neural networks

Robust Prediction for Spatial Processes

Magnons, worms and nanogratings in artificial magnetic quasicrystals