Egy új formaosztályt fedezett fel Domokos Gábor a Gömböc felfedezője, akadémikus, matematikus, a Budapesti Műszaki és Gazdaságtudományi Egyetem professzora, doktorandusz hallgatója Regős Krisztina, és G. Horváth Ákos ugyancsak a BME matematikus professzora. Bizonyították, hogy a lágy cellának elnevezett forma építi fel például, a nautilus csigáspolip házát. Domokos Gáborral és Regős Krisztinával egyebek között arról is beszélgetünk, hogy vajon miért talált ki az evolúció ilyen formát, hogy miért kíváncsi a májsebész a felfedezésükre, és hogy a lágy cellák miért olyan érdekesek az építészek számára, akik felkeresték őket.

It is shown that a normalized complex Hadamard matrix of order 6 having three distinct columns each containing at least one -1 entry, necessarily belongs to the transposed Fourier family, or to the family of 2-circulant complex Hadamard matrices. The proofs rely on solving polynomial systems of equations by Gröbner basis techniques, and make use of a structure theorem concerning regular Hadamard matrices. As a consequence, members of these two families can be easily recognized in practice.

We consider learning a probabilistic classifier from partially-labelled supervision (inputs denoted with multiple possibilities) using standard neural architectures with a softmax as the final layer. We identify a bias phenomenon that can arise from the softmax layer in even simple architectures that prevents proper exploration of alternative options, making the dynamics of gradient descent overly sensitive to initialization. We introduce a novel loss function that allows for unbiased exploration within the space of alternative outputs.

We propose an Optimal Transport (OT)-based generative model from the Wasserstein Autoencoder (WAE) family of models, with the following innovative property: the optimization of the latent point positions takes place over the full training dataset rather than over a minibatch. Our contributions are the following: We define a new class of global Wasserstein Autoencoder models, and implement an Optimal Transport-based incarnation we call the Global Sinkhorn Autoencoder. We implement several metrics for evaluating such models, both in the unsupervised setting, and in a semi-supervised setting, which are the following: the global OT loss, which measures the OT loss on the full test dataset; the reconstruction error on the full test dataset; a so-called covered area which measures how well the latent points are matched; and two types of clustering measures.