We show an organized form of quantum de Finetti theorem for Boolean independence. define a analogue easy groups the categories interval partitions, which is family sequences semigroups. construct Haar states on those The proof our based analysis states. [Modified]Definition semigroups partitions [Delete]Classification [Add]Proof positiveness functionals (in particular they are states)

Abstract Free Probability Theory (FPT) provides rich knowledge for handling mathematical difficulties caused by random matrices appearing in research related to deep neural networks (DNNs), such as the dynamical isometry, Fisher information matrix, and training dynamics. FPT suits these researches because DNN’s parameter-Jacobian input-Jacobian are polynomials of layerwise Jacobians. However, critical assumption asymptotic freeness Jacobian has not been proven mathematically so far. The...

Social VR platforms enable social, economic, and creative activities by allowing users to create share their own virtual spaces. In social VR, photography within a scene is an important indicator of visitors' activities. Although automatic identification photo spots can facilitate the process creating enhance visitor experience, there are challenges in quantitatively evaluating photos taken efficiently exploring large scene. We propose PanoTree, automated photo-spot explorer scenes. To...

Human perception integrates multisensory information, with tactile playing a key role in object and surface recognition. While human-machine interfaces haptic modalities offer enhanced system performance, existing datasets focus primarily on visual data, overlooking comprehensive information. Previous texture databases have recorded sound acceleration signals, but often ignore the nuanced differences between probe-texture finger-texture interactions. Recognizing this shortcoming, we present...

本研究では,高出力,高密度を持つ蓄熱システムを実現するために,蒸発器のない蓄熱装置を用い,高出力・高密度を可能にする反応媒体を選定し,その放熱基礎特性を明らかにした.本システムでは,固液反応によって生じた溶解液を,熱を必要とする場所に直接送り込む水和反応システムを想定し,固液反応のエンタルピー推算結果から,複数の金属塩と水の反応系の中で,CaCl2, CaBr2, or LiBr (s)/H2O (l)を本固液反応システムの反応媒体候補として選定した.そして,この3系を用いて実験を行い,その発熱量を測定した.また,これらの当量比と反応熱の関係を明確にした.本実験の結果,飽和溶解度下にて,CaBr2 (l): 622 kJ/L-water, 534 kJ/L-water,およびCaCl2 481 kJ/L-waterの水和反応発熱量を得た.また,析出防止,蓄熱密度の観点では,CaBr2は,飽和溶解度濃度57 wt%,蓄熱密度451 kJ/L-solutionと3系の中で最も高いことを実験により明らかにし,発熱量は,理論発熱量の96%であった.これらの溶解熱の出力速度は,3系とも1...

We introduce a new method to qualify the goodness of fit parameter estimation compound Wishart models. Our based on free deterministic equivalent Z-score, which we in this paper. Furthermore, an application two dimensional autoregressive moving-average model is provided. proposal generalization statistical hypothesis testing one moving average fluctuations real matrices, recent result by Hasegawa, Sakuma and Yoshida.

The Fisher information matrix (FIM) is fundamental to understanding the trainability of deep neural nets (DNN), since it describes parameter space's local metric. We investigate spectral distribution conditional FIM, which FIM given a single sample, by focusing on fully-connected networks achieving dynamical isometry. Then, while isometry known keep specific backpropagated signals independent depth, we find that metric linearly depends depth even under More precisely, reveal FIM's spectrum...

For random matrix models, the parameter estimation based on traditional likelihood functions is not straightforward in particular when we have only one sample matrix. We introduce a new optimization method for models which works even such case. The spectral distribution instead of likelihood. In method, Cauchy noise has an essential role because free deterministic equivalent, tool probability theory, allows us to approximate perturbed by noises smooth and accessible density function....

Selective forgetting or removing information from deep neural networks (DNNs) is essential for continual learning and challenging in controlling the DNNs. Such crucial also a practical sense since deployed DNNs may be trained on data with outliers, poisoned by attackers, leaked/sensitive information. In this paper, we formulate selective classification tasks at finer level than samples' level. We specify based four datasets distinguished two conditions: whether they contain to forgotten are...

Gradient regularization (GR) is a method that penalizes the gradient norm of training loss during training. While some studies have reported GR can improve generalization performance, little attention has been paid to it from algorithmic perspective, is, algorithms efficiently performance. In this study, we first reveal specific finite-difference computation, composed both ascent and descent steps, reduces computational cost GR. Next, show computation also works better in sense We...

Free Probability Theory (FPT) provides rich knowledge for handling mathematical difficulties caused by random matrices that appear in research related to deep neural networks (DNNs), such as the dynamical isometry, Fisher information matrix, and training dynamics. FPT suits these researches because DNN's parameter-Jacobian input-Jacobian are polynomials of layerwise Jacobians. However, critical assumption asymptotic freenss Jacobian has not been proven completely so far. The freeness plays a...

The interpretability of neural networks (NNs) is a challenging but essential topic for transparency in the decision-making process using machine learning. One reasons lack random weight initialization, where input randomly embedded into different feature space each layer. In this paper, we propose an interpretation method deep multilayer perceptron, which most general architecture NNs, based on identity initialization (namely, matrices). proposed allows us to analyze contribution neuron...

Multi-layer perceptron (MLP) is a fundamental component of deep learning that has been extensively employed for various problems. However, recent empirical successes in MLP-based architectures, particularly the progress MLP-Mixer, have revealed there still hidden potential improving MLPs to achieve better performance. In this study, we reveal MLP-Mixer works effectively as wide MLP with certain sparse weights. Initially, clarify mixing layer Mixer an effective expression wider whose weights...

In this study. CaBr_2 liquid-solid hydration is applied for heat storage without exchanger. Two experiments of the reaction were conducted. The amount generated vapor in equilibrium state was evaluated. instantly reaction. maximum 6.5 mol/L-solution could be generated. and its COP 0.12. regeneration CaBr_2・2H_2O completed after 320 seconds at temperature 190℃ salt layer thickness 1 mm. other cases. times all longer than that above condition, due to detachment from heating surface high...

We investigate parameter identifiability of spectral distributions random matrices. In particular, we treat compound Wishart type and signal-plus-noise type. show that each model is identifiable up to some kind rotation space. Our method based on free probability theory.

We introduce a new method to qualify the goodness of fit parameter estimation compound Wishart models. Our is based on free deterministic equivalent [Formula: see text]-score, which we in this paper. Furthermore, an application two-dimensional autoregressive moving-average model provided. proposed generalization statistical hypothesis testing one-dimensional moving average fluctuations real matrices by Hasegawa et al. [A. Hasegawa, N. Sakuma and H. Yoshida, Fluctuations Marchenko–Pastur...

We investigate parameter identifiability of spectral distributions random matrices. In particular, we treat compound Wishart type and signal-plus-noise type. show that each model is identifiable up to some kind rotation space. Our method based on free probability theory.

A well-conditioned Jacobian spectrum has a vital role in preventing exploding or vanishing gradients and speeding up learning of deep neural networks. Free probability theory helps us to understand handle the spectrum. We rigorously show almost sure asymptotic freeness layer-wise Jacobians networks as wide limit. In particular, we treat case that weights are initialized Haar distributed orthogonal matrices.

Contrastive learning has become one of the most promising approaches for image representations. However, it heavily relies on heuristic data augmentation techniques, such as Gaussian blurring and color jittering, making pairs to be contrastively compared. These augmentations are not always appropriate downstream tasks that each have their own camera illumination settings. In this paper, we aim at improving process propose an generator, a network learns augment images contrastive learning....

The interpretability of neural networks (NNs) is a challenging but essential topic for transparency in the decision-making process using machine learning. One reasons lack random weight initialization, where input randomly embedded into different feature space each layer. In this paper, we propose an interpretation method deep multilayer perceptron, which most general architecture NNs, based on identity initialization (namely, matrices). proposed allows us to analyze contribution neuron...

To obtain the targeted projection appearance in a spatial augmented reality system, we need to solve projector placement problem. However, there are only heuristic solutions for viewpoint planning, which is fundamental problem of placement. In this paper, propose star-kernel decomposition algorithm that can planning an object composed known polygons. The decomposes polygon into subpolygons have non-empty star kernels. We implemented program multiple projectors and evaluated applicability obtained