arXiv subjects

Kotaro Sakamoto

Publications and source records attributed to Kotaro Sakamoto.

3 recordsLinked to original sources

arXiv2026

The Geometry of Phase Transitions in Generative Dynamics via Projection Caustics

Continuous-state generative samplers, including diffusion and flow-matching models, evolve through continuous reverse-time dynamics, yet their samples often undergo abrupt qualitative changes: trajectories commit to modes, semantic alternatives collapse, and small perturbations in narrow time windows can produce large downstream effects. This paper develops a geometric account of such phase-transition-like behaviour. We view denoising as gradient descent on a free energy landscape and show that sharp transitions arise near projection caustics, where the nearest-point projection onto the data support ceases to be unique. Motivated by this perspective, we introduce the Critical Boundary Detector (CBD), as practical diagnostics for score-direction instability. Across toy models, standard diffusion models, and latent text-to-image diffusion models, CBD localises mode commitment, predicts intervention-sensitive windows, and supports targeted control in geometrically sensitive regions. Our results connect geometry of data and dynamics of diffusion generation.

cs.LG↗

arXiv2023

Deep Learning in Random Neural Fields: Numerical Experiments via Neural Tangent Kernel

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive fields. In this paper, we investigate such neural fields in a multilayer architecture to investigate the supervised learning of the fields. We empirically compare the performances of our field model with those of randomly connected deep networks. The behavior of a randomly connected network is investigated on the basis of the key idea of the neural tangent kernel regime, a recent development in the machine learning theory of over-parameterized networks; for most randomly connected neural networks, it is shown that global minima always exist in their small neighborhoods. We numerically show that this claim also holds for our neural fields. In more detail, our model has two structures: i) each neuron in a field has a continuously distributed receptive field, and ii) the initial connection weights are random but not independent, having correlations when the positions of neurons are close in each layer. We show that such a multilayer neural field is more robust than conventional models when input patterns are deformed by noise disturbances. Moreover, its generalization ability can be slightly superior to that of conventional models.

cs.LG↗

arXiv2018

Finding Continuity and Discontinuity in Fish Schools via Integrated Information Theory

Collective behaviour is known to be the result of diverse dynamics and is sometimes likened to a living system. Although many studies have revealed the dynamics of various collective behaviours, their main focus was on the information process inside the collective, not on the whole system itself. For example, the qualitative difference between two elements and three elements as a system has rarely been investigated. Tononi et al. have proposed Integrated Information Theory (IIT) to measure the degree of consciousness $Φ$. IIT postulates that the amount of information loss caused by certain partitions is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here we applied IIT (in particular, IIT 3.0 using PyPhi) to analyse real fish schools ({\it Plecoglossus altivelis}). Our hypothesis in this study is a very simple one: a living system evolves to raise its $Φ$ value. If we accept this hypothesis, IIT reveals the existence of continuous and discontinuous properties as group size varies. For example, leadership in the fish school emerged for a school size of four or above; but not below three. Furthermore, this transition was not observed by measuring mutual information or in a simple Boids model. This result suggests that integrated information $Φ$ can reveal some inherent properties which cannot be observed using other measures. We also discuss how the fish recognition of the figure-ground relation, that is, what determines the relevant ON and OFF states, may reveal various optimal paths for obtaining the functional evolution of collective behaviour.

physics.soc-ph↗