arXiv subjects

Yusuke Hayashi

Publications and source records attributed to Yusuke Hayashi.

12 recordsLinked to original sources

arXiv2026

Lost and Found in Translation: Variational Diagnostics for Neural Codebook Channels

Classical communication systems fail not only through random noise but also when transmitter and receiver use incompatible operational codebooks. Variational autoencoders (VAEs) train an encoder $q_\phi$ and decoder $p_\theta$ jointly, and practitioners treat the resulting latent space as a discrete code -- for clustering, conditional generation, and mechanistic interpretability. Yet standard VAE diagnostics -- ELBO, active units, mutual information, and code histograms -- certify only whether this code is used, never whether the decoder reads each latent under the encoder's code. We close this gap with the neural codebook channel $K_{e\to d}(j\mid i)$, a coupled encoder-decoder diagnostic whose off-diagonal mass is bounded by an architecture-free Bernoulli-KL certificate $d_{\mathrm{bin}}(1-\mathcal{A} \,\|\, \bar\eta_p) \le \bar\Delta$ controlled by the variational gap. The certificate is the operational specialization of the classical KL chain rule under disintegration to the encoder-decoder disagreement event, complemented by a constructive marginal-impossibility result: no combination of marginal histograms, entropies, active-code counts, or mutual information determines $K_{e\to d}$. We audit the certificate on four sklearn datasets (finite-grid exact, 5/5 seeds, 20/20 pairs satisfy the bound), a 2D model where the bound is non-vacuous at $2.71\times$ the observed disagreement and the four-term identity closes within $10^{-4}$, MNIST under importance-sampling control, and a VQ-VAE attaining the predicted limit $\hat{\mathcal{A}}=1.000$. The package $(K_{e\to d}, \mathcal{A}, R_{\mathrm{eff}}, R, \mathrm{AU})$ is an audit-ready reporting unit. More broadly, the framework makes mismatched decoding -- a failure mode classical communication theory named decades ago -- visible inside a single deep generative model.

cs.LG↗

arXiv2026

Topology and category for singular product spaces

For $\kappa$ a regular uncountable cardinal, the higher Baire and Cantor spaces ${}^\kappa\kappa$ and ${}^\kappa2$ (endowed with the ${<}\kappa$-box topology) have been relatively well-studied, but less is known about the case where $\kappa$ is singular. We will consider several spaces of functions and box topologies that could serve as higher Baire and Cantor spaces for singular cardinals. The ultimate focus of the article lies in studying cardinal characteristics of the ideal of $\kappa$-meagre subsets of these spaces.

math.LO↗

arXiv2026

Thermodynamic Limits of Physical Intelligence

Modern AI systems achieve remarkable capabilities at the cost of substantial energy consumption. To connect intelligence to physical efficiency, we propose two complementary bits-per-joule metrics under explicit accounting conventions: (1) Thermodynamic Epiplexity per Joule, new bits of structure about a specified environment-instance variable encoded in an agent's state per unit energy, and (2) Empowerment per Joule, sensorimotor channel capacity per expected energetic cost over a fixed horizon. These give two axes of physical intelligence, recognition versus control, but the resulting numbers are benchmark-relative rather than universal. Drawing on stochastic thermodynamics, we formulate a Landauer-scale closed-cycle benchmark for epiplexity acquisition by combining a thermodynamic-learning inequality with data processing, and clarify why boundary closure is required; conversely, a decoupling construction shows that without such assumptions information gain and in-boundary dissipation need not be tightly linked. For empirical settings where the latent structure variable is unavailable, we recommend compute-bounded MDL epiplexity / compression-gain surrogates. Finally, we propose a unified efficiency framework with a minimal checklist of conventions for relative bits-per-joule comparisons, and give a compact language-model reporting example.

cs.LG↗

arXiv2025

Stationary list colorings

Komjath studied the list chromatic number of infinite graphs and introduced the notion of restricted list chromatic number. For a graph $X=(V_X,E_X)$ and a cardinal $\kappa$, we say that $X$ is restricted list colorable for $\kappa$ if for every $L:V_X\to[\kappa]^\kappa$ there is a choice function $c$ of $L$ such that $c(v)\neq c(w)$ whenever ${v,w}\in E_X$. In this paper, we discuss a variation, stationary list colorability for $\kappa$, obtained by replacing $[\kappa]^\kappa$ with the set of all stationary subsets of $\kappa$. We compare the stationary list colorability with other coloring properties. Among other things, we prove that the stationary list colorability is essentially different from other coloring properties including the restricted list colorability. We also prove the consistency result showing that for some $\kappa<\lambda$, restricted and stationary list colorability at $\kappa$ do not imply the corresponding properties at $\lambda$.

math.LO↗

arXiv2025

Dominating numbers at singular cardinals

We study the generalized dominating number $\mathfrak{d}_{\mu}$ at a singular cardinal $\mu$ of cofinality $\kappa$. We show two lower bounds: in ZFC, $\mathrm{cf}([\mu]^\kappa,\subseteq) \leq \mathfrak{d}_{\mu}$, and under mild cardinal-arithmetic assumptions, $2^{<\mu} \leq \mathfrak{d}_{\mu}$. We also clarify when $\mathfrak{d}_{\mu}$ can differ from $2^{\mu}$: assuming GCH and $\kappa = \mathrm{cf}(\mu) > \omega$, a finite-support iteration of Cohen forcing of length $\mu^{++}$ yields $\mathfrak{d}_{\mu} < 2^{\mu}$. On the other hand, for $\kappa = \mathrm{cf}(\mu) = \omega$, natural $\mu$-cc posets force $\mathfrak{d}_{\mu} = 2^{\mu}$.

math.LO↗

arXiv2025

Universal AI maximizes Variational Empowerment

This paper presents a theoretical framework unifying AIXI -- a model of universal AI -- with variational empowerment as an intrinsic drive for exploration. We build on the existing framework of Self-AIXI -- a universal learning agent that predicts its own actions -- by showing how one of its established terms can be interpreted as a variational empowerment objective. We further demonstrate that universal AI's planning process can be cast as minimizing expected variational free energy (the core principle of active Inference), thereby revealing how universal AI agents inherently balance goal-directed behavior with uncertainty reduction curiosity). Moreover, we argue that power-seeking tendencies of universal AI agents can be explained not only as an instrumental strategy to secure future reward, but also as a direct consequence of empowerment maximization -- i.e. the agent's intrinsic drive to maintain or expand its own controllability in uncertain environments. Our main contribution is to show how these intrinsic motivations (empowerment, curiosity) systematically lead universal AI agents to seek and sustain high-optionality states. We prove that Self-AIXI asymptotically converges to the same performance as AIXI under suitable conditions, and highlight that its power-seeking behavior emerges naturally from both reward maximization and curiosity-driven exploration. Since AIXI can be view as a Bayes-optimal mathematical formulation for Artificial General Intelligence (AGI), our result can be useful for further discussion on AI safety and the controllability of AGI.

cs.AI↗

arXiv2024

Game-theoretic variants of splitting number

We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $\mathfrak{s}$ since the corresponding cardinal invariants behave in an interesting way. We introduce three kinds of games as reasonable realizations of the combination of the notions of splitting and infinite games. Then, we consider two cardinal invariants for each game, so we define six numbers. We prove that three of them are equal to the size of the continuum $\mathfrak{c}$ and one of them is equal to the $\sigma$-splitting number $\mathfrak{s}_\sigma$, which is defined as the minimum size of a $\sigma$-splitting family. On the other hand, we show that the remaining two numbers are consistently different from $\mathfrak{c}$, $\mathfrak{s}$ and $\mathfrak{s}_\sigma$. Moreover, though the two numbers share almost the same rule of the game, we prove that they can take distinct values from each other, and hence the slight difference of the rule is actually crucial in this sense.

math.LO↗

arXiv2024

Collective Predictive Coding as Model of Science: Formalizing Scientific Activities Towards Generative Science

This paper proposes a new conceptual framework called Collective Predictive Coding as a Model of Science (CPC-MS) to formalize and understand scientific activities. Building on the idea of collective predictive coding originally developed to explain symbol emergence, CPC-MS models science as a decentralized Bayesian inference process carried out by a community of agents. The framework describes how individual scientists' partial observations and internal representations are integrated through communication and peer review to produce shared external scientific knowledge. Key aspects of scientific practice like experimentation, hypothesis formation, theory development, and paradigm shifts are mapped onto components of the probabilistic graphical model. This paper discusses how CPC-MS provides insights into issues like social objectivity in science, scientific progress, and the potential impacts of AI on research. The generative view of science offers a unified way to analyze scientific activities and could inform efforts to automate aspects of the scientific process. Overall, CPC-MS aims to provide an intuitive yet formal model of science as a collective cognitive activity.

physics.soc-ph↗

arXiv2023

Game-theoretic variants of cardinal invariants

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the reaping number $\mathfrak{r}$, the bounding number $\mathfrak{b}$, the dominating number $\mathfrak{d}$, and the additivity number of the null ideal $\operatorname{add}(\mathsf{null})$. We also consider games, called tallness games, defined according to ideals on $\omega$ and characterize that each of Player I and Player II has a winning strategy.

math.LO↗

arXiv2022

Molecular beam homoepitaxy of N-polar AlN: enabling role of Al-assisted surface cleaning

N-polar aluminum nitride (AlN) is an important building block for next-generation high-power RF electronics. We report successful homoepitaxial growth of N-polar AlN by molecular beam epitaxy (MBE) on large-area cost-effective N-polar AlN templates. Direct growth without any in-situ surface cleaning leads to films with inverted Al-polarity. It is found that Al-assisted cleaning before growth enables the epitaxial film to maintain N-polarity. The grown N-polar AlN epilayer with its smooth, pit-free surface duplicates the structural quality of the substrate as evidenced by a clean and smooth growth interface with no noticeable extended defects generation. Near band-edge photoluminescence peaks are observed at room temperature on samples with MBE-grown layers but not on the bare AlN substrates, implying the suppression of non-radiative recombination centers in the epitaxial N-polar AlN. These results are pivotal steps towards future high-power RF electronics and deep ultraviolet photonics based on the N-polar AlN platform.

cond-mat.mtrl-sci↗

arXiv2020

Meta Cyclical Annealing Schedule: A Simple Approach to Avoiding Meta-Amortization Error

The ability to learn new concepts with small amounts of data is a crucial aspect of intelligence that has proven challenging for deep learning methods. Meta-learning for few-shot learning offers a potential solution to this problem: by learning to learn across data from many previous tasks, few-shot learning algorithms can discover the structure among tasks to enable fast learning of new tasks. However, a critical challenge in few-shot learning is task ambiguity: even when a powerful prior can be meta-learned from a large number of prior tasks, a small dataset for a new task can simply be very ambiguous to acquire a single model for that task. The Bayesian meta-learning models can naturally resolve this problem by putting a sophisticated prior distribution and let the posterior well regularized through Bayesian decision theory. However, currently known Bayesian meta-learning procedures such as VERSA suffer from the so-called {\it information preference problem}, that is, the posterior distribution is degenerated to one point and is far from the exact one. To address this challenge, we design a novel meta-regularization objective using {\it cyclical annealing schedule} and {\it maximum mean discrepancy} (MMD) criterion. The cyclical annealing schedule is quite effective at avoiding such degenerate solutions. This procedure includes a difficult KL-divergence estimation, but we resolve the issue by employing MMD instead of KL-divergence. The experimental results show that our approach substantially outperforms standard meta-learning algorithms.

stat.ML↗

arXiv2017

First Data Release of the Hyper Suprime-Cam Subaru Strategic Program

The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is a three-layered imaging survey aimed at addressing some of the most outstanding questions in astronomy today, including the nature of dark matter and dark energy. The survey has been awarded 300 nights of observing time at the Subaru Telescope and it started in March 2014. This paper presents the first public data release of HSC-SSP. This release includes data taken in the first 1.7 years of observations (61.5 nights) and each of the Wide, Deep, and UltraDeep layers covers about 108, 26, and 4 square degrees down to depths of i~26.4, ~26.5, and ~27.0 mag, respectively (5sigma for point sources). All the layers are observed in five broad bands (grizy), and the Deep and UltraDeep layers are observed in narrow bands as well. We achieve an impressive image quality of 0.6 arcsec in the i-band in the Wide layer. We show that we achieve 1-2 per cent PSF photometry (rms) both internally and externally (against Pan-STARRS1), and ~10 mas and 40 mas internal and external astrometric accuracy, respectively. Both the calibrated images and catalogs are made available to the community through dedicated user interfaces and database servers. In addition to the pipeline products, we also provide value-added products such as photometric redshifts and a collection of public spectroscopic redshifts. Detailed descriptions of all the data can be found online. The data release website is https://hsc-release.mtk.nao.ac.jp/.

astro-ph.IM↗