Ken Nakamura

Ken Nakamura, Takayuki Nozaki

This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting code if the error spheres of its states are disjoint, as classical coding theory. In addition, this paper proposes the quantum indel distance and describes insertion and deletion errors correcting capability of quantum codes by this distance.

Ken Nakamura, Tomoya Nakai, Ryuto Yashiro et al.

Artificial vision models are often evaluated against the human visual cortex by measuring how accurately their internal representations predict brain responses. However, prediction accuracy alone does not indicate which dimensions of the target brain's response space are recovered. Here, we introduce a unified framework for evaluating both model-brain and brain-brain alignment by identifying the response dimensions recovered by prediction. Using repeated fMRI measurements, we first identify target-brain response dimensions that can be reproducibly predicted across independent trial splits. We then predict target-brain responses from either another subject's brain responses or a vision model's internal representations, and quantify how strongly each of these reproducible response dimensions is recovered. Applying this framework to a subset of the Natural Scenes Dataset, in which eight subjects viewed the same natural images during fMRI, we find that the early-to-intermediate visual-cortex responses contain a low-dimensional set of reproducible dimensions. Brain-to-brain comparisons identify which of these dimensions are consistently recoverable from other subjects' brains, providing a diagnostic human reference rather than only a scalar benchmark. In some cases, pretrained and randomly initialized models achieve similar prediction accuracy while showing distinct recovery profiles across these response dimensions. These results show that prediction accuracy alone can mask model-brain mismatches. By making explicit which reproducible brain response dimensions are recovered by prediction, our framework provides a more diagnostic evaluation of alignment between artificial vision models and the human visual cortex.

Koki Sasaki, Ken Nakamura, Takayuki Nozaki

This paper focuses on Hagiwara codes, which are quantum deletion-correcting codes constructed by the quantum Reed-Solomon codes. Although Hagiwara codes can correct composite errors consisting of deletions and insertions, an efficient decoding algorithm to such errors remains an open problem. In this paper, we provide a decoding algorithm to such errors for Hagiwara codes.

Ken Nakamura, Masahiko Ueda

Repeated games are a framework for investigating long-term interdependence of multi-agent systems. In repeated games, zero-determinant (ZD) strategies attract much attention in evolutionary game theory, since they can unilaterally control payoffs. Especially, fair ZD strategies unilaterally equalize the payoff of the focal player and the average payoff of the opponents, and they were found in several games including the social dilemma games. Although the existence condition of ZD strategies in repeated games was specified, its extension to stochastic games is almost unclear. Stochastic games are an extension of repeated games, where a state of an environment exists, and the state changes to another one according to an action profile of players. Because of the transition of an environmental state, the existence condition of ZD strategies in stochastic games is more complicated than that in repeated games. Here, we investigate the existence condition of fair ZD strategies in the periodic prisoner's dilemma game, which is one of the simplest stochastic games. We show that fair ZD strategies do not necessarily exist in the periodic prisoner's dilemma game, in contrast to the repeated prisoner's dilemma game. Furthermore, we also prove that the Tit-for-Tat strategy, which imitates the opponent's action, is not necessarily a fair ZD strategy in the periodic prisoner's dilemma game, whereas the Tit-for-Tat strategy is always a fair ZD strategy in the repeated prisoner's dilemma game. Our results highlight difference between ZD strategies in the periodic prisoner's dilemma game and ones in the standard repeated prisoner's dilemma game.

Haruka Asanuma, Naoko Koide-Majima, Ken Nakamura et al.

Recent studies have revealed that human emotions exhibit a high-dimensional, complex structure. A full capturing of this complexity requires new approaches, as conventional models that disregard high dimensionality risk overlooking key nuances of human emotions. Here, we examined the extent to which the latest generation of rapidly evolving Multimodal Large Language Models (MLLMs) capture these high-dimensional, intricate emotion structures, including capabilities and limitations. Specifically, we compared self-reported emotion ratings from participants watching videos with model-generated estimates (e.g., Gemini or GPT). We evaluated performance not only at the individual video level but also from emotion structures that account for inter-video relationships. At the level of simple correlation between emotion structures, our results demonstrated strong similarity between human and model-inferred emotion structures. To further explore whether the similarity between humans and models is at the signle item level or the coarse-categorical level, we applied Gromov Wasserstein Optimal Transport. We found that although performance was not necessarily high at the strict, single-item level, performance across video categories that elicit similar emotions was substantial, indicating that the model could infer human emotional experiences at the category level. Our results suggest that current state-of-the-art MLLMs broadly capture the complex high-dimensional emotion structures at the category level, as well as their apparent limitations in accurately capturing entire structures at the single-item level.