Considering the proliferation of responses to Piantadosi's original paper and the ongoing debate sparked by this special issue of the Italian Journal of Linguistics, it is clear that the discussion has touched a raw nerve in linguistic theorizing . In the original target paper (Chesi, this issue), I illustrated three prototypical (and in many respects, extreme) positions -- the computational, theoretical, and experimental perspectives -- without explicitly endorsing any of them. Instead, I attempted to highlight what I believe are the key weaknesses o f each of these prototypical stances, ultimately concluding that formal (i.e., ' generative ') linguistics -- more specifically, Minimalis m, my theoretical comfort zone -- must adopt practices and tools that are common in both computational and experimental fields . As noted by most respondents, the title and some of the more extreme statements were intended as mild provocations to draw attention to core issues affecting linguistic theorizing . M y position -- somehow obscured behind the ' three - body problem ' -- is that any relevant scientific progress is driven by theoretical insight, not by trawling using experimental or computational methods that are cost - inefficient, energy - intensive, and ultimately unsustainable . Moreover, in full agreement with most of the replies, I believe that the success of certain large language models (L L Ms), which are based on specific architectural assumptions, do es not constitute a refutation of the generative paradigm. On the contrary, it strongly supports several key intuitions that have emerged within the generative linguistic tradition (Rizzi this issue) . H owever, a concrete problem of ' incommensurability ' arises (Hao this issue), as differing methodologies and specialized jargon (Butt this issue) often result in circular, unresolved discussions .

In this study, we discuss the relationship between two families of density-power-based divergences with functional degrees of freedom -- the H\"{o}lder divergence and the functional density power divergence (FDPD) -- based on their intersection and generalization. These divergence families include the density power divergence and the $\gamma$-divergence as special cases. First, we prove that the intersection of the H\"{o}lder divergence and the FDPD is limited to a general divergence family introduced by Jones et al. (Biometrika, 2001). Subsequently, motivated by the fact that H\"{o}lder's inequality is used in the proofs of nonnegativity for both the H\"{o}lder divergence and the FDPD, we define a generalized divergence family, referred to as the $\xi$-H\"{o}lder divergence. The nonnegativity of the $\xi$-H\"{o}lder divergence is established through a combination of the inequalities used to prove the nonnegativity of the H\"{o}lder divergence and the FDPD. Furthermore, we derive an inequality between the composite scoring rules corresponding to different FDPDs based on the $\xi$-H\"{o}lder divergence. Finally, we prove that imposing the mathematical structure of the H\"{o}lder score on a composite scoring rule results in the $\xi$-H\"{o}lder divergence.

This paper investigates a novel nonlinear update rule based on temporal difference (TD) errors in reinforcement learning (RL). The update rule in the standard RL states that the TD error is linearly proportional to the degree of updates, treating all rewards equally without no bias. On the other hand, the recent biological studies revealed that there are nonlinearities in the TD error and the degree of updates, biasing policies optimistic or pessimistic. Such biases in learning due to nonlinearities are expected to be useful and intentionally leftover features in biological learning. Therefore, this research explores a theoretical framework that can leverage the nonlinearity between the degree of the update and TD errors. To this end, we focus on a control as inference framework, since it is known as a generalized formulation encompassing various RL and optimal control methods. In particular, we investigate the uncomputable nonlinear term needed to be approximately excluded in the derivation of the standard RL from control as inference. By analyzing it, Weber-Fechner law (WFL) is found, namely, perception (a.k.a. the degree of updates) in response to stimulus change (a.k.a. TD error) is attenuated by increase in the stimulus intensity (a.k.a. the value function). To numerically reveal the utilities of WFL on RL, we then propose a practical implementation using a reward-punishment framework and modifying the definition of optimality. Analysis of this implementation reveals that two utilities can be expected i) to increase rewards to a certain level early, and ii) to sufficiently suppress punishment. We finally investigate and discuss the expected utilities through simulations and robot experiments. As a result, the proposed RL algorithm with WFL shows the expected utilities that accelerate the reward-maximizing startup and continue to suppress punishments during learning.

In reinforcement learning (RL), temporal difference (TD) error is known to be related to the firing rate of dopamine neurons. It has been observed that each dopamine neuron does not behave uniformly, but each responds to the TD error in an optimistic or pessimistic manner, interpreted as a kind of distributional RL. To explain such a biological data, a heuristic model has also been designed with learning rates asymmetric for the positive and negative TD errors. However, this heuristic model is not theoretically-grounded and unknown whether it can work as a RL algorithm. This paper therefore introduces a novel theoretically-grounded model with optimism and pessimism, which is derived from control as inference. In combination with ensemble learning, a distributional value function as a critic is estimated from regularly introduced optimism and pessimism. Based on its central value, a policy in an actor is improved. This proposed algorithm, so-called DROP (distributional and regular optimism and pessimism), is compared on dynamic tasks. Although the heuristic model showed poor learning performance, DROP showed excellent one in all tasks with high generality. In other words, it was suggested that DROP is a new model that can elicit the potential contributions of optimism and pessimism.

Model-based reinforcement learning has attracted much attention due to its high sample efficiency and is expected to be applied to real-world robotic applications. In the real world, as unobservable disturbances can lead to unexpected situations, robot policies should be taken to improve not only control performance but also robustness. Adversarial learning is an effective way to improve robustness, but excessive adversary would increase the risk of malfunction, and make the control performance too conservative. Therefore, this study addresses a new adversarial learning framework to make reinforcement learning robust moderately and not conservative too much. To this end, the adversarial learning is first rederived with variational inference. In addition, light robustness, which allows for maximizing robustness within an acceptable performance degradation, is utilized as a constraint. As a result, the proposed framework, so-called LiRA, can automatically adjust adversary level, balancing robustness and conservativeness. The expected behaviors of LiRA are confirmed in numerical simulations. In addition, LiRA succeeds in learning a force-reactive gait control of a quadrupedal robot only with real-world data collected less than two hours.

We consider the problem of finding the ``best'' approximation of an $n$-dimensional probability measure $\rho$ using a measure $\nu$ whose support is parametrized by $f : \mathbb{R}^m \to \mathbb{R}^n$ where $m < n$. We quantify the performance of the approximation with the Monge-Kantorovich $p$-cost (also called the Wasserstein $p$-cost) $\mathbb{W}_p^p(\rho, \nu)$, and constrain the complexity of the approximation by bounding the $W^{k,q}$ Sobolev norm of $f$, which acts as a ``budget.'' We may then reformulate the problem as minimizing a functional $\mathscr{J}_p(f)$ under a constraint on the Sobolev budget. We treat general $k \geq 1$ for the Sobolev differentiability order (though $q, m$ are chosen to restrict $W^{k,q}$ to the supercritical regime $k q > m$ to guarantee existence of optimizers). The problem is closely related to (but distinct from) principal curves with length constraints when $m=1, k = 1$ and smoothing splines when $k > 1$. New aspects and challenges arise from the higher order differentiability condition. We study the gradient of $\mathscr{J}_p$, which is given by a vector field along $f$ we call the barycenter field. We use it to construct improvements to a given $f$, which gives a nontrivial (almost) strict monotonicty relation between the functional $\mathscr{J}_p$ and the Sobolev budget. We also provide a natural discretization scheme and establish its consistency. We use this scheme to model a generative learning task; in particular, we demonstrate that adding a constraint like ours as a soft penalty yields substantial improvement in training a GAN to produce images of handwritten digits, with performance competitive with weight-decay.

Recently, research in human-robot interaction began to consider a robot's influence at the group level. Despite the recent growth in research investigating the effects of robots within groups of people, our overall understanding of what happens when robots are placed within groups or teams of people is still limited. This paper investigates several key problems for social robots that manage conversations in a group setting, where the number of participants is more than two. In a group setting, the conversation dynamics are a lot more complicated than the conventional one-to-one conversation, thus, there are more challenges need to be solved.

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

This paper introduces a novel method of adding intrinsic bonuses to task-oriented reward function in order to efficiently facilitate reinforcement learning search. While various bonuses have been designed to date, they are analogous to the depth-first and breadth-first search algorithms in graph theory. This paper, therefore, first designs two bonuses for each of them. Then, a heuristic gain scheduling is applied to the designed bonuses, inspired by the iterative deepening search, which is known to inherit the advantages of the two search algorithms. The proposed method is expected to allow agent to efficiently reach the best solution in deeper states by gradually exploring unknown states. In three locomotion tasks with dense rewards and three simple tasks with sparse rewards, it is shown that the two types of bonuses contribute to the performance improvement of the different tasks complementarily. In addition, by combining them with the proposed gain scheduling, all tasks can be accomplished with high performance.