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Characterising the intelligence of biological organisms is challenging. This work considers intelligent algorithms developed evolutionarily within neural systems. Mathematical analyses unveil a natural equivalence between canonical neural networks, variational Bayesian inference under a class of partially observable Markov decision processes, and differentiable Turing machines, by showing that they minimise the shared Helmholtz energy. Consequently, canonical neural networks can biologically plausibly equip Turing machines and conduct variational Bayesian inferences of external Turing machines in the environment. Applying Helmholtz energy minimisation at the species level facilitates deriving active Bayesian model selection inherent in natural selection, resulting in the emergence of adaptive algorithms. In particular, canonical neural networks with two mental actions can separately memorise transition mappings of multiple external Turing machines to form a universal machine. These propositions were corroborated by numerical simulations of algorithm implementation and neural network evolution. These notions offer a universal characterisation of biological intelligence emerging from evolution in terms of Bayesian model selection and belief updating.

Given the rapid advancement of artificial intelligence, understanding the foundations of intelligent behaviour is increasingly important. Active inference, regarded as a general theory of behaviour, offers a principled approach to probing the basis of sophistication in planning and decision-making. In this paper, we examine two decision-making schemes in active inference based on 'planning' and 'learning from experience'. Furthermore, we also introduce a mixed model that navigates the data-complexity trade-off between these strategies, leveraging the strengths of both to facilitate balanced decision-making. We evaluate our proposed model in a challenging grid-world scenario that requires adaptability from the agent. Additionally, our model provides the opportunity to analyze the evolution of various parameters, offering valuable insights and contributing to an explainable framework for intelligent decision-making., Comment: 13 pages, 8 figures

Recent advances in theoretical biology suggest that basal cognition and sentient behaviour are emergent properties of in vitro cell cultures and neuronal networks, respectively. Such neuronal networks spontaneously learn structured behaviours in the absence of reward or reinforcement. In this paper, we characterise this kind of self-organisation through the lens of the free energy principle, i.e., as self-evidencing. We do this by first discussing the definitions of reactive and sentient behaviour in the setting of active inference, which describes the behaviour of agents that model the consequences of their actions. We then introduce a formal account of intentional behaviour, that describes agents as driven by a preferred endpoint or goal in latent state-spaces. We then investigate these forms of (reactive, sentient, and intentional) behaviour using simulations. First, we simulate the aforementioned in vitro experiments, in which neuronal cultures spontaneously learn to play Pong, by implementing nested, free energy minimising processes. The simulations are then used to deconstruct the ensuing predictive behaviour, leading to the distinction between merely reactive, sentient, and intentional behaviour, with the latter formalised in terms of inductive planning. This distinction is further studied using simple machine learning benchmarks (navigation in a grid world and the Tower of Hanoi problem), that show how quickly and efficiently adaptive behaviour emerges under an inductive form of active inference., Comment: 33 pages, 9 figures

Bayesian mechanics is a framework that addresses dynamical systems that can be conceptualised as Bayesian inference. However, the elucidation of requisite generative models is required for empirical applications to realistic self-organising systems. This work shows that the Hamiltonian of generic dynamical systems constitutes a class of generative models, thus rendering their Helmholtz energy naturally equivalent to variational free energy under the identified generative model. The self-organisation that minimises the Helmholtz energy entails matching the system's Hamiltonian with that of the environment, leading to an ensuing emergence of their generalised synchrony. In short, these self-organising systems can be read as performing variational Bayesian inference of the interacting environment. These properties have been demonstrated with coupled oscillators, simulated and living neural networks, and quantum computers. This notion offers foundational characterisations and predictions regarding asymptotic properties of self-organising systems exchanging with the environment, providing insights into potential mechanisms underlying emergence of intelligence.

Transparent conducting oxides (TCOs) are essential components of optoelectronic devices and various materials have been explored for highly efficient TCOs having a combination of high transmittance and low sheet resistance. Here, we focus on a misfit thermoelectric oxide [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$] and fabricate the transparent low-layered crystals by a mechanical tape-peeling method using the single-crystalline samples. From the transmittance measurement, we find that the thickness of low-layered samples is several orders of hundred nanometers, which is comparable with the estimation from the scanning electron microscopy images. Compared to the previous results on the polycrystalline and $c$-axis oriented transparent films, the electrical resistivity is reduced owing to the single-crystalline nature. The figure of merit for the transparent conducting materials in the present low-layered samples is then evaluated to be higher than the values in the previous reports. The present results on the low-layered single-crystalline [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$] may offer a unique class of multi-functional transparent thermoelectric oxides., Comment: 6 pages, 4 figures, 1 table. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing

We present an angle-resolved photoemission spectroscopy study of the single-layer T*-type structured cuprate SmLa$_{1-x}$Sr$_x$CuO$_4$ with unique five-fold pyramidal oxygen coordination. Upon varying oxygen content, T*-SmLa$_{1-x}$Sr$_x$CuO$_4$ evolved from a Mott-insulating to a metallic state where the Luttinger sum rule breaks down under the assumption of a large hole-like Fermi surface. This is in contrast with the known doping evolution of the structural isomer La$_{2-x}$Sr$_x$CuO$_4$ with six-fold octahedral coordination. In addition, quantitatively characterized Fermi surface suggests that the empirical $T_\mathrm{c}$ rule for octahedral oxygen-coordination systems does not apply to T*-SmLa$_{1-x}$Sr$_x$CuO$_4$. The present results highlight unique properties of the T*-type cuprates possibly rooted in its oxygen coordination, and necessitate thorough investigation with careful evaluation of disorder effects., Comment: Accepted for publication in Phys. Rev. B

We investigate the bound orbits of massive/massless, neutral particles and photons moving around regular black holes of Fan and Wang. For massive particles, we show the existence of stable/unstable circular orbits and the charge dependence of the radius of the innermost stable circular orbit. Remarkably, we find an unstable circular orbit of photons inside the event horizon. For massless particles and photons, we show that both stable and unstable circular orbits can exist in a regular and horizonless spacetime with a slight overcharge. Then, we also discuss the periapsis shift of massive neutral particles orbiting around the black hole, and show that the charge gives a negative correction to the shift for black holes with small nonlinearity of electrodynamics., Comment: 19 pages, 8 figures; v2: analysis of photon orbits improved, refs added, 21 pages; v3: published version, fixed minor typos, fixed figures, 20 pages

This paper presents a combined task and motion planner for a robot arm to carry out 3D metal wire curving tasks by collaborating with a bending machine. We assume a collaborative robot that is safe to work in a human environment but has a weak payload to bend objects with large stiffness, and developed a combined planner for the robot to use a bending machine. Our method converts a 3D curve to a bending set and generates the feasible bending sequence, machine usage, robotic grasp poses, and pick-and-place arm motion considering the combined task and motion level constraints. Compared with previous deformable linear object shaping work that relied on forces provided by robotic arms, the proposed method is suitable for the material with high stiffness. We evaluate the system using different tasks. The results show that the proposed system is flexible and robust to generate robotic motion to corporate with the designed bending machine.

The Kalman filter is an algorithm for the estimation of hidden variables in dynamical systems under linear Gauss-Markov assumptions with widespread applications across different fields. Recently, its Bayesian interpretation has received a growing amount of attention especially in neuroscience, robotics and machine learning. In neuroscience, in particular, models of perception and control under the banners of predictive coding, optimal feedback control, active inference and more generally the so-called Bayesian brain hypothesis, have all heavily relied on ideas behind the Kalman filter. Active inference, an algorithmic theory based on the free energy principle, specifically builds on approximate Bayesian inference methods proposing a variational account of neural computation and behaviour in terms of gradients of variational free energy. Using this ambitious framework, several works have discussed different possible relations between free energy minimisation and standard Kalman filters. With a few exceptions, however, such relations point at a mere qualitative resemblance or are built on a set of very diverse comparisons based on purported differences between free energy minimisation and Kalman filtering. In this work, we present a straightforward derivation of Kalman filters consistent with active inference via a variational treatment of free energy minimisation in terms of gradient descent. The approach considered here offers a more direct link between models of neural dynamics as gradient descent and standard accounts of perception and decision making based on probabilistic inference, further bridging the gap between hypotheses about neural implementation and computational principles in brain and behavioural sciences.

The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational cost to identify an approximate global minimum for a class of cost functions defined under a high-dimensional discrete state space. Then, we derive an optimal global search scheme that minimises the computational cost. Mathematical analyses demonstrate that a combination of the gradient descent algorithm and the selection and crossover algorithm--with a biased crossover weight--maximises the search efficiency. Remarkably, its computational cost is of the square root order in contrast to that of the conventional gradient descent algorithms, indicating a quadratic speedup of global search. We corroborate this proposition using numerical analyses of the travelling salesman problem. The simple computational architecture and minimal computational cost of the proposed scheme are highly desirable for biological organisms and neuromorphic hardware., Comment: 52 pages, 4 figures, 1 table