Deep neural networks have received a considerable attention due to the success of their training for real world machine learning applications.

Despite extensive theoretical work on biologically plausible learning rules, clear evidence about whether and how such rules are implemented in the brain has been difficult to obtain.

Over the past decades, we have witnessed a rapid emergence of soft and reconfigurable robots thanks to their capability to interact safely with humans and adapt to complex environments. However, their softness makes accurate control very challenging. High-fidelity sensing is critical in improving control performance, especially posture and contact estimation. To this end, traditional camera-based sensors and load cells have limited portability and accuracy, and they will inevitably increase the robot's cost and weight. In this study, instead of using specialized sensors, we only collect distributed pressure data inside a pneumatics-driven soft arm and apply the physical reservoir computing principle to simultaneously predict its kinematic posture (i.e., bending angle) and payload status (i.e., payload mass). Our results show that, with careful readout training, one can obtain accurate bending angle and payload mass predictions via simple, weighted linear summations of pressure readings. In addition, our comparative analysis shows that, to guarantee low prediction errors within 10\%, bending angle prediction requires less training data than payload prediction. This result reveals that balanced linear and nonlinear body dynamics are critical for the physical reservoir to accomplish complex proprioceptive and exteroceptive information perception tasks. Finally, the method of exploring the most efficient readout training methods presented in this paper could be extended to other soft robotic systems to maximize their perception capabilities.

Artificial neural networks often struggle with catastrophic forgetting when learning multiple tasks sequentially, as training on new tasks degrades the performance on previously learned ones. Recent theoretical work has addressed this issue by analysing learning curves in synthetic frameworks under predefined training protocols. However, these protocols relied on heuristics and lacked a solid theoretical foundation assessing their optimality. In this paper, we fill this gap combining exact equations for training dynamics, derived using statistical physics techniques, with optimal control methods. We apply this approach to teacher-student models for continual learning and multi-task problems, obtaining a theory for task-selection protocols maximising performance while minimising forgetting. Our theoretical analysis offers non-trivial yet interpretable strategies for mitigating catastrophic forgetting, shedding light on how optimal learning protocols can modulate established effects, such as the influence of task similarity on forgetting. Finally, we validate our theoretical findings on real-world data.

Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning. However, the nature of the emergent representations, which we call the `coding scheme', is still unclear. To understand the emergent coding scheme, we investigate fully-connected, wide neural networks learning classification tasks using the Bayesian framework where learning shapes the posterior distribution of the network weights. Consistent with previous findings, our analysis of the feature learning regime (also known as `non-lazy', `rich', or `mean-field' regime) shows that the networks acquire strong, data-dependent features. Surprisingly, the nature of the internal representations depends crucially on the neuronal nonlinearity. In linear networks, an analog coding scheme of the task emerges. Despite the strong representations, the mean predictor is identical to the lazy case. In nonlinear networks, spontaneous symmetry breaking leads to either redundant or sparse coding schemes. Our findings highlight how network properties such as scaling of weights and neuronal nonlinearity can profoundly influence the emergent representations.

Deep neural networks have received a considerable attention due to the success of their training for real world machine learning applications. They are also of great interest to the understanding of sensory processing in cortical sensory hierarchies. The purpose of this work is to advance our theoretical understanding of the computational benefits of these architectures. Using a simple model of clustered noisy inputs and a simple learning rule, we provide analytically derived recursion relations describing the propagation of the signals along the deep network. By analysis of these equations, and defining performance measures, we show that these model networks have optimal depths. We further explore the dependence of the optimal architecture on the system parameters.

Hub structure, characterized by a few highly interconnected nodes surrounded by a larger number of nodes with fewer connections, is a prominent topological feature of biological brains, contributing to efficient information transfer and cognitive processing across various species. In this paper, a mathematical model of hub structure is presented. The proposed method is versatile and can be broadly applied to both computational neuroscience and Recurrent Neural Networks (RNNs) research. We employ the Echo State Network (ESN) as a means to investigate the mechanistic underpinnings of hub structures. Our findings demonstrate a substantial enhancement in performance upon incorporating the hub structure. Through comprehensive mechanistic analyses, we show that the hub structure improves model performance by facilitating efficient information processing and better feature extractions.

In this paper, we experimentally examine the cognitive capability of a simple, paper-based Miura-ori -- using the physical reservoir computing framework -- to achieve different information perception tasks. The body dynamics of Miura-ori (aka. its vertices displacements), which is excited by a simple harmonic base excitation, can be exploited as the reservoir computing resource. By recording these dynamics with a high-resolution camera and image processing program and then using linear regression for training, we show that the origami reservoir has sufficient computing capacity to estimate the weight and position of a payload. It can also recognize the input frequency and magnitude patterns. Furthermore, multitasking is achievable by simultaneously applying two targeted functions to the same reservoir state matrix. Therefore, we demonstrate that Miura-ori can assess the dynamic interactions between its body and ambient environment to extract meaningful information -- an intelligent behavior in the mechanical domain. Given that Miura-ori has been widely used to construct deployable structures, lightweight materials, and compliant robots, enabling such information perception tasks can add a new dimension to the functionality of such a versatile structure.

Online learning via Bayes' theorem allows new data to be continuously integrated into an agent's current beliefs. However, a naive application of Bayesian methods in non stationary environments leads to slow adaptation and results in state estimates that may converge confidently to the wrong parameter value. A common solution when learning in changing environments is to discard/downweight past data; however, this simple mechanism of "forgetting" fails to account for the fact that many real-world environments involve revisiting similar states. We propose a new framework, Bayes with Adaptive Memory (BAM), that takes advantage of past experience by allowing the agent to choose which past observations to remember and which to forget. We demonstrate that BAM generalizes many popular Bayesian update rules for non-stationary environments. Through a variety of experiments, we demonstrate the ability of BAM to continuously adapt in an ever-changing world.