Neural codes are inevitably shaped by various kinds of biological constraints, e.g.

We thank all reviewers for their comments. We will correct all typos and address all minor comments in the final paper. Other criticisms for BP (spiking and recurrent neural networks) remain? This work was published on 7 Jun 2020 (after the NeurIPS'20 It includes another approximation to BP but no equivalence; we will add it to the related work. Please see line 8 in the response to Reviewer #1.

Agentic AI represents a transformative shift in artificial intelligence, but its rapid advancement has led to a fragmented understanding, often conflating modern neural systems with outdated symbolic models -- a practice known as conceptual retrofitting. This survey cuts through this confusion by introducing a novel dual-paradigm framework that categorizes agentic systems into two distinct lineages: the Symbolic/Classical (relying on algorithmic planning and persistent state) and the Neural/Generative (leveraging stochastic generation and prompt-driven orchestration). Through a systematic PRISMA-based review of 90 studies (2018--2025), we provide a comprehensive analysis structured around this framework across three dimensions: (1) the theoretical foundations and architectural principles defining each paradigm; (2) domain-specific implementations in healthcare, finance, and robotics, demonstrating how application constraints dictate paradigm selection; and (3) paradigm-specific ethical and governance challenges, revealing divergent risks and mitigation strategies. Our analysis reveals that the choice of paradigm is strategic: symbolic systems dominate safety-critical domains (e.g., healthcare), while neural systems prevail in adaptive, data-rich environments (e.g., finance). Furthermore, we identify critical research gaps, including a significant deficit in governance models for symbolic systems and a pressing need for hybrid neuro-symbolic architectures. The findings culminate in a strategic roadmap arguing that the future of Agentic AI lies not in the dominance of one paradigm, but in their intentional integration to create systems that are both adaptable and reliable. This work provides the essential conceptual toolkit to guide future research, development, and policy toward robust and trustworthy hybrid intelligent systems.

The ever-increasing scale of modern neural networks has brought unprecedented performance alongside daunting challenges in efficiency and interpretability. This paper addresses the core question of how to build large neural systems that learn efficient, modular, and interpretable representations. We propose Neuronal Group Communication (NGC), a theory-driven framework that reimagines a neural network as a dynamical system of interacting neuronal groups rather than a monolithic collection of neural weights. Instead of treating each weight as an independent trainable parameter, NGC treats weights as transient interactions between embedding-like neuronal states, with neural computation unfolding through iterative communication among groups of neurons. This low-rank, modular representation yields compact models: groups of neurons exchange low-dimensional signals, enabling intra-group specialization and inter-group information sharing while dramatically reducing redundant parameters. By drawing on dynamical systems theory, we introduce a neuronal stability metric (analogous to Lyapunov stability) that quantifies the contraction of neuron activations toward stable patterns during sequence processing. Using this metric, we reveal that emergent reasoning capabilities correspond to an external driving force or ``potential'', which nudges the neural dynamics away from trivial trajectories while preserving stability. Empirically, we instantiate NGC in large language models (LLMs) and demonstrate improved performance on complex reasoning benchmarks under moderate compression. NGC consistently outperforms standard low-rank approximations and cross-layer basis-sharing methods at comparable compression rates. We conclude by discussing the broader implications of NGC, including how structured neuronal group dynamics might relate to generalization in high-dimensional learning systems.

Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium dynamics of stochastic neural trajectories. Non-equilibrium thermodynamics and representational geometry offer theoretical foundations, but we need scalable data-driven techniques for modeling collective properties of high-dimensional neural networks from partial subsampled observations. Renormalization is a coarse-graining technique central to studying emergent scaling properties of many-body and nonlinear dynamical systems. While widely applied in physics and machine learning, coarse-graining complex dynamical networks remains unsolved, affecting many computational sciences. Recent diffusion-based renormalization, inspired by quantum statistical mechanics, coarse-grains networks near entropy transitions marked by maximal changes in specific heat or information transmission. Here I explore diffusion-based renormalization of neural systems by generating symmetry-breaking representations across scales and offering scalable algorithms using tensor networks. Diffusion-guided renormalization bridges microscale and mesoscale dynamics of dissipative neural systems. For microscales, I developed a scalable graph inference algorithm for discovering community structure from subsampled neural activity. Using community-based node orderings, diffusion-guided renormalization generates renormalization group flow through metagraphs and joint probability functions. Towards mesoscales, diffusion-guided renormalization targets learning the effective non-equilibrium dynamics of dissipative neural trajectories occupying lower-dimensional subspaces, enabling coarse-to-fine control in systems neuroscience and artificial intelligence.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: The authors present a continuous attractor neural model which implements (anticipative) tracking. The authors show that spike frequency adaptation (SFA) can induce traveling waves under certain conditions. Interestingly, they show that the effects induced by SFA are similar to those that can be obtained by introducing asymmetric coupling between neurons as in [14], with the advantage that this method does not depend on hard-wired connections. The bulk of the paper is a theoretical analysis of a simplified model and simulations with the complete model for verification.

To extract motion information, the brain needs to compensate for time delays that are ubiquitous in neural signal transmission and processing. Here we propose a simple yet effective mechanism to implement anticipative tracking in neural systems. The proposed mechanism utilizes the property of spike-frequency adaptation (SFA), a feature widely observed in neuronal responses. We employ continuous attractor neural networks (CANNs) as the model to describe the tracking behaviors in neural systems. Incorporating SFA, a CANN exhibits intrinsic mobility, manifested by the ability of the CANN to support self-sustained travelling waves. In tracking a moving stimulus, the interplay between the external drive and the intrinsic mobility of the network determines the tracking performance. Interestingly, we find that the regime of anticipation effectively coincides with the regime where the intrinsic speed of the travelling wave exceeds that of the external drive. Depending on the SFA amplitudes, the network can achieve either perfect tracking, with zero-lag to the input, or perfect anticipative tracking, with a constant leading time to the input. Our model successfully reproduces experimentally observed anticipative tracking behaviors, and sheds light on our understanding of how the brain processes motion information in a timely manner.

To extract motion information, the brain needs to compensate for time delays that are ubiquitous in neural signal transmission and processing. Here we propose a simple yet effective mechanism to implement anticipative tracking in neural systems. The proposed mechanism utilizes the property of spike-frequency adaptation (SFA), a feature widely observed in neuronal responses. We employ continuous attractor neural networks (CANNs) as the model to describe the tracking behaviors in neural systems. Incorporating SFA, a CANN exhibits intrinsic mobility, manifested by the ability of the CANN to hold self-sustained travelling waves. In tracking a moving stimulus, the interplay between the external drive and the intrinsic mobility of the network determines the tracking performance. Interestingly, we find that the regime of anticipation effectively coincides with the regime where the intrinsic speed of the travelling wave exceeds that of the external drive. Depending on the SFA amplitudes, the network can achieve either perfect tracking, with zero-lag to the input, or perfect anticipative tracking, with a constant leading time to the input. Our model successfully reproduces experimentally observed anticipative tracking behaviors, and sheds light on our understanding of how the brain processes motion information in a timely manner.

Persistent activity refers to the phenomenon that cortical neurons keep firing even after the stimulus triggering the initial neuronal responses is moved. Persistent activity is widely believed to be the substrate for a neural system retaining a memory trace of the stimulus information. In a conventional view, persistent activity is regarded as an attractor of the network dynamics, but it faces a challenge of how to be closed properly. Here, in contrast to the view of attractor, we consider that the stimulus information is encoded in a marginally unstable state of the network which decays very slowly and exhibits persistent firing for a prolonged duration. We propose a simple yet effective mechanism to achieve this goal, which utilizes the property of short-term plasticity (STP) of neuronal synapses. STP has two forms, short-term depression (STD) and short-term facilitation (STF), which have opposite effects on retaining neuronal responses. We find that by properly combining STF and STD, a neural system can hold persistent activity of graded lifetime, and that persistent activity fades away naturally without relying on an external drive. The implications of these results on neural information representation are discussed.