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NeuroHex is a brain-inspired hexagonal coordinate system designed to support highly efficient world models and reference frames for online adaptive AI systems. Inspired by the hexadirectional firing structure of grid cells in the human brain, NeuroHex adopts a cubic isometric hexagonal coordinate formulation that provides full 60° rotational symmetry and low-cost translation, rotation and distance computation. We develop a mathematical framework that incorporates ring indexing, quantized angular encoding, and a hierarchical library of foundational, simple, and complex geometric shape primitives. These constructs allow low-overhead point-in-shape tests and spatial matching operations that are expensive in Cartesian coordinate systems. To support realistic settings, we also develop a novel tool (OSM2Hex) that can process OpenStreetMap (OSM) data sets and convert them into the NeuroHex coordinate system. The OSM2Hex spatial abstraction processing pipeline can achieve a reduction of 90-99% in geometric complexity while maintaining the relevant spatial structure map for navigation. Our initial results, based on actual city and neighborhood scale data sets, demonstrate that NeuroHex offe

The Quantum-Inspired Stacked Integrated Concept Graph Model (QISICGM) is an innovative machine learning framework that harnesses quantum-inspired techniques to predict diabetes risk with exceptional accuracy and efficiency. Utilizing the PIMA Indians Diabetes dataset augmented with 2,000 synthetic samples to mitigate class imbalance (total: 2,768 samples, 1,949 positives), QISICGM integrates a self-improving concept graph with a stacked ensemble comprising Random Forests (RF), Extra Trees (ET), transformers, convolutional neural networks (CNNs), and feed-forward neural networks (FFNNs). This approach achieves an out-of-fold (OOF) F1 score of 0.8933 and an AUC of 0.8699, outperforming traditional methods. Quantum inspired elements, such as phase feature mapping and neighborhood sequence modeling, enrich feature representations, enabling CPU-efficient inference at 8.5 rows per second. This paper presents a detailed architecture, theoretical foundations, code insights, and performance evaluations, including visualizations from the outputs subfolder. The open-source implementation (v1.0.0) is available at https://github.com/keninayoung/QISICGM, positioning QISICGM as a potential benchm

Reinforcement learning (RL) agents often face challenges in balancing exploration and exploitation, particularly in environments where sparse or dense rewards bias learning. Biological systems, such as human toddlers, naturally navigate this balance by transitioning from free exploration with sparse rewards to goal-directed behavior guided by increasingly dense rewards. Inspired by this natural progression, we investigate the Toddler-Inspired Reward Transition in goal-oriented RL tasks. Our study focuses on transitioning from sparse to potential-based dense (S2D) rewards while preserving optimal strategies. Through experiments on dynamic robotic arm manipulation and egocentric 3D navigation tasks, we demonstrate that effective S2D reward transitions significantly enhance learning performance and sample efficiency. Additionally, using a Cross-Density Visualizer, we show that S2D transitions smooth the policy loss landscape, resulting in wider minima that improve generalization in RL models. In addition, we reinterpret Tolman's maze experiments, underscoring the critical role of early free exploratory learning in the context of S2D rewards.

Despite its successes, to date Artificial Intelligence (AI) is still characterized by a number of shortcomings with regards to different application domains and goals. These limitations are arguably both conceptual (e.g., related to underlying theoretical models, such as symbolic vs. connectionist), and operational (e.g., related to robustness and ability to generalize). Biologically inspired AI, and more specifically brain-inspired AI, promises to provide further biological aspects beyond those that are already traditionally included in AI, making it possible to assess and possibly overcome some of its present shortcomings. This article examines some conceptual, technical, and ethical issues raised by the development and use of brain-inspired AI. Against this background, the paper asks whether there is anything ethically unique about brain-inspired AI. The aim of the paper is to introduce a method that has a heuristic nature and that can be applied to identify and address the ethical issues arising from brain-inspired AI. The conclusion resulting from the application of this method is that, compared to traditional AI, brain-inspired AI raises new foundational ethical issues and so

Inspired by the proof of the Bertrand postulate given by P. ErdőS, we carefully examine and solve one less usual inequality in positive integers which could help to find an arithmetically pure proof that for every positive integer $n\ge2$ there is a prime $p$ such that $n<p<2n$.

This article gives an overview of some recent results in commutative algebra that are inspired by the work of Wiles, Taylor and Wiles, Diamond, Lenstra and others on the modularity of elliptic curves.

In this short note we study Born-Infeld Inspired Gravity together with an action functional for ideal fluid. We obtain corresponding equations of motion and also determine canonical form of this action.

In our effort to find an arithmetically pure proof of the Bertrand postulate, we investigate and solve (using only elementary arithmetical methods) another less usual inequality in positive integers inspired by the classical proof of the postulate given by P. Erdős.

Traditional neural networks, while powerful, rely on biologically implausible learning mechanisms such as global backpropagation. This paper introduces the Structurally Adaptive Predictive Inference Network (SAPIN), a novel computational model inspired by the principles of active inference and the morphological plasticity observed in biological neural cultures. SAPIN operates on a 2D grid where processing units, or cells, learn by minimizing local prediction errors. The model features two primary, concurrent learning mechanisms: a local, Hebbian-like synaptic plasticity rule based on the temporal difference between a cell's actual activation and its learned expectation, and a structural plasticity mechanism where cells physically migrate across the grid to optimize their information-receptive fields. This dual approach allows the network to learn both how to process information (synaptic weights) and also where to position its computational resources (network topology). We validated the SAPIN model on the classic Cart Pole reinforcement learning benchmark. Our results demonstrate that the architecture can successfully solve the CartPole task, achieving robust performance. The netwo

In spiking neural networks (SNNs), the main unit of information processing is the neuron with an internal state. The internal state generates an output spike based on its component associated with the membrane potential. This spike is then communicated to other neurons in the network. Here, we propose a general multiple-input multiple-output (MIMO) spiking neuron model that goes beyond this traditional single-input single-output (SISO) model in the SNN literature. Our proposed framework is based on interpreting the neurons as state-space models (SSMs) with linear state evolutions and non-linear spiking activation functions. We illustrate the trade-offs among various parameters of the proposed SSM-inspired neuron model, such as the number of hidden neuron states, the number of input and output channels, including single-input multiple-output (SIMO) and multiple-input single-output (MISO) models. We show that for SNNs with a small number of neurons with large internal state spaces, significant performance gains may be obtained by increasing the number of output channels of a neuron. In particular, a network with spiking neurons with multiple-output channels may achieve the same level

The entorhinal-hippocampal formation is the mammalian brain's navigation system, encoding both physical and abstract spaces via grid cells. This system is well-studied in neuroscience, and its efficiency and versatility make it attractive for applications in robotics and machine learning. While continuous attractor networks (CANs) successfully model entorhinal grid cells for encoding physical space, integrating both continuous spatial and abstract spatial computations into a unified framework remains challenging. Here, we attempt to bridge this gap by proposing a mechanistic model for versatile information processing in the entorhinal-hippocampal formation inspired by CANs and Vector Symbolic Architectures (VSAs), a neuro-symbolic computing framework. The novel grid-cell VSA (GC-VSA) model employs a spatially structured encoding scheme with 3D neuronal modules mimicking the discrete scales and orientations of grid cell modules, reproducing their characteristic hexagonal receptive fields. In experiments, the model demonstrates versatility in spatial and abstract tasks: (1) accurate path integration for tracking locations, (2) spatio-temporal representation for querying object locati

Artificial neural networks (ANNs) were inspired by the architecture and functions of the human brain and have revolutionised the field of artificial intelligence (AI). Inspired by studies on the latent geometry of the brain, in this perspective paper we posit that an increase in the research and application of hyperbolic geometry in ANNs and machine learning will lead to increased accuracy, improved feature space representations and more efficient models across a range of tasks. We examine the structure and functions of the human brain, emphasising the correspondence between its scale-free hierarchical organization and hyperbolic geometry, and reflecting on the central role hyperbolic geometry plays in facilitating human intelligence. Empirical evidence indicates that hyperbolic neural networks outperform Euclidean models for tasks including natural language processing, computer vision and complex network analysis, requiring fewer parameters and exhibiting better generalisation. Despite its nascent adoption, hyperbolic geometry holds promise for improving machine learning models through brain-inspired geometric representations.

We study Born-Infeld inspired gravity in covariant canonical formalism. We determine corresponding Hamiltonian and equations of motion.

Modern data-driven machine learning system designs exploit inductive biases in architectural structure, invariance and equivariance requirements, task-specific loss functions, and computational optimization tools. Previous works have illustrated that human-specified quasi-invariant filters can serve as a powerful inductive bias in the early layers of the encoder, enhancing robustness and transparency in learned classifiers. This paper explores this further within the context of representation learning with bio-inspired Hebbian learning rules. We propose a modular framework trained with a bio-inspired variant of contrastive predictive coding, comprising parallel encoders that leverage different invariant visual descriptors as inductive biases. We evaluate the representation learning capacity of our system in classification scenarios using diverse image datasets (GTSRB, STL10, CODEBRIM) and video datasets (UCF101). Our findings indicate that this form of inductive bias significantly improves the robustness of learned representations and narrows the performance gap between models using local Hebbian plasticity rules and those using backpropagation, while also achieving superior perfor

Deep learning for image super-resolution (SR) has been investigated by numerous researchers in recent years. Most of the works concentrate on effective block designs and improve the network representation but lack interpretation. There are also iterative optimization-inspired networks for image SR, which take the solution step as a whole without giving an explicit optimization step. This paper proposes an unfolding iterative shrinkage thresholding algorithm (ISTA) inspired network for interpretable image SR. Specifically, we analyze the problem of image SR and propose a solution based on the ISTA method. Inspired by the mathematical analysis, the ISTA block is developed to conduct the optimization in an end-to-end manner. To make the exploration more effective, a multi-scale exploitation block and multi-scale attention mechanism are devised to build the ISTA block. Experimental results show the proposed ISTA-inspired restoration network (ISTAR) achieves competitive or better performances than other optimization-inspired works with fewer parameters and lower computation complexity.

Snakes and their bio-inspired robot counterparts have demonstrated locomotion on a wide range of terrains. However, dynamic vertical climbing is one locomotion strategy that has received little attention in the existing snake robotics literature. We demonstrate a new scansorial gait and robot inspired by the locomotion of the Pacific Lamprey. This new gait allows a robot to steer while climbing on flat, near-vertical surfaces. A reduced-order model is developed and used to explore the relationship between body actuation and vertical and lateral motions of the robot. Trident, the new wall climbing lamprey-inspired robot, demonstrates dynamic climbing on flat vertical surfaces with a peak net vertical stride displacement of 4.1 cm per step. Actuating at 1.3 Hz, Trident attains a vertical climbing speed of 4.8 cm/s (0.09 Bl/s) at specific resistance of 8.3. Trident can also traverse laterally at 9 cm/s (0.17 Bl/s). Moreover, Trident is able to make 14\% longer strides than the Pacific Lamprey when climbing vertically. The computational and experimental results demonstrate that a lamprey-inspired climbing gait coupled with appropriate attachment is a useful climbing strategy for snake

Sense and avoid capability enables insects to fly versatilely and robustly in dynamic complex environment. Their biological principles are so practical and efficient that inspired we human imitating them in our flying machines. In this paper, we studied a novel bio-inspired collision detector and its application on a quadcopter. The detector is inspired from LGMD neurons in the locusts, and modeled into an STM32F407 MCU. Compared to other collision detecting methods applied on quadcopters, we focused on enhancing the collision selectivity in a bio-inspired way that can considerably increase the computing efficiency during an obstacle detecting task even in complex dynamic environment. We designed the quadcopter's responding operation imminent collisions and tested this bio-inspired system in an indoor arena. The observed results from the experiments demonstrated that the LGMD collision detector is feasible to work as a vision module for the quadcopter's collision avoidance task.

We propose a Quantum-Inspired Subspace(QIS) Ensemble Method for generating feature ensembles based on feature selections. We assign each principal component a Fraction Transition Probability as its probability weight based on Principal Component Analysis and quantum interpretations. In order to generate the feature subset for each base regressor, we select a feature subset from principal components based on Fraction Transition Probabilities. The idea originating from quantum mechanics can encourage ensemble diversity and the accuracy simultaneously. We incorporate Quantum-Inspired Subspace Method into Random Forest and propose Quantum-Inspired Forest. We theoretically prove that the quantum interpretation corresponds to the first order approximation of ensemble regression. We also evaluate the empirical performance of Quantum-Inspired Forest and Random Forest in multiple hyperparameter settings. Quantum-Inspired Forest proves the significant robustness of the default hyperparameters on most data sets. The contribution of this work is two-fold, a novel ensemble regression algorithm inspired by quantum mechanics and the theoretical connection between quantum interpretations and machi

In this paper we highlight the scopes of engineering bio-inspired political systems, which are political systems based on the properties of life that self-organize the increasing complexity of human social systems. We describe bio-inspired political systems and conjecture about various ways to get to them, most notably, metaheuristics, modeling and simulation and complexified topologies. Bio-inspired political systems operate with nature-based dynamics, inspired on the knowledge that has been acquired about complexity from natural social systems and life. Bio-inspired political systems are presented as the best alternative for organizing human sociopolitical interactions as computation and microelectronics-based technology profoundly modify the ways in which humans decide. Therefore, weakening classical political systems. For instance, dwindling top-down power structures, modifying the notion of geographical spatiality and augmenting the political granularity. We also argue that, more than a new theoretical proposal, bio-inspired political systems are coming to be the political systems of the future.