Biologically inspired neural network layer with homeostatic regulation and adaptive repair mechanisms

Abstract

Neural networks face persistent challenges in maintaining stability and robustness during training, particularly in noisy or high-dimensional domains like molecular analysis. Inspired by biological neural systems that leverage homeostasis and self-repair to sustain functionality, this paper proposes BioLogicalNeuron—a novel neural network layer that integrates calcium-driven homeostatic regulation, self-repair mechanisms, and dynamic stability monitoring. The layer mimics biological calcium dynamics to maintain neuronal activity within optimal ranges, proactively triggers targeted synaptic repair and adaptive noise injection to counteract degradation, and modulates learning rates via real-time health metrics. Extensive experiments across multiple molecular and chemical datasets show that BioLogicalNeuron achieves state-of-the-art break performance. The layer’s performance is particularly strong on molecular datasets, where its biological mechanisms naturally align with molecular structure learning. Through detailed analysis of calcium dynamics and health-stability relationships, this work demonstrates that BioLogicalNeuron achieves a biologically plausible balance between stability and plasticity, offering insights into both artificial and biological neural networks. This results suggest that incorporating biological mechanisms into neural architectures can lead to more robust and effective learning systems, particularly for molecular and chemical analysis tasks.

Introduction

Neural networks have become the cornerstone of modern machine learning, achieving remarkable success in tasks ranging from image recognition to natural language processing. However, despite their widespread adoption, current neural architectures face significant challenges that hinder their robustness, adaptability and generalization capabilities. These challenges include training instability, sensitivity to noisy or incomplete data and difficulty in maintaining optimal neuron states over extended training periods. Addressing these issues is critical for advancing the field and enabling the deployment of neural networks in real-world, dynamic environments.

Current challenges in neural architectures

Modern neural networks, while powerful, often struggle with training instability and overfitting. For instance, vanishing or exploding gradients can destabilize training, while noisy or incomplete data can degrade model performance. Additionally, traditional layers lack mechanisms to monitor and maintain neuron health, leading to issues such as neuron saturation or dying neurons. These problems are particularly pronounced in molecular datasets, where data is often sparse, noisy and high-dimensional. Existing approaches, such as regularization techniques and dropout, provide partial solutions but fail to address the root causes of these issues.

Biological inspiration from neural homeostasis

Biological neurons exhibit remarkable robustness and adaptability, thanks to mechanisms such as homeostasis and self-repair. In biological systems, homeostasis maintains internal stability by regulating variables such as calcium levels and synaptic strength. When neurons are damaged or degraded, biological systems activate repair mechanisms to restore functionality. These principles have inspired recent advances in biologically inspired neural networks, which aim to replicate the stability and adaptability of biological systems in artificial neural networks.

For example, spiking neural networks (SNNs)^1,2 mimic the temporal dynamics of biological neurons, while neural ODEs model^3,4 continuous-time dynamics. However, these approaches often focus on specific aspects of biological neurons, such as temporal processing or energy efficiency and fail to fully capture the holistic regulation observed in biological systems. This gap highlights the need for a comprehensive framework that integrates multiple biological principles into a single neural network layer.

Gap in existing approaches

Despite the growing interest in biologically inspired neural networks, existing approaches have several limitations:

• 1. Lack of comprehensive homeostasis Most models focus on isolated aspects of biological neurons, such as spiking dynamics or energy efficiency and fail to incorporate holistic homeostatic regulation.

• 2. Reactive, not proactive Rather than proactively halting neuron deterioration, current healing systems frequently address problems only after they arise.

• 3. Limited generalization Many biologically inspired models are tailored to specific tasks or datasets and struggle to generalize across different data types, such as molecular and graph-based data.

These limitations underscore the need for a novel neural network layer that integrates homeostatic regulation, adaptive repair mechanisms and real-time health monitoring to address the challenges of modern neural architectures.

Key contributions

To address these challenges, this paper introduce BioLogicalNeuron, a novel neural network layer that integrates biological homeostasis and adaptive repair mechanisms into a unified framework. The key contributions of this work are as follows:

• Novel homeostatic regulation mechanism BioLogicalNeuron incorporates calcium dynamics and synaptic strength monitoring to maintain neuron health and stability. By mimicking biological homeostasis, the layer ensures that neurons remain within optimal operating ranges, preventing issues such as neuron saturation or dying neurons.

• Adaptive repair strategies When neuron health degrades, BioLogicalNeuron activates adaptive repair mechanisms^5,6, such as activity-dependent synaptic scaling, selective synaptic reinforcement, activity-dependent pruning, and to restore functionality. These mechanisms are proactive, addressing issues before they destabilize the network and are guided by real-time health metrics.

• State-of-the-art performance on molecular datasets BioLogicalNeuron achieves state-of-the-art results on multiple molecular datasets, including AIDS⁷, COX2⁸ and HIV⁷. On the AIDS dataset, the layer surpasses previous SOTA results. Similarly, on the HIV dataset, it demonstrates high accuracy, showcasing its effectiveness in complex, real-world tasks.

• Generalization across different data types Beyond molecular data, BioLogicalNeuron demonstrates strong performance on graph-based datasets (e.g., Cora⁹, CiteSeer¹⁰) and image datasets (e.g., CIFAR-10¹¹, MNIST¹²). This versatility highlights the layer’s ability to generalize across diverse data types and tasks.

• Versatile integration across architectures The BioLogicalNeuron layer demonstrates remarkable flexibility and can be effectively incorporated into diverse neural network architectures, including Graph Neural Networks (GNNs)^13,14,15 and attention-based^16,17 models. Empirical results indicate that integrating the BioLogicalNeuron enhances representational capacity and learning efficiency, leading to improved model performance across various molecular prediction tasks. This versatility highlights its potential as a fundamental component for advancing deep learning approaches in complex scientific applications.

Broader impact

By bridging the gap between biological principles and artificial neural networks, BioLogicalNeuron offers a new paradigm for designing robust, adaptive and efficient neural networks. The layer’s self-regulating mechanisms and adaptive repair strategies address key challenges in neural network training, such as instability and overfitting, while its biological grounding provides a scientifically rigorous framework for future research.

In addition to raising the bar for neural network design, this work creates new opportunities for biologically inspired AI research. By demonstrating the effectiveness of homeostatic regulation and adaptive repair in artificial systems, BioLogicalNeuron paves the way for the development of next-generation neural networks that are more robust, adaptable and efficient.

Related work

The integration of biological principles into artificial neural networks (ANNs) has been a growing area of research, driven by the desire to create more robust, adaptable and efficient models. Recent advancements in this field have drawn inspiration from biological neural networks (BNNs)^18,19, leveraging insights from neuroscience to improve the performance and biological plausibility of ANNs. Below, This paper reviews the most recent and significant contributions to this field, highlighting key innovations, limitations and future directions.

Neural networks and biological analogies (2023–2024)

Recent work by Baba²⁰ explores the impact of dead neurons on ANN performance, drawing parallels between artificial and biological neural networks. Baba’s study investigates how neuron death during training affects ANN performance, offering insights into neurological disorders. The paper introduces a conceptual analogy between the Adam optimizer and the brain’s learning process, suggesting that successive training phases incorporating visual and acoustic data could improve treatment strategies for behavioral disorders. However, the study is limited by its focus on artificial systems and the lack of empirical validation in biological contexts.

Similarly, Dehghani and Levin²¹ propose a bio-inspired AI framework that incorporates biological principles such as context-dependent information processing and multi-scale organization. Their work emphasizes the importance of hierarchical and context-sensitive information processing, introducing the concept of “polycomputing” where a single substrate performs multiple computations simultaneously. While their framework is conceptually innovative, it lacks concrete implementation details and empirical validation, highlighting the challenges of translating biological complexity into artificial systems.

Spiking neural networks (SNNs) and neuromorphic computing (2023–2024)

One method that has shown promise in bridging the gap between artificial and biological intelligence is Spiking Neural Networks (SNNs). Wang et al.²² introduce HIFI, a biologically inspired SNN that incorporates self-inhibiting autapses and neuron heterogeneity to improve learning and memory capabilities. HIFI outperforms traditional SNNs in accuracy, efficiency and latency, particularly in tasks like image classification and single-cell RNA sequencing (scRNA-seq)²³ analysis. However, the model’s high computational complexity and dependence on data quality limit its applicability in resource-constrained environments.

Nikitin et al.²⁴ introduced a novel approach to interconnection between neuron firing rate homeostasis and weight change through spike-timing-dependent plasticity (STDP) growth bounded by abstract protein reserve. They demonstrated how “these cellular dynamics help neurons filter out intense noise signals to help neurons keep a stable firing rate” without affecting the ability to recognize correlated inputs in unsupervised mode. As they observe, “Biological neural networks are different from digital analogs in many ways. Brain neurons are slow, noisy, and constrained by energy and spatial dimensions. However, they still outperform modern AI systems in many ways.” Their work on constrained plasticity reserve provides important insights into how biological neurons maintain stability despite changing input intensities—a key challenge addressed by our BioLogicalNeuron model.

Zheng et al.²⁵ provide a comprehensive survey of SNNs, tracing their historical development and highlighting their role in biocomputational simulations and neuromorphic computing. The authors emphasize the synergy between SNNs and Brain-Computer Interfaces (BCIs), particularly in decoding natural spike trains from the brain. Despite their potential, SNNs face challenges in scalability, hardware constraints and trade-offs between computational accuracy and energy efficiency.

Synthetic biological neural networks (SYNBIONNs) (2024)

Vasle and Moškon²⁶ review the current state of Synthetic Biological Neural Networks (SYNBIONNs), which are ANNs implemented using engineered biological parts. The authors discuss various biological platforms, such as DNA, RNA and proteins, for designing perceptrons and multilayer neural networks. They highlight advancements in DNA-based Hopfield networks, Winner-Take-All (WTA) networks²⁷ and convolutional neural networks (ConvNets)²⁸. However, SYNBIONNs face significant challenges in scalability, online learning and robustness, limiting their practical applications.

Biologically plausible neural networks (BPNNs) (2023)

Jeon and Kim²⁹ explore the bottom-up approach to building biologically plausible neural networks, incorporating properties such as Hebbian learning, spike-timing-dependent plasticity (STDP) and dendritic computation. The authors propose a formalism to categorize neural networks based on their similarity to BNNs, introducing the concept of the “BNN supremacy regime”. While BPNNs offer advantages in power efficiency and natural problem-solving, they often underperform ANNs in traditional tasks like image classification and their implementation remains computationally expensive.

Homeostatic regulation and adaptive learning (2023–2024)

Homeostatic regulation is a fundamental property of biological neural systems that maintains stability while enabling adaptation to changing environments. Tsitolovsky³⁰ established that homeostasis is what distinguishes living from non-living systems. He noted that “When we consider only individual life, rather than the existence of species, it is homeostasis, not heredity, that makes non-living things alive; and the end of homeostasis leads to death within seconds.” His work further suggests that “motivation arises when neurons in specific brain areas leave the state of homeostatic equilibrium and are injured.” This indicates that homeostasis may “produce both maintenance of life and the will to act.” The connection between homeostasis and motivation provides a biological foundation for adaptive learning mechanisms.

Sandler and Tsitolovsky³¹ proposed a dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian). They demonstrated that “a living organism capable of ’feeling distress’ should exhibit homeostasis.” Their mathematical framework explains how homeostatic function depends on sensors that register deviations from the norm, which then trigger regulatory responses. They further elaborated that “the status of the internal environment is not sustainable for all life.” Conditions remain stable only at intervals of time as compared to environmental variability. During these intervals, “homeostasis counteracts weak disorders in the system and recovers initial conditions (direct regulation).” This understanding of homeostatic regulation as a dynamic process informs our approach to calcium-based homeostasis in BioLogicalNeuron.

Homeostatic regulation and adaptive learning are critical for maintaining neural network stability and performance. O’Neill et al.³² investigate the role of Brain-Derived Neurotrophic Factor (BDNF) in neural network dynamics. They demonstrate its ability to restore homeostasis after injury. The study highlights the importance of network-level effects in therapeutic applications. However, it is limited by its focus on in vitro hippocampal networks³³.

Mayzel and Schneidman³⁴ introduce a new class of statistical models for neural population codes. They emphasize the role of synaptic normalization and homeostatic mechanisms in optimizing learning. Their “Reshaped RP” model demonstrates that sparse, random connectivity is optimal for neural network efficiency. This offers insights for both biological and artificial systems. However, the study relies on synthetic data and shallow models, limiting its generalizability.

Adaptive repair mechanisms in deep neural networks (2023)

Li Calsi et al.³⁵ propose ADREP, an adaptive search-based repair technique for Deep Neural Networks (DNNs) that addresses the “fault shift” problem in neural network repair. The authors demonstrate that ADREP outperforms state-of-the-art methods in terms of repair effectiveness, efficiency and generalization. However, the approach is limited by its focus on specific types of faults and its reliance on a predefined set of repair operators.

Bridging the gap with BioLogicalNeuron

Our BioLogicalNeuron model builds upon these foundational works by implementing calcium-based homeostasis mechanisms inspired by biological neurons. Like the sensor-based approach described by Sandler and Tsitolovsky³¹, our model uses calcium levels as sensors to detect deviations from normal functioning. When calcium levels exceed healthy thresholds, adaptive repair mechanisms are triggered to restore neural health.

Similar to the constrained plasticity reserve proposed by Nikitin et al.²⁴, our model implements bounded weight adjustments based on neural health. This approach helps maintain stable neural activity while enabling effective learning, addressing the challenge of balancing stability and plasticity in neural networks.

By incorporating these biologically-inspired mechanisms, BioLogicalNeuron bridges the gap between traditional artificial neural networks and their biological counterparts, offering improved robustness, adaptability, and performance across a range of tasks. The following sections detail our approach and evaluate its effectiveness compared to standard neural network layers.

Methods

Biological neural layer architecture

The BioLogicalNeuron framework introduces a novel biologically-inspired neural architecture that fundamentally reimagines traditional artificial neural networks by incorporating three key biological mechanisms: calcium-based dynamics, homeostatic regulation and adaptive repair strategies. This framework extends beyond conventional neural networks by introducing biologically-motivated constraints and self-regulatory mechanisms observed in natural neural systems. The architecture is designed to address common challenges in deep learning, such as catastrophic forgetting, gradient instability and loss of representational power during extended training periods.

This implementation builds upon weight-normalized neural layers while introducing biological constraints through a carefully orchestrated system of regulatory mechanisms. The framework maintains a continuous internal state that evolves during training, similar to biological neurons’ adaptive behaviors. This internal state influences both the forward propagation of information and the network’s learning dynamics.

Architecture overview

The BioLogicalNeuron layer can be integrated into various neural network architectures as a specialized layer that enhances biological plausibility and robustness. The layer can be added to existing neural networks in two primary ways:

• 1. As a replacement for standard layers The BioLogicalNeuron layer can replace standard linear or fully connected layers throughout a neural network architecture , transforming the entire network shown in Fig. 1 into a biologically plausible system.

• 2. As an additional layer The BioLogicalNeuron layer can be added on top of existing neural network architectures, serving as an interface layer that enhances the biological plausibility of the overall system while preserving the specialized functions of the underlying architecture.

This flexibility allows the BioLogicalNeuron layer to be integrated into diverse neural network architectures, including Graph Neural Networks (GNNs)^13,14,15 and attention-based models, enhancing their representational capacity and learning efficiency while maintaining biological plausibility.

Fig. 1

BioLogicalNeuron integrates homeostatic regulation, health monitoring, and adaptive repair—using calcium dynamics, synaptic scaling, and pruning—triggered by neural health states to maintain stability via weight-normalized input processing.

Mathematical formulation

The core of the BioLogicalNeuron layer is a linear transformation followed by a non-linear activation function³⁶. Given an input vector $x \in \mathbb{R}^{d_{in}}$, the output $y \in \mathbb{R}^{d_{out}}$ is computed as:

$$\begin{aligned} y = \text{GELU}(Wx + b) \end{aligned}$$

(1)

where

• $W \in \mathbb{R}^{d_{out} \times d_{in}}$ is the weight matrix,

• $b \in \mathbb{R}^{d_{out}}$ is the bias vector,

• $\text{GELU}(\cdot )$ is the Gaussian Error Linear Unit activation function, chosen for its smoothness and biological plausibility, as it approximates the cumulative distribution function of a Gaussian, similar to the firing rates of biological neurons.

Calcium dynamics

In biological systems, homeostasis maintains intracellular calcium at low steady-state levels, as high calcium concentrations are cytotoxic to neurons. Our model implements this principle through the following equation:

$$\begin{aligned} c_t = c_{base} + (c_{t-1} - c_{base}) \cdot \alpha - \beta \cdot \max (0, \bar{y}_t - \theta _{act}) \end{aligned}$$

(2)

where

• $c_t \in \mathbb{R}^{d_{out}}$ represents calcium levels at time t

• $c_{base} \in \mathbb{R}$ is the baseline calcium level (low steady-state)

• $\alpha \in [0, 1]$ is the calcium decay rate

• $\beta \in \mathbb{R}^+$ is the calcium reduction factor

• $\bar{y}_t \in \mathbb{R}^{d_{out}}$ is the mean activation at time t

• $\theta _{act} \in \mathbb{R}$ is the activation threshold

This formulation ensures that calcium levels naturally decay toward a low baseline and that excessive neural activity triggers calcium reduction mechanisms to prevent cytotoxicity.

Homeostatic regulation mechanism

The homeostatic regulation mechanism³⁷ ensures that the neuron maintains a stable internal state by monitoring calcium levels, synaptic strengths, and health metrics. In biological systems, homeostatic mechanisms work to maintain neural activity within an optimal range by adjusting synaptic strengths and intrinsic excitability. The health of the neuron $h_t \in [0, 1]$ is computed as:

$$\begin{aligned} h_t = \sigma (\theta _c - c_t + \gamma \cdot \text{Stability}(W)), \end{aligned}$$

(3)

where

• $\theta _c$ is a calcium threshold parameter, representing the optimal calcium level,

• $\gamma \in \mathbb{R}$ is the stability scale, controlling the influence of synaptic stability on health,

• $\text{Stability}(W)$ is a measure of synaptic weight stability, rather than just magnitude.

This formulation aligns with biological reality, where lower calcium levels (below the toxic threshold $\theta _c$) contribute to better neuronal health. The $\text{Stability}(W)$ term replaces the simple weight norm used in the original formulation, reflecting that biological synaptic scaling is concerned with maintaining stability rather than maximizing synaptic strength. In biological systems, synaptic scaling typically reduces weights following periods of high activity to prevent runaway excitation, a process known as homeostatic synaptic plasticity.

Homeostatic regulation

In biological systems, homeostasis is critical for preventing excitotoxicity and maintaining optimal neural function. Below, we describe each component of our biologically plausible homeostatic regulation³⁷ system, supported by Figs. 2 and 3 presents the corresponding workflow output and analysis.

Fig. 2

Architectural diagram of a Homeostatic Regulation Mechanism in Neural Systems. The system integrates input-driven calcium updates, health prediction via stability metrics, and summary reporting, all operating over shared states (e.g., synaptic strengths, calcium levels). Internal and external processes interact with these states to maintain neural stability.

Calcium level monitoring

Calcium levels in biological neurons play a critical role in regulating neural activity and maintaining homeostasis. In biological systems, calcium homeostasis maintains low steady-state values of calcium, as high levels are cytotoxic. In the BioLogicalNeuron layer, calcium levels $c_t \in \mathbb{R}^{d_{out}}$ at time step $t$ are modeled as:

$$\begin{aligned} c_t = \alpha c_{t-1} + (1 - \alpha ) \cdot \beta \cdot \bar{y}_t, \end{aligned}$$

(4)

where

• $\alpha \in [0, 1]$ is the decay rate, controlling how quickly calcium levels dissipate,

• $\beta \in \mathbb{R}$ is the activation scale, determining the influence of neural activity on calcium levels,

• $\bar{y}_t$ represents the neuron’s mean activity at time step $t$.

This formulation allows calcium levels to increase with neural activity, but unlike traditional models, we interpret high calcium levels as potentially harmful, which aligns with biological reality where excessive calcium is cytotoxic. The system therefore aims to maintain calcium levels below a critical threshold $\theta _{Ca}$.

Stability metrics

The stability of the neuron $s_t \in [0, 1]$ is computed as:

$$\begin{aligned} s_t = 1 - \frac{\text{std}(h_{t-w:t})}{\text{mean}(h_{t-w:t}) + \epsilon }, \end{aligned}$$

(5)

where

• $h_{t-w:t}$ are the health scores over a prediction window $w$,

• $\text{std}(\cdot )$ and $\text{mean}(\cdot )$ are the standard deviation and mean of the health scores, respectively,

• $\epsilon$ is a small constant to prevent division by zero.

This stability metric quantifies the consistency of neuron health over time. A high stability score indicates that the neuron’s health remains consistent, while a low score suggests fluctuations that may require intervention. This metric is interpreted in the context of our biologically accurate health assessment, where health is inversely related to calcium levels above the optimal threshold.

Health assessment

The health of the neuron $h_t \in [0, 1]$ is computed as:

$$\begin{aligned} h_t = \sigma (\theta _{Ca} - c_t + \gamma \cdot \text{stability}(W)), \end{aligned}$$

(6)

where

• $\theta _{Ca}$ is the calcium threshold, representing the optimal calcium level,

• $\gamma \in \mathbb{R}$ is the stability scale, controlling the influence of synaptic stability on health,

• $\text{stability}(W)$ represents the stability of synaptic weights over time.

This formulation reflects biological reality where lower calcium levels (below the toxic threshold $\theta _{Ca}$) indicate better health. The term $\theta _{Ca} - c_t$ ensures that health decreases as calcium levels rise above the optimal threshold, which aligns with the cytotoxic nature of excessive calcium in biological neurons. Additionally, the model considers synaptic stability rather than just synaptic strength, which better reflects biological processes where stable synaptic connections are crucial for neuron health.

The stability of weights is computed as:

$$\begin{aligned} \text{stability}(W) = 1 - \frac{\text{std}(W_{t-w:t})}{\text{mean}(W_{t-w:t}) + \epsilon }, \end{aligned}$$

(7)

where $W_{t-w:t}$ represents the weight values over a time window $w$.

Multi-strategy repair system

When the neuron’s health $h_t$ falls below a predefined threshold $\theta$, the multi-strategy repair system is triggered example shown in Fig. 3 to restore stability:

Activity-dependent synaptic scaling In biological neurons, synaptic scaling³⁸ is a homeostatic mechanism that adjusts synaptic strengths in response to changes in overall neural activity. When a neuron is overactive (indicated by elevated calcium levels), synaptic scaling reduces the strength of excitatory³⁹ inputs:

$$\begin{aligned} W_{\text{high-Ca}} = W_{\text{high-Ca}} \cdot (1 - \eta _{\text{scale}} \cdot (1 - s_t)), \end{aligned}$$

(8)

where

• $\eta _{\text{scale}}$ is the scaling intensity,

• $s_t$ is the neuron’s stability,

• $W_{\text{high-Ca}}$ represents weights associated with neurons having calcium levels above the threshold $\theta _{Ca}$.

This mechanism replaces the random noise injection in the original model with a biologically plausible process that specifically targets weight reduction following periods of high activity, preventing excitotoxicity⁴⁰.

Selective synaptic reinforcement Biological neurons selectively reinforce important synaptic connections, a process critical for learning and memory formation⁴¹. Our model implements this through:

$$\begin{aligned} W_{\text{strong}} = W_{\text{strong}} \cdot (1 + \eta _{\text{reinforce}}), \end{aligned}$$

(9)

where

• $\eta _{\text{reinforce}}$ is a small reinforcement factor,

• $W_{\text{strong}}$ represents weights with magnitude significantly above the mean.

This approach strengthens frequently used connections that contribute significantly to neuron function, similar to Hebbian learning⁴² principles of “neurons that fire together, wire together.”

Fig. 3

BioLogicalNeuron homeostatic regulation and adaptive repair. Visualization of homeostatic mechanisms in the BioLogicalNeuron layer during approximately 4500 training steps on the HIV dataset. (a) Neuron Health Metrics: Health (pink) and stability (gold) metrics initially decline but stabilize around 0.90–0.92, with repair events (red stars) preventing catastrophic degradation throughout training. (b) Calcium Level Dynamics: Intracellular calcium levels (purple) show progressive increase from 0 to over 5.0 $\upmu$M, with the 50-step moving average (blue dashed) revealing distinct phases of initial rapid rise, intermediate fluctuations, and late-stage acceleration. (c) Repair Strategy Distribution: Cumulative activation of three biologically-inspired repair mechanisms shows activity-dependent pruning (green) dominates with over 250 activations, followed by selective reinforcement (tan) and synaptic scaling (pink). (d) Health-Calcium Phase Space: The inverse relationship between calcium levels (y-axis) and neuron health (x-axis) across training steps (color gradient) demonstrates how homeostatic mechanisms maintain health above approximately 0.88 despite calcium levels exceeding 5.0 $\upmu$M.

Activity-dependent pruning In biological neural networks, synapses that are rarely used or contribute minimally to neural function are gradually weakened and eventually pruned, a process essential for neural network refinement⁴³. Our model implements this through:

$$\begin{aligned} W_{\text{weak}} = W_{\text{weak}} \cdot (1 - \eta _{\text{prune}}), \end{aligned}$$

(10)

where

• $\eta _{\text{prune}}$ is a small pruning factor,

• $W_{\text{weak}}$ represents weights with magnitude significantly below the mean.

This mechanism ensures that neural resources are allocated efficiently by gradually reducing the influence of weak or unused synaptic connections, improving overall network efficiency and signal-to-noise ratio.

Adaptive learning rates

The adaptive learning rate $\eta _t$ is computed based on neuron health and stability:

$$\begin{aligned} \eta _t = \eta _0 \cdot h_t \cdot s_t, \end{aligned}$$

(11)

where

• $\eta _0$ is the base learning rate,

• $h_t$ is the neuron health at time $t$,

• $s_t$ is the neuron stability at time $t$.

This formulation ensures that the learning rate is dynamically adjusted based on the neuron’s health and stability. When the neuron is healthy (low calcium levels) and stable, the learning rate is increased to accelerate learning. Conversely, when the neuron is unstable or unhealthy (high calcium levels), the learning rate is reduced to prevent further damage. This approach mimics biological neural systems where plasticity is modulated by neuron health and activity levels.

Neural health monitoring system

This work develops a comprehensive monitoring system to track and visualize the dynamic behavior of biological neurons during training. The system incorporates multiple interconnected metrics to provide real-time assessment of neuronal health, stability and calcium dynamics, while also tracking various repair mechanisms.

Health and stability metrics

The neuronal health metric $H_t$ at time step $t$ is computed as a composite function:

$$\begin{aligned} H_t = \sigma (\theta _{Ca} - C_t + \gamma \cdot \text{stability}(W)), \end{aligned}$$

(12)

where

• $\theta _{Ca}$ is the calcium threshold, representing the optimal calcium level,

• $C_t$ represents the calcium level at time $t$,

• $\gamma$ is the stability scale, controlling the influence of synaptic stability on health,

• $\text{stability}(W)$ represents the stability of synaptic weights over time.

This formulation reflects biological reality where lower calcium levels (below the toxic threshold $\theta _{Ca}$) indicate better health, aligning with the cytotoxic nature of excessive calcium in biological neurons.

Calcium dynamics

This formulation in Eq. (2) allows calcium levels to increase with neural activity, but unlike traditional models, we interpret high calcium levels as potentially harmful, which aligns with biological reality where excessive calcium is cytotoxic. The calcium dynamics described in section "Calcium dynamics" complement the stability metrics presented in section "Stability metrics" to provide a comprehensive model of neuronal health.

The system tracks both instantaneous calcium levels and their rolling averages over windows of size $w$:

$$\begin{aligned} \bar{C}_t = \frac{1}{w}\sum _{i=t-w+1}^t C_i. \end{aligned}$$

(13)

Repair strategy monitoring

The system implements four biologically plausible repair strategies, whose activation probabilities are determined by the current state:

1. Activity-dependent synaptic scaling

$$\begin{aligned} P(\text{scaling}) = \gamma _1 \cdot \mathbb{I}(C_t > \theta _{Ca}), \end{aligned}$$

(14)

where $\mathbb{I}(\cdot )$ is the indicator function, activating synaptic scaling when calcium levels exceed the threshold $\theta _{Ca}$, with $\gamma _1$ controlling the baseline probability.

2. Selective synaptic reinforcement

$$\begin{aligned} P(\text{reinforcement}) = \gamma _2 \cdot \mathbb{I}(|W| > \theta _{\text{strong}}), \end{aligned}$$

(15)

where reinforcement is applied to synapses with strength exceeding $\theta _{\text{strong}}$, with $\gamma _2$ controlling the baseline probability.

3. Activity-dependent pruning

$$\begin{aligned} P(\text{pruning}) = \gamma _3 \cdot \mathbb{I}(|W| < \theta _{\text{weak}}), \end{aligned}$$

(16)

where pruning is applied to synapses with strength below $\theta _{\text{weak}}$, with $\gamma _3$ controlling the baseline probability.

Phase space analysis

The system generates phase diagrams mapping the relationship between health metrics and calcium levels, defined by the transformation:

$$\begin{aligned} \Phi : (H_t, C_t) \mapsto \mathbb{R}^2. \end{aligned}$$

(17)

The temporal evolution of the system in this phase space is characterized by the vector field:

$$\begin{aligned} \vec{F}(H, C) = \begin{pmatrix} \frac{dH}{dt} \\ \frac{dC}{dt} \end{pmatrix}. \end{aligned}$$

(18)

In this phase space, repair events are triggered when health falls below a threshold (corresponding to high calcium levels), ensuring neuron stability through homeostatic regulation. This visualization provides insights into the relationship between calcium levels and neuron health, highlighting the biological principle that excessive calcium is cytotoxic.

Implementation details

The monitoring system is implemented using PyTorch for computational efficiency and matplotlib/seaborn for visualization. Data collection occurs at regular intervals during training, with adaptive sampling rates based on system dynamics. The visualization pipeline generates both real-time updates and comprehensive summaries, storing all metrics in a hierarchical data structure for post-hoc analysis.

The system maintains separate buffers for different metrics:

• Health history: $\{H_t\}_{t=1}^T$,

• Stability measurements: $\{S_t\}_{t=1}^T$,

• Calcium dynamics: $\{C_t\}_{t=1}^T$,

• Repair events: $\{(t_i, H_{t_i}, \text{strategy}_i)\}_{i=1}^R$,

where $T$ is the total number of training steps, $R$ is the number of repair events, and $\text{strategy}_i$ indicates which of the four repair strategies was activated.

Visualization framework

The visualization framework implements multiple views of the system’s state:

• Temporal evolution of health and stability metrics,

• Calcium dynamics with rolling averages, highlighting periods of potential cytotoxicity,

• Phase space trajectories with repair event markers,

• Cumulative repair strategy distribution across all four biologically plausible mechanisms,

• Comprehensive summary plots combining all metrics.

Each visualization is automatically generated and saved with appropriate metadata, enabling systematic analysis of long-term trends and intervention efficacy. The visualizations are designed to highlight the biological principles underlying the BioLogicalNeuron, particularly the relationship between calcium levels, neuron health, and repair mechanisms.

Theoretical analysis of calcium dynamics and repair mechanisms

In this section, we provide theoretical guarantees for the stability, convergence, and generalization of the BioLogicalNeuron layer. These guarantees are derived from the layer’s biologically inspired mechanisms, including calcium dynamics, homeostatic regulation, and adaptive repair strategies.

Stability of calcium dynamics

In biological neurons, calcium homeostasis⁴⁴ is a critical regulatory mechanism that maintains intracellular calcium at low steady-state levels, as high calcium concentrations are cytotoxic. As introduced in section "Calcium dynamics", our model implements this biological principle through the calcium dynamics equation (Eq. 2).

To analyze stability, we define a Lyapunov function $V(c_t) = \frac{1}{2}(c_t - c_{base})^2$. The system is stable if $V(c_{t+1}) \le V(c_t)$. Under the assumption that $\bar{y}_t$ is bounded (i.e., $|\bar{y}_t| \le M$), we can show that:

$$\begin{aligned} V(c_{t+1}) \le \alpha ^2 V(c_t) + \beta ^2 \max (0, M - \theta _{act})^2. \end{aligned}$$

(19)

For $\alpha \in (0, 1)$, the system is stable, and the calcium levels $c_t$ remain bounded near the baseline level $c_{base}$. This ensures that the neuron’s calcium levels do not rise to cytotoxic levels, maintaining stability during training.

The health of the neuron $h_t \in [0, 1]$ is computed as:

$$\begin{aligned} h_t = \sigma (\theta _c - c_t + \gamma \cdot \text{Stability}(W)), \end{aligned}$$

(20)

where $\sigma (\cdot )$ is the sigmoid function, $\theta _c$ is a calcium threshold parameter, and $\gamma$ is the stability scale. This formulation aligns with biological reality, where lower calcium levels (below the toxic threshold $\theta _c$) contribute to better neuronal health.

Energy efficiency analysis

The energy efficiency of neural computations is a critical consideration in both biological and artificial systems. In biological neurons, calcium regulation mechanisms consume significant energy, but are essential for maintaining neural health and preventing excitotoxicity⁴⁰.

Our empirical analysis of the BioLogicalNeuron layer reveals the following energy efficiency metrics shwon in Table 1 compared to standard neural networks:

Table 1 Energy efficiency comparison between BioLogicalNeuron and standard neural layers.

The increased computational time of approximately 69.6% in the BioLogicalNeuron layer is attributed to its incorporation of calcium dynamics, self-repair mechanisms, and enhanced visualization processes. Despite this additional overhead, the trade-off is justified by the significantly improved performance metrics:

• Perfect validation accuracy The BioLogicalNeuron achieves 100% validation accuracy compared to 98.5% for standard approaches, representing a 1.5% improvement.

• Accelerated convergence BioLogicalNeuron reaches 96%+ accuracy in just 1 epoch, compared to 4 epochs for standard approaches—a 75% reduction in training time to reach high accuracy.

This performance-efficiency trade-off mirrors biological systems, where energy investment in homeostatic mechanisms yields significant benefits in learning efficiency and robustness.

Convergence rate analysis

The convergence properties of the BioLogicalNeuron layer are influenced by its biologically plausible repair mechanisms. These mechanisms, as detailed in “Multi-strategy repair system”, include:

• 1. Activity-dependent synaptic scaling (Eq. 8): This mechanism specifically targets weight reduction following periods of high activity, preventing excitotoxicity.

• 2. Selective synaptic reinforcement (Eq. 9): This mechanism strengthens frequently used connections, similar to Hebbian learning principles.

• 3. Activity-dependent pruning (Eq. 10): This mechanism ensures efficient resource allocation by reducing the influence of weak connections.

Our empirical analysis shows that these biologically-inspired mechanisms significantly accelerate convergence:

• Epochs to 96%+ accuracy BioLogicalNeuron reaches this threshold in just 1 epoch, compared to 4 epochs for standard approaches—a 75% reduction.

• Best validation accuracy BioLogicalNeuron achieves perfect accuracy (1.0) compared to standard approaches (0.985), a 1.5% improvement.

Using stochastic approximation theory, we can show that the weight updates satisfy the Robbins-Monro conditions:

$$\begin{aligned} \sum _{t=1}^\infty \eta _t = \infty \quad \text{and} \quad \sum _{t=1}^\infty \eta _t^2 < \infty , \end{aligned}$$

(21)

where $\eta _t$ is the learning rate at time $t$. Under these conditions, the weights $W_t$ converge to a local minimum of the loss function, ensuring robust convergence even in the presence of noise.

Coverage rate and resource utilization

The coverage rate as shown in Fig. 4, defined as the percentage of neurons actively contributing to the network’s function, provides insights into resource utilization efficiency. Our analysis shows that the BioLogicalNeuron layer maintains consistently higher neuron activation rates compared to standard approaches:

• Average coverage rate (BioLogicalNeuron) 87.22%.

• Average coverage rate (standard) 78.54%.

• Improvement 11.05%.

This improved coverage efficiency can be attributed to the homeostatic mechanisms that prevent neuron saturation and the repair strategies that reactivate underutilized neurons. The higher coverage rate indicates more efficient utilization of network capacity, with fewer “dead” or inactive neurons.

Classification accuracy analysis with standard layers

The BioLogicalNeuron layer demonstrates superior classification accuracy across multiple datasets, as shown in Table 2.

Table 2 Classification accuracy across benchmark datasets.

The BioLogicalNeuron layer achieves an average accuracy of 90.75% across all evaluated datasets, reflecting a substantial improvement of 9.30% over standard linear layers and 6.17% over the next best alternative (Dropout-Regularized layers). This consistent performance advantage underscores the effectiveness of the incorporated biological mechanisms in enhancing the network’s learning capability and generalization performance.

Comparison with current state of the art graph neural network methods

Graph Neural Networks (GNNs) represent the current state-of-the-art for molecular datasets. Table 3 presents a comprehensive comparison of BioLogicalNeuron against leading GNN approaches.

Table 3 Performance comparison with state-of-the-art graph neural networks.

The results demonstrate that BioLogicalNeuron consistently outperforms state-of-the-art GNN methods across both datasets. On the AIDS dataset, our model achieves a remarkable 99.8% accuracy and 99.49% auc, significantly outperforming the current state-of-the-art FIT-GNN (84.3%). While GIN shows a higher AUC (0.955) on AIDS, our model demonstrates better overall performance when considering both metrics. On the HIV dataset, our model achieves 97.2% accuracy and 0.953 AUC, outperforming specialized methods like TREE-G (0.835 AUC) and CIN++ (0.806 AUC). The average rank of 1.00 confirms the consistent superiority of our approach.

Convergence rate analysis

Beyond accuracy metrics, we analyzed the convergence behavior of different methods. Figure 4 illustrates the training dynamics on the AIDS dataset.

Fig. 4

Convergence rate comparison on the AIDS dataset. The BioLogicalNeuron model (red) reaches 95% accuracy in significantly fewer epochs than competing methods.

The BioLogicalNeuron model demonstrates superior convergence properties, reaching 100% validation accuracy in just 3 epochs on the AIDS⁷ dataset, compared to 12 epochs for GraphConv + Focal and 15 epochs for DGCNN. This accelerated learning can be attributed to the calcium-based homeostatic mechanisms that adaptively regulate learning rates based on neuronal health.

Robustness analysis

To evaluate model robustness, we tested performance under varying levels of input noise. Table 4 presents the accuracy degradation under Gaussian noise injection.

Table 4 Robustness comparison: accuracy (%) under Gaussian noise.

The BioLogicalNeuron model demonstrates superior robustness to noise, with an average accuracy degradation of only 8.6% compared to 13.7–17.0% for other methods. This enhanced robustness is particularly important for molecular datasets that may contain experimental noise. The model’s self-repair mechanisms actively maintain stability under perturbations, a key advantage for real-world applications.

Ablation study

To understand the contribution of individual biological mechanisms, we conducted an ablation study by selectively disabling components of the BioLogicalNeuron model. Table 5 presents the results on the HIV dataset.

Table 5 Ablation study on HIV dataset.

The ablation study reveals that all biological mechanisms contribute to the model’s performance, with homeostatic regulation having the largest impact (3.4% accuracy decrease when disabled). The complete removal of all biological mechanisms (equivalent to a standard neural network) results in a substantial performance drop of 12.9%, highlighting the collective importance of these biologically-inspired components.

Discussion

Our comprehensive evaluation demonstrates that the BioLogicalNeuron model consistently outperforms state-of-the-art methods across multiple dimensions:

• Classification performance Superior accuracy and competitive AUC across both molecular datasets, with statistically significant improvements over specialized methods.

• Convergence efficiency Faster learning with fewer training epochs required, reducing computational costs and enabling quicker model deployment.

• Robustness Enhanced stability under noise and perturbations, crucial for real-world applications where data quality may vary.

• Mechanism contribution Each biological component provides measurable performance benefits, with homeostatic regulation being particularly important.

These results validate the effectiveness of incorporating biological principles into neural network design. The calcium-based homeostatic mechanisms, repair strategies, and adaptive learning rates collectively enable more efficient and robust learning, particularly for complex molecular classification tasks.

The consistent performance advantages across multiple established benchmarks (AIDS⁷ and HIV) demonstrate that the BioLogicalNeuron model represents a significant advancement over existing approaches for molecular data analysis. By focusing on these well-established datasets and providing in-depth comparisons with state-of-the-art methods, we have demonstrated both the performance benefits and the mechanistic advantages of our biologically-inspired approach.

Results

In this section, this paper presents the experimental results of the BioLogicalNeuron layer, both in isolation and in combination with attention mechanisms and jumping connections, across molecular datasets (AIDS, HIV, COX2, Protein), graph datasets (Cora, DD, MUTAG, Citeseer, PubMed) and image datasets (CIFAR-10, MNIST, Fashion-MNIST). The results demonstrate that the BioLogicalNeuron layer consistently achieves state-of-the-art (SOTA) or near-SOTA performance, often outperforming previous methods. Below, this paper provides a detailed analysis of the results, supported by visualizations and summary plots for each dataset, along with insights into how the BioLogicalNeuron layer behaves during training.

Molecular dataset performance

HIV dataset results (97.15%)

The Drug Therapeutics Program (DTP) AIDS Antiviral Screen created the HIV dataset⁷ by evaluating more than 40,000 drugs’ capacity to prevent HIV replication. After evaluation, the screening findings were divided into three groups: confirmed moderately active (CM), confirmed active (CA) and confirmed inactive (CI). The BioLogicalNeuron layer demonstrates strong performance and achieve state of the art result on this dataset

• Model: BioLogicalNeuron + Attention + Jumping Connections

  • Test accuracy 97.15% (10-fold cross-validation).

  • Comparison with SOTA Previous SOTA was 96.86%⁵³.

  • Insight The full model achieves a slight improvement over the previous SOTA, demonstrating the effectiveness of the BioLogicalNeuron layer in combination with attention and jumping connections.

• Model: BioLogicalNeuron (alone)

  • Test accuracy 96.95% (10-fold cross-validation).

  • Comparison with SOTA Surpasses previous SOTA (96.86%)⁵³.

  • Insight The BioLogicalNeuron layer alone achieves SOTA performance, highlighting its ability to generalize well on biological datasets.

Model behavior analysis

• Health and Stability The neuron health metrics plot in Fig. 5 demonstrates rapid initial decline from peak values (1.08) to a stable homeostatic range of 0.90–0.95 within the first 500 training steps. Multiple repair events (red stars) are concentrated in the early training phase (steps 0–800), with sporadic interventions throughout the remaining 1200 steps, indicating successful establishment of stable operating conditions. The stability metric (yellow line) exhibits lower baseline values (0.90–0.92) but follows similar dynamics, confirming the neuron’s capacity to maintain functional integrity across 2000 training steps.

• Calcium dynamics The calcium level dynamics plot reveals a characteristic three-phase progression: initial rapid accumulation to  1.0 $\upmu$M (0–400 steps), sustained elevation with moderate fluctuations reaching  1.5 $\upmu$M (400–1000 steps), and dramatic escalation to peak concentrations of  3.5 $\upmu$M with high-amplitude oscillations (1000–2000 steps). The 50-step moving average (dashed line) confirms the underlying upward trend despite significant short-term variability. This pattern suggests successful calcium buffering mechanisms operating even at potentially cytotoxic concentrations, with the final phase indicating either adaptive tolerance or approaching regulatory limits.

• Repair strategy distribution The stacked area plot demonstrates progressive activation of all three repair mechanisms, with activity-dependent pruning (green) dominating the later training phases, reaching maximum utilization of  125 strategy counts by step 2000. Synaptic scaling (pink) shows steady moderate engagement throughout training (40 counts), while selective reinforcement (tan) exhibits intermediate activation (80 counts). This distribution indicates a hierarchical repair system where activity-dependent pruning becomes the primary homeostatic mechanism as training progresses, suggesting adaptation to sustained high-calcium conditions.

• Phase space analysis The health-calcium phase space scatter plot reveals a complex nonlinear relationship with distinct training phases visible through the color gradient (dark purple to bright yellow). The trajectory shows initial high health states (> 1.00) at low calcium concentrations (<0.5 $\upmu$M), followed by rapid transition to a stable operating corridor at health values of 0.90–0.95 and calcium levels of 1.5–3.5 $\upmu$M. The dense clustering in this region demonstrates robust homeostatic regulation, with the neuron maintaining functional health despite sustained exposure to elevated calcium concentrations that would typically induce cytotoxicity in biological systems.

Fig. 5

Analysis of neuron health and calcium dynamics during 1200 training steps on HIV dataset. The figure shows neuron health metrics and stability (top left), calcium level dynamics (top right), repair strategy distribution (bottom left), and the health-calcium phase space with training progression (bottom right). Red stars indicate repair events triggered during training.

AIDS dataset analysis (99.7%)

The AIDS dataset⁷ is a graph. The AIDS Antiviral Screen Database of Active Compounds is used to create the 2000 graphs that depict molecular compounds. 4395 chemical compounds are included in it; 423 of these are classified as CA, 1081 as CM and the other compounds as CI.The BioLogicalNeuron layer achieves state-of-the-art performance on this dataset. Details correalation shown in Fig. 6.

• Model: BioLogicalNeuron + Attention + Jumping Connections

  • Test accuracy 99.63% (average of 3 runs: 99.8%, 99.6%, 99.5%; 10-fold cross-validation each).

  • Comparison with SOTA Surpasses previous SOTA of 99.55%⁵³.

  • Insight While the full architecture exceeds prior SOTA, its average accuracy is slightly lower than the standalone BioLogicalNeuron layer (99.8%). This suggests the added components (attention and jumping connections) may introduce unnecessary complexity or variability, with marginal gains observed only in individual runs (e.g., 99.8% peak).

• Model: BioLogicalNeuron (alone)

  • Test accuracy 99.8% (average of 3 runs: 99.9%, 99.8%, 99.7%; 10-fold cross-validation each).

  • Comparison with SOTA Significantly surpasses previous SOTA (99.55%).

  • Insight The standalone BioLogicalNeuron layer achieves superior and consistent performance (peaking at 99.9%), demonstrating its inherent robustness and sufficiency for biological datasets. This simplicity avoids potential instability from auxiliary components.

COX2 performance (83.25%)

The COX2 dataset⁸ focuses on cyclooxygenase-2 (COX-2) inhibitors, crucial for anti-inflammatory drug discovery. It includes chemical compounds represented by molecular structures (e.g., SMILES), labeled with biological activity (active/inactive or inhibition potency). Used for QSAR modeling, classification, regression and virtual screening, it aids in predicting COX-2 inhibition and identifying drug candidates. Publicly available, it is a benchmark in cheminformatics and drug discovery research.On this dataset also The BioLogicalNeuron layer demonstrates strong performance and achieve state of the art result.

• Model: BioLogicalNeuron + Attention + Jumping Connections

  • Test accuracy 82.71% (average of 5 runs: 83.40%, 82.12%, 82.55%, 83.40%, 82.12%; 10-fold cross-validation each).

  • Comparison with SOTA Surpasses previous SOTA of 82.6%⁵⁴.

  • Insight The full model slightly outperforms the previous SOTA, demonstrating the benefits of combining the BioLogicalNeuron layer with attention and jumping connections.

• Model: BioLogicalNeuron (alone)

  • Test accuracy 80.84% (average of 5 runs: 81.27%, 81.27%, 80.85%, 80.42%, 80.42% 10-fold cross-validation each).

  • Comparison with SOTA Below previous SOTA (82.6%)⁵⁴.

  • Insight While the BioLogicalNeuron layer alone does not surpass the previous SOTA, it still achieves competitive performance, indicating its potential for further optimization.

Protein dataset achievements (75.89%)

A collection of proteins categorised as either enzymes or non-enzymes is called PROTEINS⁵⁵. The amino acids are represented by nodes and if two nodes are less than six Angstroms apart, they are connected by an edge. based on the paperwithcode information the BioLogicalNeuron layer achieves state of the art result on this dataset.

• Model: BioLogicalNeuron + Attention + Jumping Connections

  • Test accuracy 74.65% (10-fold cross-validation)

  • Comparison with SOTA Previous SOTA was 72%⁵⁶ Paper With Code 10-fold Accuracy.

  • Insight The full model significantly outperforms the previous SOTA, demonstrating the benefits of combining the BioLogicalNeuron layer with attention and jumping connections.

• Model: BioLogicalNeuron (alone)

  • Test accuracy 75.89% (10-fold cross-validation)

  • Comparison with SOTA Surpasses previous SOTA (72%)⁵⁶ Paper With Code 10-fold Accuracy.

  • Insight The BioLogicalNeuron layer alone achieves SOTA performance, indicating its effectiveness on graph datasets.

Graph dataset performance

DD dataset analysis (80%)

The DD dataset⁵⁷ contains 1178 protein structures represented as graphs, with nodes as amino acids and edges as spatial proximities.

• Model: BioLogicalNeuron + Attention + Jumping Connections

  • Test accuracy 76% (10-fold cross-validation).

  • Comparison with SOTA Below previous SOTA (95%)⁵⁸.

  • Insight The full model underperforms compared to the previous SOTA, indicating potential limitations on certain graph datasets.

• Model: BioLogicalNeuron (alone)

  • Test accuracy 80% (10-fold cross-validation).

  • Comparison with SOTA Below previous SOTA (95%)⁵⁸.

  • Insight The BioLogicalNeuron layer alone performs better than the full model but still falls short of the previous SOTA, suggesting that further optimization may be needed for this dataset.

MUTAG dataset analysis (83.33%)

Specifically, MUTAG⁵⁵ is a group of nitroaromatic chemicals whose mutagenicity towards Salmonella typhimurium is to be predicted. Chemical compounds are represented as input networks, in which atoms are represented by vertices labelled with their kind (expressed by one-hot encoding) and bonds between atoms are represented by edges connecting vertices. 188 chemical compound samples with seven distinct node labels are included.

• Model: BioLogicalNeuron + Attention + Jumping Connections

  • Test accuracy 78% (10-fold cross-validation).

  • Comparison with SOTA Below previous SOTA (100%)⁵⁹.

  • Insight The full model underperforms compared to the previous SOTA, indicating potential limitations on certain graph datasets.

• Model: BioLogicalNeuron (alone)

  • Test accuracy 83.33% (10-fold cross-validation.)

  • Comparison with SOTA Below previous SOTA (100%)⁵⁹.

  • Insight The BioLogicalNeuron layer alone performs better than the full model but still falls short of the previous SOTA, suggesting that further optimization may be needed for this dataset.

Table 6 Comprehensive performance analysis.

Cora, Citeseer and PubMed datasets: experimental results

For the Cora⁹, Citeseer⁶⁰ and PubMed⁶¹ datasets, this paper conducted experiments to evaluate the effectiveness of the BioLogicalNeuron layer when combined with existing deep learning methods, such as graph attention¹⁶ mechanisms and jumping connections. While this paper did not visualize the bio layer’s behavior for these datasets, the results are highly promising and demonstrate the layer’s potential to enhance performance.

Table 7 Comprehensive performance analysis for citation network datasets.

• Cora dataset

  • Performance The bio layer combined with GAT attention¹⁶ achieved 88.56% accuracy (15-fold crossvalidation), a significant improvement over the BaseBioLayer’s 74.53%. However, it slightly underperformed compared to the SOTA result of 90.26%⁶³.

  • Analysis There are 2708 scientific publications in the Cora dataset, which are divided into seven classes.

  • Implications The substantial improvement over the BaseBioLayer (+ 14.02%) highlights the effectiveness of integrating attention mechanisms with the bio layer. While the result is slightly below the SOTA (− 1.70%), it suggests that further tuning and optimization could bridge this gap, leveraging the bio layer’s homeostatic regulation and repair mechanisms.

• Citeseer dataset

  • Performance The bio layer combined with GAT attention¹⁶ achieved 76.87% accuracy (10-fold crossvalidation), outperforming the BaseBioLayer’s 72.37% but falling short of the SOTA result of 82.07%⁶².

  • Analysis The CiteSeer collection contains 3312 scientific publications in six different classes. The citation network contains 4732 links. Each publication is characterized by a 0/1-valued word vector indicating the presence/absence of corresponding dictionary words from a vocabulary of 3703 unique terms.

  • Implications The improvement over the BaseBioLayer (+3.67%) demonstrates the bio layer’s potential, but the gap to the SOTA (− 5.20%) may be attributed to the dataset’s inherent complexity and sparsity. Architectural refinements and hyperparameter optimization could help close this gap.

• PubMed dataset

  • Performance The bio layer combined with GAT attention¹⁶ achieved 88.28% accuracy (10-fold crossvalidation), showing marginal improvement over the BaseBioLayer’s 88.18%. However, it underperformed compared to the SOTA result of 91.67%. Table 7 shows the performance visualization of citation datasets.

  • Analysis: The PubMed dataset comprises 19,717 diabetes-related scholarly publications from the PubMed database, divided into three categories.

  • Implications The PubMed dataset’s size and complexity make it a rigorous test for any model. The bio layer’s ability to achieve 88.28% accuracy without extensive tuning highlights its potential for large-scale graph tasks. Parameter optimization and architectural adjustments could potentially close the gap with SOTA (− 3.39%).

Image dataset performance

The BioLogicalNeuron layer demonstrates robust performance across multiple image datasets, including CIFAR-10¹¹, MNIST¹² and Fashion-MNIST⁶⁴. These experiments were designed to evaluate the layer’s versatility and ability to generalize across diverse domains. Below, this paper presents a structured analysis of the results.

CIFAR-10 dataset

Performance The bio layer achieved an accuracy of 90.42% with the SE attention mechanism (2-fold cross-validation), compared to 89.656% without the bio layer. This represents a 0.77% improvement, highlighting the bio layer’s ability to enhance performance on complex image classification tasks shown in Table 8.

Analysis CIFAR-10¹¹ is a widely used benchmark for image classification, known for its diversity and complexity. The bio layer’s performance is competitive, demonstrating its capacity to handle intricate image data. The integration of the bio layer with SE attention mechanisms yields a marginal but consistent improvement, suggesting complementary benefits between the two components.

Implications The results indicate that the bio layer can effectively augment modern deep learning architectures, such as attention-based models, even on challenging datasets like CIFAR-10. While the improvement is modest, it underscores the bio layer’s potential as a complementary component in deep learning pipelines.

MNIST dataset

Performance The bio layer achieved near-perfect accuracy of 99.43% on MNIST when combined with the SE attention mechanism, demonstrating exceptional performance on this well-established benchmark.

Analysis MNIST¹², a dataset of grayscale handwritten digits, is widely used to evaluate image classification models. The bio layer’s adaptive learning rate and repair mechanisms contribute to stable and efficient training, enabling near-perfect accuracy. The high health and stability metrics observed during training further validate the bio layer’s effectiveness on simpler datasets.

Implications The bio layer’s performance on MNIST highlights its potential for applications requiring high accuracy and stability, particularly in scenarios where overfitting is less of a concern.

Fashion-MNIST dataset

Performance The bio layer achieved an accuracy of 91.18% on Fashion-MNIST when combined with the SE attention mechanism, demonstrating competitive performance on this more challenging variant of the MNIST dataset.

Analysis Fashion-MNIST⁶⁴ features grayscale images of clothing items, presenting a more complex classification task compared to MNIST. The bio layer’s adaptive learning rate and repair mechanisms contribute to stable training and improved generalization, even with the increased complexity and diversity of image classes.

Implications The bio layer’s performance on Fashion-MNIST underscores its effectiveness for more complex image classification tasks, validating its potential for applications requiring high accuracy and robustness.

Table 8 Comprehensive performance analysis for image datasets.

The BioLogicalNeuron layer consistently achieves competitive performance across image datasets summary results shown at Table 8, demonstrating its robustness, scalability and versatility. The layer’s biologically inspired mechanisms, including calcium dynamics, homeostatic regulation and adaptive repair strategies, contribute to its ability to maintain stable and efficient training, even in complex and challenging domains. These results highlight the potential of the BioLogicalNeuron layer as a powerful and generalizable component for deep learning models.

Fig. 6

(A) Average Health of all datasets. (B) Repair Event of all datasets. (C) Health vs Performance and (D) Repair Event vs Performance.

Discussion and conclusion

The BioLogicalNeuron layer represents a fundamental shift in neural network architecture design, demonstrating how biologically inspired homeostatic regulation and self-repair mechanisms can enhance neural network performance across diverse domains. this comprehensive empirical evaluation reveals several profound implications for the field of machine learning and provides new insights into the relationship between biological neural systems and artificial neural networks. Below, this paper discusses the biological plausibility of the bio layer, analyze its performance gains, address its limitations and outline future research directions.

Mechanistic analysis of biological inspiration

The design of the BioLogicalNeuron layer is deeply rooted in biological principles, particularly those observed in biological neurons and their ability to maintain homeostasis and self-repair. this implementation of homeostatic regulation through calcium dynamics and multi-modal health metrics reveals striking parallels with biological neural systems:

• Calcium-based homeostasis

  • The bio layer’s calcium dynamics are inspired by the role of calcium in biological neurons, where it regulates synaptic plasticity and signal transmission. The calcium levels are updated based on the neuron’s activations, with an adaptive momentum term (ranging from 0.9 to 0.95) ensuring smooth updates. This mechanism provides stability while allowing for rapid response to changing conditions.

  • The calcium levels are used to compute the neuron’s base health, which reflects its overall stability and functionality. This approach mimics the biological process of maintaining neural activity within an optimal range.

• Multi-modal health metrics

  • The bio layer integrates multiple factors to monitor neural health:

    • Base health Derived from calcium levels and synaptic strength.

    • Stability Measured across time windows to assess the neuron’s consistency.

    • Calcium trend Analyzed to detect dynamic changes in neural activity.

  • This multi-modal approach provides a more comprehensive view of neural health than traditional loss-based monitoring, enabling the bio layer to maintain stable and robust performance.

• Self-repair mechanisms

  • The bio layer replicates the self-repair capabilities of biological neurons through biologically plausible repair mechanisms, including activity-dependent synaptic scaling, selective synaptic reinforcement, activity-dependent pruning, and homeostatic adjustment. These mechanisms are triggered when the neuron’s health degrades below a defined threshold, ensuring that it recovers quickly from suboptimal states.

  • The activity-dependent synaptic scaling reduces weights after periods of high activity, mimicking how biological neurons prevent overexcitation. Selective synaptic reinforcement strengthens important connections while the activity-dependent pruning mechanism removes weak synapses, similar to biological neural pruning. Finally, homeostatic adjustment applies global normalization to prevent runaway excitation. This multi-strategy approach is particularly effective in molecular datasets, as evidenced by the results presented in Tables 6, 7 and 8.

Technical innovation in neural health monitoring

The BioLogicalNeuron layer introduces a modular monitoring system that provides unprecedented visibility into neural network health. This system enables:

• Real-time health visualization

  • The bio layer’s health monitoring system tracks key metrics such as current health, stability, base health and calcium trend. These metrics are visualized in real-time, allowing researchers to monitor the neuron’s behavior during training.

  • The system also tracks the effectiveness of repair strategies, providing insights into how the bio layer adapts to changing conditions.

• Adaptive learning dynamics

  • The bio layer’s ability to modulate learning rates based on health metrics represents a novel approach to optimization. The adaptive learning rate ensures that the neuron learns at an optimal rate, avoiding both slow convergence and instability.

Broader implications for machine learning

The success of the BioLogicalNeuron layer has several important theoretical and practical implications:

• Theoretical insights

  • The bio layer’s ability to maintain performance while enabling adaptation provides new insights into the stability-plasticity dilemma in neural networks.

  • The biological repair mechanisms appear to provide implicit regularization, as evidenced by strong generalization performance across datasets.

• Practical applications

  • The bio layer’s capabilities suggest immediate applications in:

    • Drug discovery and development Molecular property prediction, protein structure analysis and drug-target interaction prediction.

    • Network analysis Scientific citation network analysis, social network dynamics and knowledge graph enhancement.

    • Robust learning systems Systems requiring long-term stability, applications with noisy or incomplete data and continuous learning environments.

Limitations and challenges

While the BioLogicalNeuron layer demonstrates significant improvements over existing methods, it is not without limitations and challenges:

• Computational overhead

  • The bio layer’s homeostatic regulation, repair mechanisms and monitoring system introduce additional computational overhead, particularly for large-scale datasets (Specially when the monitoring system is enable). This overhead may limit the bio layer’s applicability to real-time or resource-constrained applications.

• Hyperparameter sensitivity

  • The bio layer’s performance is sensitive to hyperparameters such as the plasticity rate, repair threshold and adaptive learning, rate,decay rate, activation scale, prediction window, stability threshold. Tuning these hyperparameters for optimal performance can be challenging, particularly for new datasets or tasks.

• Scalability

  • While the bio layer performs well on smaller datasets, as shown in Table 6, its scalability to larger datasets (e.g., ImageNet, large-scale graph datasets) remains an open question. Further research is needed to evaluate the bio layer’s performance on large-scale tasks.

• Underperformance on certain datasets

  • The bio layer underperforms on some datasets compared to the previous SOTA, as detailed in Table 6. This underperformance may be attributed to the dataset’s inherent complexity or the bio layer’s inability to fully capture their structure.

Future research directions

The BioLogicalNeuron layer opens up several exciting avenues for future research:

• Scaling to larger architectures

  • Future work should focus on evaluating the bio layer’s performance in larger architectures, such as transformers, large-scale vision models and multi modal task.

• Hyperparameter optimization

  • Future research should focus on developing automated hyperparameter optimization techniques for the bio layer (Specially For Automate Repair Threshold), leveraging methods such as Bayesian optimization, evolutionary algorithms, or meta-learning.

• Biological validation

  • The bio layer’s mechanisms should be validated against biological data to ensure their biological plausibility. This validation could involve neuroscientific experiments or comparisons with biological neural networks.

• Applications in real-world domains

  • The bio layer’s potential for real-world applications, such as healthcare, drug discovery and autonomous systems, should be explored. These applications could benefit from the bio layer’s stability, robustness and generalization capabilities.