SynaNN: A Synaptic Neural Network presents an innovative approach to neural networks, drawing inspiration from neuroscience. The key highlights of the SynaNN include:
Synapse Model: The core idea is the construction of a synaptic neural network (SynaNN), where synapses connect neurons using excitatory and inhibitory channels. This model is based on the opening probability of these channels, which was built using a nonlinear synapse function below,
$$S(x,y; \alpha,\beta)=\alpha x(1-\beta y)$$
Surprisal Space: SynaNN introduces a concept from information theory called surprisal space, which maps probabilities into a logarithmic space. In this space, the inhibitory synapse function is shown to be topologically conjugate to the complementary probability function, enabling the SynaNN to perform more effectively by leveraging surprisal representations.
Assume that the total number of input of the synapse graph equals the total number of outputs, the fully-connected synapse graph is defined as $$y_{i}(\textbf{x}; \pmb\beta_i)=\alpha_i x_{i}{\prod_{j=1}^{n}(1-\beta_{ij}x_{j})},\ for\ all\ i \in [1,n]$$ Transformed to tensor representation, we have the log synapse in surprisal space, $$log(\textbf{y})=log(\textbf{x})+{\textbf{1}_{|x|}}*log\big( \textbf{1}_{|\beta|}-diag(\textbf{x})*\pmb{\beta}^T \big) $$Bose-Einstein Distribution: The paper establishes a connection between the synapse learning process and the Bose-Einstein distribution, showing that the derivative of the synapse in surprisal space follows this statistical distribution. This provides insights into the thermodynamic behavior of the synapses during learning.
Synapse Learning and Back-propagation: Synaptic learning can be implemented using standard gradient descent and back-propagation methods. The synapse gradient is formulated in surprisal space, and synaptic learning is driven by updating parameters using negative Bose-Einstein distribution.
Log-Concavity: The function of synapse has the log-concavity property, which suggests stability and robustness in the learning process, particularly useful for applications in fields like financial technology.
Experiments: SynaNN can construct a multi-layer perceptron (MLP) model for the image recognition. The results demonstrate that the SynaNN model achieves performance comparable to standard neural networks.
In conclusion, SynaNN introduces a neuroscience-inspired model that blends principles from physics (Bose-Einstein statistics) and information theory (surprisal space) to create a new framework for learning in neural networks. The proposed model is highly explainable, offering deeper insights into the underlying learning mechanisms in comparison to traditional neural networks.
SynaNN differs from traditional neural networks in several key ways, primarily due to its focus on modeling synapses and its integration of concepts from neuroscience, information theory, and statistical physics. Here’s how SynaNN stands out:
Traditional Neural Networks: Focus primarily on neurons and treat synapses as simple, weighted connections between neurons. The weights are adjusted during training, but there is little focus on the detailed structure or behavior of synapses themselves.
SynaNN: Places a significant emphasis on the synapse as a central computational element. It models synapses based on the excitatory and inhibitory channels found in biological synapses, capturing more complex interactions compared to traditional neural networks that rely on basic weight matrices.
Traditional Neural Networks: The connections between neurons are typically modeled as linear operations (weights and biases) followed by nonlinear activation functions like ReLU or sigmoid.
SynaNN: Uses a nonlinear synapse function that accounts for the opening probabilities of excitatory and inhibitory channels in synapses. This leads to a more biologically plausible model of how neurons interact via synapses, rather than simply adjusting weights between neurons.
Traditional Neural Networks: Operate purely in probability space without introducing alternative representations.
SynaNN: Introduces surprisal space, a concept from information theory. In surprisal space, probabilities are transformed into logarithmic values, which leads to a more natural handling of synaptic behavior, particularly in modeling inhibitory effects. This transformation provides a novel way to interpret neural computation, making SynaNN more explainable and mathematically tractable.
Traditional Neural Networks: Do not use topological structures or conjugate functions in their framework.
SynaNN: Demonstrates that the inhibitory synapse function $$-log(1 - e^{-x})$$ is topologically conjugate to the complementary probability function 1-x. This means that the dynamical behavior of synapses in probability space and surprisal space is equivalent, providing a deeper understanding of how inhibitory synapses operate.
Traditional Neural Networks: Utilize backpropagation and gradient descent to adjust weights, without any specific connection to physical or thermodynamic principles.
SynaNN: Discovers a relationship between the Bose-Einstein distribution and synapse learning in surprisal space. The update of synaptic parameters (weights) follows this distribution, which adds a new dimension of physical realism, connecting neural network learning to concepts from quantum statistics.
Traditional Neural Networks: Often referred to as "black boxes" due to the difficulty in interpreting how they learn and process information.
SynaNN: Is more explainable because its learning processes are tied to well-defined mathematical and physical principles, such as surprisal space and Bose-Einstein statistics. The authors propose that the synapse acts as a quantum processing unit (QPU), offering a potential link between biological neural networks and quantum phenomena.
Traditional Neural Networks: Do not inherently account for log-concavity, which impacts the stability and convergence properties of the learning algorithm.
SynaNN: Proves that its synapse function is log-concave, a property that ensures stability in the learning process. Log-concavity is crucial for reliable optimization, especially when dealing with complex probability distributions, making SynaNN potentially more robust than traditional models.
Traditional Neural Networks: Inspired by the structure of biological neurons but tend to abstract away many details of actual biological synapses.
SynaNN: Is heavily inspired by the detailed workings of biological synapses, focusing on the chemical and electrical processes that occur at these connections. This leads to a more faithful simulation of brain-like processes.
Traditional Neural Networks: Represent neuron connections through weight matrices.
SynaNN: Represents the connections in the form of a synapse graph and a synapse tensor, which encapsulate the interactions between neurons in a more complex and biologically realistic manner.
Traditional Neural Networks: Remain classical in their approach, even though there are emerging quantum neural network frameworks.
SynaNN: Proposes that synapses may function as quantum processing units (QPUs), implying that biological neural networks could operate with principles from quantum mechanics. This idea is a speculative but intriguing difference from classical neural network models.
SynaNN's ability to process and integrate sensor, device, network, cloud, and energy layers makes it highly effective in complex, multi-layered systems. Its biologically inspired architecture allows it to adapt dynamically, conserve energy, and make efficient use of network resources, which are all essential in modern IoT applications and smart infrastructures. By enabling real-time adaptation and reducing cloud dependency, SynaNN provides a robust foundation for future smart systems across a wide range of industries.
SynaNN is highly suitable for space and ocean exploration, where extreme conditions, sparse data, and limited resources make traditional neural networks challenging to apply. With its biologically inspired, adaptable architecture, SynaNN can handle noisy data from temperature, pressure, and volume sensors, process information efficiently on-device, and minimize energy consumption. This makes SynaNN a valuable asset for missions in harsh, remote, and data-intensive environments, enabling breakthroughs in understanding planetary atmospheres, ocean ecosystems, and potentially even signs of life in extreme locations.
SynaNN application for image classification through deep learning such as MNIST solution with Tensorflow or PyTorch framework.
SynaNN solves TSP optimization problem.
This paper introduces a method using SynaNN (Synaptic Neural Network) to process sensor data, specifically by learning parameters for physical equations such as the van der Waals equation for non-ideal gases. It highlights SynaNN's capacity for efficient, real-time data processing, which is crucial for applications with limited power resources, like environmental monitoring in closed systems. Through gradient-based optimization, SynaNN accurately models pressure, temperature, and volume relationships, making it ideal for high-stakes applications like pressure monitoring in closed carbins and optimization in industrial scrubbers. This approach conserves computational resources, providing an adaptable and energy-efficient alternative to traditional large-scale neural networks. It demostrated that SynaNN is highly suitable for space and ocean exploration with AI/ML.
The method described using SynaNN to learn parameters from sensor data is a general approach for applying machine learning to physical equations, not limited to the non-ideal gas (van der Waals) equation. This approach can be adapted to any physical system where a relationship between variables needs to be modeled and parameters estimated based on observed data. SynaNN’s design, which balances excitatory and inhibitory inputs, enables it to capture complex patterns and adapt parameters in real time, making it versatile for various physical models.
Flexible Equation Structure:
Any physical equation that describes relationships between measurable quantities (like temperature, pressure, volume, or time) and involves parameters (e.g., constants or coefficients) can be fit using this approach. The same principles can apply to equations in thermodynamics, fluid dynamics, electromagnetism, kinetics, and more.
Adaptability of SynaNN:
SynaNN’s synaptic weights and adjustable parameters provide flexibility in representing different types of interactions between variables. These interactions can be designed to reflect linear, non-linear, exponential, or logarithmic relationships, depending on the physical system being modeled.
For example, if modeling a harmonic oscillator, SynaNN could learn parameters related to mass, spring constant, or damping coefficients by adjusting weights based on sensor-measured positions and velocities.
Loss Function Customization:
By defining a custom loss function that matches the structure of the target physical equation, SynaNN can be trained to minimize the error between predicted and observed values, regardless of the equation’s form.
This loss function-based approach means that as long as the relationship between variables is known or hypothesized, SynaNN can adjust its parameters to fit the equation.
Fluid Dynamics:
In fluid dynamics, SynaNN can be used to learn parameters like viscosity, flow rate constants, or drag coefficients by processing sensor data for pressure, velocity, and density.
By training with a loss function tailored to the Navier-Stokes equations, SynaNN could predict flow behaviors under varying conditions.
Thermodynamic Systems:
For systems where heat transfer and energy changes are involved, SynaNN could learn thermal conductivity, heat capacity, or entropy parameters by analyzing temperature and energy data.
This would allow it to adapt to different materials and environmental conditions in real time.
Electromagnetic Systems:
In electromagnetic systems, SynaNN could be used to learn properties like inductance, resistance, or capacitance by processing voltage, current, and magnetic field data.
Using a loss function aligned with Maxwell’s equations or circuit equations, SynaNN could model and predict electromagnetic behaviors.
Chemical Kinetics and Reaction Rates:
In reaction kinetics, SynaNN could model reaction rate constants or activation energies by processing concentration, temperature, and time data.
This approach could help predict reaction rates under varying conditions, valuable for applications in industrial chemistry and environmental science.
Structural Mechanics:
SynaNN could process stress, strain, and displacement data to learn material properties like elasticity or tensile strength.
This would allow real-time monitoring and prediction of structural behavior under load, useful in engineering and construction applications.