Training deep neural networks is often hindered by the fragility of gradient-based methods, which suffer from vanishing or exploding gradients, sensitivity to initialization, and entrapment in poor local minima. In response to these shortcomings, we introduce a new gradient-free algorithm called Quantum-Inspired Adaptive Superposition Optimization (QIASO), which views weight learning as a probabilistic superposition of candidate solutions, a fundamentally new optimization approach. In contrast to being dedicated to a single weight ensemble, QIASO maintains a distribution over several candidates, which are amplified and suppressed according to dynamically changing weights assigned to them. The variational formulation of the amplitude evolution leads to a KL-regularized formulation of their evolution, which generalizes statistical physics, information geometry, and online optimization viewpoints. To prevent invalid convergence, QIASO incorporates a stochastic perturbation operator based on quantum tunnelling into the optimizer, enabling the optimization process to overcome local minima on the loss surface and converge to the optimal solution. We provide theoretical bounds, monotone convergence of loss reduction, and almost-sure convergence to local optima with mild assumptions. Complexity analysis via empirical techniques suggests that QIASO scales more efficiently than Grover-based quantum-inspired algorithms and incurs no overhead in gradient computation compared to ADAM. The overall findings indicated that QIASO is a viable option for neural training, particularly when combined with other paradigms that utilise either large-scale or gradient-free approaches.
Training deep neural networks is often hindered by the fragility of gradient-based methods, which suffer from vanishing or exploding gradients, sensitivity to initialization, and entrapment in poor local minima. In response to these shortcomings, we introduce a new gradient-free algorithm called Quantum-Inspired Adaptive Superposition Optimization (QIASO), which views weight learning as a probabilistic superposition of candidate solutions, a fundamentally new optimization approach. In contrast to being dedicated to a single weight ensemble, QIASO maintains a distribution over several candidates, which are amplified and suppressed according to dynamically changing weights assigned to them. The variational formulation of the amplitude evolution leads to a KL-regularized formulation of their evolution, which generalizes statistical physics, information geometry, and online optimization viewpoints. To prevent invalid convergence, QIASO incorporates a stochastic perturbation operator based on quantum tunnelling into the optimizer, enabling the optimization process to overcome local minima on the loss surface and converge to the optimal solution. We provide theoretical bounds, monotone convergence of loss reduction, and almost-sure convergence to local optima with mild assumptions. Complexity analysis via empirical techniques suggests that QIASO scales more efficiently than Grover-based quantum-inspired algorithms and incurs no overhead in gradient computation compared to ADAM. The overall findings indicated that QIASO is a viable option for neural training, particularly when combined with other paradigms that utilise either large-scale or gradient-free approaches.
Deep learning models have achieved remarkable success in various domains, but their training process often faces challenges, particularly in navigating complex, high-dimensional loss landscapes. Traditional stochastic optimization methods like gradient descent can get trapped in local minima, hindering convergence and overall performance. This paper proposes a novel optimization algorithm, "Quantum-Inspired Stochastic Descent" (QISD), inspired by the principles of quantum mechanics, specifically superposition and interference. QISD leverages probabilistic amplitude modulation and interference patterns to guide the search for optimal parameters within deep learning models. The algorithm's core mechanism involves dynamically adjusting the probabilities (amplitudes) associated with different parameter updates, effectively creating interference patterns that enhance exploration and potentially escape local minima. We demonstrate that QISD can improve the convergence speed and final performance of deep learning models compared to standard stochastic gradient descent methods. The key contributions of this work lie in translating fundamental quantum concepts into a practical and effective optimization technique, addressing a critical bottleneck in the training of deep neural networks.
Training deep neural networks remains difficult due to vanishing gradients, non-convex loss surfaces, and hyperparameter sensitivity. These obstacles are compounded by quantum machine learning, where barren plateaus, circuit depth, and hardware noise restrict the applicability of gradient-based approaches. To overcome these drawbacks, this study presents adaptive Grover-driven parallel quantum optimization (AG-PQO), a hybrid, gradient-free scheme that leverages Grover's quadratic search speedup, along with adaptive loss-aware discretization and fidelity-based regularization. In contrast to more classical optimizers, such as Adam or evolutionary strategies (ES), which are either sensitive to the adequacy of the gradient update or exhibit poor scaling behavior, AG-PQO optimizes by performing Grover-accelerated candidate exploration across layers and reuses high-quality solutions in quantum memory caching. Testing indicates that AG-PQO yields higher accuracy, 2%–3% above Adam and ES, and faster convergence with less end-value loss than Adam, ES, and quantum feedforward-backpropagation (QFB). It is worth noting that AG-PQO remains stable at the simulated noise level of NISQ and has the potential to scale to near-term quantum processors.
Deep learning's remarkable success hinges on iterative optimization algorithms like stochastic gradient descent (SGD). However, training deep neural networks often encounters challenges navigating highly non-convex loss landscapes, frequently leading to convergence issues, slow training speeds, and susceptibility to getting trapped in local minima. This paper introduces a novel optimization algorithm, Quantum-Inspired Adaptive Optimization (QIAO), drawing inspiration from quantum measurement processes—specifically probabilistic sampling and collapse models—to address these limitations. QIAO employs a probabilistic strategy to sample regions of the loss landscape and utilizes a collapse model to iteratively refine the search, effectively mimicking the behavior of quantum measurement. The core idea is to leverage the inherent uncertainty and probabilistic nature of quantum mechanics to guide the optimization process more effectively than traditional gradient-based methods. We propose a framework for QIAO that incorporates adaptive step size adjustments and a dynamically adjusted sampling strategy. We demonstrate the efficacy of QIAO through theoretical analysis and illustrate its potential through conceptual examples, highlighting its ability to adapt to complex loss landscapes. This approach aims to provide a fundamentally different strategy for deep learning optimization, potentially offering improved convergence rates and robustness compared to conventional methods.
Training deep neural networks remains a computationally intensive and often challenging process. Traditional optimization methods, such as stochastic gradient descent (SGD) and its variants, frequently struggle to escape local minima and converge to optimal solutions, leading to suboptimal network performance. This paper proposes a novel approach to neural network training that leverages principles inspired by quantum mechanics. Specifically, we investigate the application of quantum-inspired optimization techniques, including simulated annealing and quantum walks, to dynamically adjust the training process. The core idea is to mimic the probabilistic exploration inherent in quantum systems to effectively navigate the complex loss landscape of neural networks. We formulate the training process as a quantum-inspired optimization problem, where the network's weights are treated as quantum bits (Qubits) and the optimization algorithm seeks to find the lowest energy state, analogous to finding the minimum loss. The proposed method demonstrates the potential for accelerating convergence and improving the overall accuracy of neural networks compared to conventional optimization strategies. Our analysis focuses on the key aspects of the approach, including the mathematical formulation of the quantum-inspired optimization problem and the selection of appropriate parameters to govern the exploration and exploitation phases. We present a theoretical framework for understanding the dynamics of this approach and discuss potential avenues for further research, including hybrid quantum-classical algorithms and the integration of quantum computing hardware.
This paper presents a novel optimization algorithm, Quantum-Inspired Stochastic Gradient Descent (QISGD), designed to accelerate convergence in training machine learning models. QISGD leverages concepts from quantum mechanics, specifically quantum tunneling and superposition, to introduce adaptive noise into gradient estimates. The algorithm dynamically adjusts the noise level based on the training progress, aiming to escape local minima more effectively and navigate the loss landscape with greater precision. Unlike traditional stochastic gradient descent (SGD) which relies solely on random perturbations, QISGD incorporates a nuanced noise strategy informed by quantum principles, offering a potentially more robust and efficient approach to optimization. The core idea is to mimic the probabilistic nature of quantum systems, allowing the algorithm to explore the search space more thoroughly. This research explores the theoretical underpinnings of QISGD and provides a framework for its implementation and evaluation. The algorithm's performance is assessed through simulations, demonstrating its potential to outperform standard SGD in specific scenarios.
Stochastic Gradient Descent (SGD) is a cornerstone algorithm in deep learning, widely employed for optimizing model parameters. However, SGD is susceptible to getting trapped in local minima, leading to suboptimal solutions and hindering the training process. This paper proposes a novel approach, Quantum-Inspired Stochastic Gradient Descent (QISGD), which leverages principles from quantum walks to enhance exploration and overcome the limitations of traditional SGD. The core idea is to adaptively adjust the learning rate based on the uncertainty associated with the gradient estimate, mirroring the probabilistic nature of quantum walks. Specifically, QISGD employs a stochastic update rule where the step size is dynamically modified, promoting wider exploration of the parameter space. The theoretical framework establishes connections between the proposed method and quantum walk concepts, highlighting its potential to improve training speed and convergence rates. We demonstrate, through analysis and mathematical formulation, that QISGD can effectively mitigate the issues of local minima and enhance the overall optimization performance of deep learning models. The presented formulation offers a new perspective on SGD, blending classical optimization with quantum-inspired concepts for enhanced training.