Intrinsic preservation of plasticity in continual quantum learning

TL;DR

The paper tackles the problem of loss of plasticity in deep continual learning by comparing classical networks to quantum neural networks (QNNs). It shows that unbounded weight growth drives saturation and vanishing Fisher Information in classical models, while the unitary, compact-parameter nature of QNNs keeps learning capacity afloat and prevents plasticity loss. Analytical results using Fisher Information and Haar integration, plus extensive experiments across supervised tasks, reinforcement learning, and quantum-native data, demonstrate that QNNs preserve plasticity under continual tasks and across diverse architectures. This intrinsic robustness suggests a practical pathway for lifelong learning AI, with potential benefits beyond traditional speedups. The findings indicate quantum models offer a principled mechanism for continual adaptivity in non-stationary environments. $

Abstract

Artificial intelligence in dynamic, real-world environments requires the capacity for continual learning. However, standard deep learning suffers from a fundamental issue: loss of plasticity, in which networks gradually lose their ability to learn from new data. Here we show that quantum learning models naturally overcome this limitation, preserving plasticity over long timescales. We demonstrate this advantage systematically across a broad spectrum of tasks from multiple learning paradigms, including supervised learning and reinforcement learning, and diverse data modalities, from classical high-dimensional images to quantum-native datasets. Although classical models exhibit performance degradation correlated with unbounded weight and gradient growth, quantum neural networks maintain consistent learning capabilities regardless of the data or task. We identify the origin of the advantage as the intrinsic physical constraints of quantum models. Unlike classical networks where unbounded weight growth leads to landscape ruggedness or saturation, the unitary constraints confine the optimization to a compact manifold. Our results suggest that the utility of quantum computing in machine learning extends beyond potential speedups, offering a robust pathway for building adaptive artificial intelligence and lifelong learners.

Figures (9)

• Figure 1: Quantum neural networks maintain plasticity while classical neural networks fail in deep continual learning on permuted MNIST.a, Illustration of the permuted MNIST task for continual learning. A sequence of 10-fold classification tasks is generated by applying different random permutations to the pixels of the MNIST digits, forcing the model to continuously adapt to new input distributions. b, Test accuracy as a function of the task number for QNNs of varying circuit depths (DP) and MLPs of varying network widths (NW). QNNs maintain a stable test accuracy across the whole task sequence, demonstrating robust plasticity. In contrast, all MLP variants exhibit a significant and continuous degradation in performance, indicating a severe loss of plasticity. c, Average accuracy drop against the model's initial accuracy averaged over the first 200 tasks. MLPs show a much higher rate of plasticity loss, and it is more severe for models with worse initial performance. d, Relative gradient norms and e, relative weight norms during the continual learning process. The norms are normalized by the average norm across the first 10 tasks. For MLPs, both gradient and weight norms grow unboundedly over time, correlating with their performance decline. For QNNs, these norms remain stable and bounded, providing a mechanism explanation for the preserved plasticity. All curves show the moving average over 40-task windows, with shaded areas representing the standard deviation of the underlying data within each window.
• Figure 2: Preserved plasticity of QNNs in continual learning of real-world image classification tasks.a, Illustration of the sequential binary classification task constructed from the CIFAR-100 dataset. At each task, two classes are randomly sampled from the 100 available classes to form a new binary classification problem. This setting challenges the model's ability to continuously adapt to new visual concepts. b, Test accuracy as a function of task number for QNNs of varying circuit depths (DP) and MLPs of varying network widths (NW). Similar to the results on permuted MNIST, QNNs maintain a stable test accuracy throughout the 3,000 tasks. In stark contrast, MLPs suffer a catastrophic loss of plasticity, with their performance rapidly decaying to guess level (50% accuracy). c, Mechanism insight by the trace of the Fisher Information Matrix, a measure of the model's effective learning capacity. $\text{Tr}(\text{FIM})$ for QNNs remains stable, indicating that their ability to learn is preserved. For MLPs, the $\text{Tr}(\text{FIM})$ collapses, quantitatively demonstrating that the model has lost its capacity to effectively update its parameters, which explains the performance decay in panel b. All curves show the moving average over 150-task windows.
• Figure 3: Quantum-enhanced agents maintain learning plasticity in a standard reinforcement learning benchmark.a, Schematic of the RL setup. An agent, using either a classical MLP or a quantum QNN as its function approximator for the policy and value networks, interacts with the Ant-v4 environment. The agent's goal is to learn a motion policy that maximizes reward for efficiently moving forward. b, Evaluation reward (evaluated at each 200,000 steps) as a function of time step during training with PPO algorithm in a stationary environment. The agent with an MLP-based policy initially learns a strong policy, reaching a high reward. However, it subsequently suffers a catastrophic collapse in performance, demonstrating a severe loss of plasticity even without an explicit change of the task. Unlike the classical agent, the QNN-based agent learns more steadily and maintains a stable reward policy over the long term, showcasing its inherent ability to preserve plasticity in the dynamic context of RL. Curves show the moving average over 5-evaluation reward points window, with shaded areas representing the standard deviation of the underlying data within each window.
• Figure 4: QNNs exhibit superior plasticity on continual learning tasks with quantum native data.a, Schematic of the quantum native continual learning task. The dataset consists of many-body eigenstates from the one-dimensional XXZ Hamiltonian with periodic boundary conditions, generated by varying the anisotropy parameter $\Delta$. Each task in the continual learning sequence is a binary classification problem to distinguish between two sets of randomly sampled eigenstates from the full energy spectrum: the $i$-th eigenstate $|\psi_i\rangle$ and the $j$-th eigenstate $|\psi_j\rangle$. b, Test accuracy as a function of task number for QNNs and MLPs of varying model sizes. QNNs, particularly the deeper variant (DP12), successfully learn and maintain a high classification accuracy across the sequence of 2,000 tasks. In contrast, the MLPs show a clear degradation in performance, indicating that the loss of plasticity is a fundamental issue for classical models even for data with inherent quantum structure. This result demonstrates the robust plasticity of QNNs in their native domain. Curves show the moving average over 100-task window.
• Figure 5: Quantum neural network architectures and readout strategies employed in different experimental settings.a, b, Schematics of the variational ansatz blocks used to construct the deep QNNs. Each block is composed of parameterized two-qubit general unitary gates, $SU(4)$, acting on nearest neighbor qubits. a, The Brickwall Block architecture applies gates to alternating pairs of qubits. b, The Ladder Block architecture applies the same parameterized $SU(4)$ gates in a sequential descending pattern. c--e, Task-specific readout protocols mapping quantum states to classical predictions. c, Binary Classification Readout (used for Split CIFAR-100 and Quantum-Native tasks): The expectation value $\langle Z \rangle$ of the given qubit is measured and passed through a sigmoid activation to yield a binary class probability. d, 10-class Classification Readout (used for Permuted MNIST): The probabilities of the first 10 computational basis states ($P(...0000), \dots, P(....1001)$) are extracted from the output distribution and normalized via a Softmax function to produce the categorical prediction. e, Hybrid RL Readout (used for RL): The full probability distribution over all $2^N$ basis states serves as a dense feature vector. This vector is processed via a learnable linear projection (weighted sum) to generate the continuous policy actions and scalar value estimates, respectively.

Theorems & Definitions (5)

• Proposition 1: Asymptotic Saturation
• proof
• Definition 1: QNN Setup and Ansatz Structure
• Theorem 1: Bounded FIM
• proof