Geometry of learning dynamics: Gradient descent versus natural gradient on the ridge of optimization
本文通过几何分析对比梯度下降与自然梯度下降方法在高容量联想记忆模型优化过程中的表现，揭示了自然梯度下降能更稳定、高效地解决学习动力学问题。
0 citationsRead paper
Selected work
Representative Papers
Information Geometric Self-Organization at the Edge of Stability in High-Capacity Kernel Associative Memories
研究通过分析梯度下降在核逻辑回归训练的Hopfield网络中的学习轨迹，揭示了优化动力学在几何奇异性边界上的自稳定行为，解决了高容量关联存储器的稳定性问题。
0 citationsRead paper
Path Following Control System of Line-of-Sight Guidance for Robotic Dolphin with Multi-Link Mechanism in Underwater Simulator
This study addresses the challenge of adapting existing path-following methods to the complex dynamics of multi-link biomimetic underwater robots, which has been hindered by insufficient simulation validation. Focusing on a biomimetic dolphin robot, this work proposes the first line-of-sight (LOS) guidance-based path-following framework specifically designed for multi-link architectures. By integrating an accurate dynamic model with a high-fidelity underwater simulation environment, the approach enables efficient tuning of control parameters and thorough validation of the control strategy. The proposed method not only fills a critical gap in dedicated path-following control for multi-link biomimetic underwater vehicles but also demonstrates its effectiveness and feasibility through comprehensive simulations in a realistic virtual setting.
0 citationsRead paper
Efficient event-driven retrieval in high-capacity kernel Hopfield networks
This work addresses the challenge of deploying high-capacity kernel Hopfield networks on event-driven neuromorphic hardware, which is hindered by their reliance on synchronous updates. The study investigates the asynchronous retrieval dynamics of kernel logistic regression–based Hopfield networks and demonstrates that, through careful tuning of kernel parameters, asynchronous sequential updates become statistically equivalent to their synchronous counterparts while preserving high recall accuracy. For the first time, it is shown that asynchronous dynamics can operate stably at storage capacities approaching \( P/N \approx 30 \), surpassing the classical Hopfield limit, and exhibit a smooth energy landscape amenable to event-driven computation. The number of state transitions required for convergence scales approximately with the initial Hamming distance, without significant spurious oscillations, enabling efficient and low-power associative memory retrieval.
0 citationsRead paper
Geometric analysis of attractor boundaries and storage capacity limits in kernel Hopfield networks
This work investigates the dynamical and geometric mechanisms underlying attractor stability in Hopfield networks trained with kernel logistic regression, revealing fundamental limits to their storage capacity. Through experiments involving random sequences and CIFAR-10 embeddings, manifold interpolation, effective barrier analysis, critical slowing-down observations, and signal-to-noise ratio evaluation grounded in Cover’s theorem, the study demonstrates that attractors reside on an “optimization ridge” separated by phase-transition-like boundaries. The findings indicate that the storage limit arises from dynamical instability rather than inseparability in feature space, establishing the network’s operation as a localized exemplar memory system. The model achieves a capacity of P/N ≈ 16 on random data and up to P/N ≈ 20 on structured data, with optimal retrieval performance occurring just before dynamical collapse.
0 citationsRead paper
Recent publications
Latest Papers
Geometry of learning dynamics: Gradient descent versus natural gradient on the ridge of optimization
本文通过几何分析对比梯度下降与自然梯度下降方法在高容量联想记忆模型优化过程中的表现，揭示了自然梯度下降能更稳定、高效地解决学习动力学问题。
0 citationsRead paper
Information Geometric Self-Organization at the Edge of Stability in High-Capacity Kernel Associative Memories
研究通过分析梯度下降在核逻辑回归训练的Hopfield网络中的学习轨迹，揭示了优化动力学在几何奇异性边界上的自稳定行为，解决了高容量关联存储器的稳定性问题。
0 citationsRead paper
Path Following Control System of Line-of-Sight Guidance for Robotic Dolphin with Multi-Link Mechanism in Underwater Simulator
This study addresses the challenge of adapting existing path-following methods to the complex dynamics of multi-link biomimetic underwater robots, which has been hindered by insufficient simulation validation. Focusing on a biomimetic dolphin robot, this work proposes the first line-of-sight (LOS) guidance-based path-following framework specifically designed for multi-link architectures. By integrating an accurate dynamic model with a high-fidelity underwater simulation environment, the approach enables efficient tuning of control parameters and thorough validation of the control strategy. The proposed method not only fills a critical gap in dedicated path-following control for multi-link biomimetic underwater vehicles but also demonstrates its effectiveness and feasibility through comprehensive simulations in a realistic virtual setting.
0 citationsRead paper
Efficient event-driven retrieval in high-capacity kernel Hopfield networks
This work addresses the challenge of deploying high-capacity kernel Hopfield networks on event-driven neuromorphic hardware, which is hindered by their reliance on synchronous updates. The study investigates the asynchronous retrieval dynamics of kernel logistic regression–based Hopfield networks and demonstrates that, through careful tuning of kernel parameters, asynchronous sequential updates become statistically equivalent to their synchronous counterparts while preserving high recall accuracy. For the first time, it is shown that asynchronous dynamics can operate stably at storage capacities approaching \( P/N \approx 30 \), surpassing the classical Hopfield limit, and exhibit a smooth energy landscape amenable to event-driven computation. The number of state transitions required for convergence scales approximately with the initial Hamming distance, without significant spurious oscillations, enabling efficient and low-power associative memory retrieval.
0 citationsRead paper
Geometric analysis of attractor boundaries and storage capacity limits in kernel Hopfield networks
This work investigates the dynamical and geometric mechanisms underlying attractor stability in Hopfield networks trained with kernel logistic regression, revealing fundamental limits to their storage capacity. Through experiments involving random sequences and CIFAR-10 embeddings, manifold interpolation, effective barrier analysis, critical slowing-down observations, and signal-to-noise ratio evaluation grounded in Cover’s theorem, the study demonstrates that attractors reside on an “optimization ridge” separated by phase-transition-like boundaries. The findings indicate that the storage limit arises from dynamical instability rather than inseparability in feature space, establishing the network’s operation as a localized exemplar memory system. The model achieves a capacity of P/N ≈ 16 on random data and up to P/N ≈ 20 on structured data, with optimal retrieval performance occurring just before dynamical collapse.
0 citationsRead paper