11 papers
Information Geometric Self-Organization at the Edge of Stability in High-Capacity Kernel Associative Memories
Akira Tamamori
High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit exceptional storage capabilities and robustness. Previous empirical studies identified a hyperp…
Geometry of learning dynamics: Gradient descent versus natural gradient on the ridge of optimization
Akira Tamamori
High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit a "Ridge of Optimization" characterized by extreme stability and a highly skewed weight spectru…
Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks
Akira Tamamori
High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit strong storage capabilities, but the dynamical and geometric mechanisms underlying their stabil…
Efficient event-driven retrieval in high-capacity kernel Hopfield networks
Akira Tamamori
High-capacity associative memory models, such as Kernel Logistic Regression (KLR) Hopfield networks, have demonstrated strong storage capabilities but typically rely on computation…
Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory
Akira Tamamori
High-capacity associative memories based on Kernel Logistic Regression (KLR) achieve strong retrieval performance but typically require substantial computational resources. This pa…
Spectral Concentration at the Edge of Stability: Information Geometry of Kernel Associative Memory
Akira Tamamori
High-capacity kernel Hopfield networks exhibit a \textit{Ridge of Optimization} characterized by extreme stability. While previously linked to \textit{Spectral Concentration}, its…
Self-Organization and Spectral Mechanism of Attractor Landscapes in High-Capacity Kernel Hopfield Networks
Akira Tamamori
Kernel-based learning methods can dramatically increase the storage capacity of Hopfield networks, yet the dynamical mechanisms behind this enhancement remain poorly understood. We…
Localized Kernel Projection Outlyingness: A Two-Stage Approach for Multi-Modal Outlier Detection
Akira Tamamori
This paper presents Two-Stage LKPLO, a novel multi-stage outlier detection framework that overcomes the coexisting limitations of conventional projection-based methods: their relia…
Quantitative Attractor Analysis of High-Capacity Kernel Hopfield Networks
Akira Tamamori
Kernel-based learning methods such as Kernel Logistic Regression (KLR) can substantially increase the storage capacity of Hopfield networks, but the principles governing their perf…
Kernel Ridge Regression for Efficient Learning of High-Capacity Hopfield Networks
Akira Tamamori
Hopfield networks using Hebbian learning suffer from limited storage capacity. While supervised methods like Linear Logistic Regression (LLR) offer some improvement, kernel methods…
Kernel Logistic Regression Learning for High-Capacity Hopfield Networks
Akira Tamamori
Hebbian learning limits Hopfield network storage capacity (pattern-to-neuron ratio around 0.14). We propose Kernel Logistic Regression (KLR) learning. Unlike linear methods, KLR us…