Research map / Learning theory and algorithms / Kernels and regression theory

Relating Hopfield Networks to Episodic Control

NeurIPS 2024 · Learning theory and algorithms › Kernels and regression theory · approach: Neural tangent kernel analysis · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Shows that Neural Episodic Control's differentiable neural dictionary is an instance of the Universal Hopfield Network, derives continuous-approximation energy functions, and benchmarks k-Max vs Max/Softmax and Euclidean vs Manhattan kernels on MNIST, CIFAR10 and Tiny ImageNet associative memory tasks.

Problem

Neural Episodic Control's differentiable dictionary is used as non-parametric episodic memory but lacks a theoretical link to associative memory models such as Hopfield networks; its retrieval performance as associative memory is also unclear, and standard absolute-threshold evaluation can reward da

Approach

Recasts DND lookup as similarity (inverse squared Euclidean distance), k-nearest-neighbor separation, and projection within the Universal Hopfield Network framework; introduces a sigmoid-based continuous k-Max with a dynamic threshold to obtain Lyapunov energy functions; and proposes a relative (memorization) retrieval criterion that compares against all other stored memories.

Key results

• Under the new memorization criterion, Max separation (k=1) gives the best capacity on MNIST, and k=1 almost always outperforms other k values for retrieval.
• Manhattan similarity outperforms Euclidean similarity especially at low k; e.g., MNIST capacity under the absolute criterion reaches 0.887 at k=5 with Manhattan versus 0.851 with Euclidean.
• Softmax separation can outperform k-Max in most conditions (all except CIFAR10 with Euclidean similarity and absolute criterion).

Measured effects reported in the paper

Surprising findings

• Under the absolute threshold criterion, the identity and 50-Max functions perform surprisingly well on MNIST even at very high noise, suggesting the threshold criterion rewards modeling dataset statistics rather than memorization.
• Max separation, previously argued to be optimal, is best under the memorization criterion while k>1 wins under the absolute criterion.

Limitations

• Evaluation is limited to associative memory tasks on image datasets; no reinforcement learning experiments are reported.
• The k-Max separation used in experiments is the discrete version; the continuous approximation is not evaluated empirically.
• Best k depends strongly on dataset, so no single setting is robust.

Experimental setup

Datasets: MNIST CIFAR10 Tiny ImageNet

Benchmarks: MNIST CIFAR10 Tiny ImageNet

Metrics: fraction correctly retrieved (absolute threshold criterion) fraction correctly retrieved (memorization criterion)

Baselines: Max separation Softmax separation Identity (no separation) Euclidean similarity Manhattan similarity

Builds on: Universal Hopfield Network Neural Episodic Control Modern Hopfield Networks Sparse distributed memory

Closest papers by meaning

• Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models (ICML 2022 · similarity 0.89)
• Long Sequence Hopfield Memory (NeurIPS 2023 · similarity 0.89)
• Continual Learning in Modern Hopfield Networks with an Application to Diffusion Models (NeurIPS 2026 · similarity 0.86)
• Rectified Lagrangian for Out-of-Distribution Detection in Modern Hopfield Networks (AAAI 2025 · similarity 0.85)
• Recurrent Reinforcement Learning with Memoroids (NeurIPS 2024 · similarity 0.85)
• Exponential Dynamic Energy Network for High Capacity Sequence Memory (NeurIPS 2025 · similarity 0.85)