Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits | Paper Citation Record

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This paper cites Hopfield.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Hopfield

Reference 1

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This paper cites The perceptron: a probabilistic model for information storage and organization in the brain.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits The perceptron: a probabilistic model for information storage and organization in the brain

Reference 2

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This paper cites Non-holographic associative memory.Nature, 222(5197):960–962, 1969.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Non-holographic associative memory.Nature, 222(5197):960–962, 1969

Reference 3

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This paper cites Learning patterns and pattern sequences by self-organizing nets of threshold elements.IEEE Transactions on computers, 100(11):1197–1206, 1972.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Learning patterns and pattern sequences by self-organizing nets of threshold elements.IEEE Transactions on computers, 100(11):1197–1206, 1972

Reference 4

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This paper cites The existence of persistent states in the brain.Mathematical biosciences, 19(1-2):101–120, 1974.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits The existence of persistent states in the brain.Mathematical biosciences, 19(1-2):101–120, 1974

Reference 5

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Observation e75d376d-452c-41af-b4d4-ecbfe36e5377 · outbound

This paper cites Exactly soluble model of a spin glass.Soviet Journal of Low Temperature Physics, 3(6):378–383, 1977.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Exactly soluble model of a spin glass.Soviet Journal of Low Temperature Physics, 3(6):378–383, 1977

Reference 6

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This paper cites A logical calculus of the ideas immanent in nervous activity.The bulletin of mathematical biophysics, 5:115–133, 1943.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits A logical calculus of the ideas immanent in nervous activity.The bulletin of mathematical biophysics, 5:115–133, 1943

Reference 7

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Observation 36c13425-f33d-4157-a060-8f061927373b · outbound

This paper cites Robust exponential memory in Hopfield networks.The Journal of Mathematical Neuroscience, 8:1–20, 2018.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Robust exponential memory in Hopfield networks.The Journal of Mathematical Neuroscience, 8:1–20, 2018

Reference 8

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This paper cites Hidden hypergraphs, error-correcting codes, and critical learning in Hopfield networks.Entropy, 23(11), 2021.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Hidden hypergraphs, error-correcting codes, and critical learning in Hopfield networks.Entropy, 23(11), 2021

Reference 9

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This paper cites Efficient and optimal binary Hopfield associative memory storage using minimum probability flow.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Efficient and optimal binary Hopfield associative memory storage using minimum probability flow

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This paper cites Finding hidden cliques in linear time with high probability.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Finding hidden cliques in linear time with high probability

Reference 11

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This paper cites Storing infinite numbers of patterns in a spin-glass model of neural networks.Physical Review Letters, 55(14):1530, 1985.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Storing infinite numbers of patterns in a spin-glass model of neural networks.Physical Review Letters, 55(14):1530, 1985

Reference 12

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This paper cites The space of interactions in neural network models.Journal of Physics A: Mathematical and General, 21(1):257, 1988.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits The space of interactions in neural network models.Journal of Physics A: Mathematical and General, 21(1):257, 1988

Reference 13

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This paper cites Storage capacity of memory networks with binary couplings.Journal de Physique, 50(20):3057–3066, 1989.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Storage capacity of memory networks with binary couplings.Journal de Physique, 50(20):3057–3066, 1989

Reference 14

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Observation 82957488-08f1-4649-97de-5beeb106f68a · outbound

This paper cites McEliece, Edward C.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits McEliece, Edward C

Reference 15

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Observation f01b1afe-5b55-4de1-8cff-bf9be15e3893 · outbound

This paper cites Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition.IEEE Transactions on Electronic Computers, 14(14):326–334, 1965.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition.IEEE Transactions on Electronic Computers, 14(14):326–334, 1965

Reference 16

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Unresolved cited work

Reference 17

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Observation 5e1438e6-6f86-4406-943b-26c89c804f07 · outbound

This paper cites Characteristics of sparsely encoded associative memory.Neural networks, 2(6):451–457, 1989.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Characteristics of sparsely encoded associative memory.Neural networks, 2(6):451–457, 1989

Reference 18

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This paper cites Dense associative memory for pattern recognition.Advances in Neural Information Processing Systems (NeurIPS), 29, 2016.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Dense associative memory for pattern recognition.Advances in Neural Information Processing Systems (NeurIPS), 29, 2016

Reference 19

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This paper cites Capacities of multiconnected memory models.Journal de Physique, 49(3):389–395, 1988.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Capacities of multiconnected memory models.Journal de Physique, 49(3):389–395, 1988

Reference 20

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This paper cites Hopfield networks is all you need.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Hopfield networks is all you need

Reference 21

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This paper cites On a model of associative memory with huge storage capacity.Journal of Statistical Physics, 168(2):288–299, 2017.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits On a model of associative memory with huge storage capacity.Journal of Statistical Physics, 168(2):288–299, 2017

Reference 22

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This paper cites Generalization in a Hopfield network.Journal de Physique, 51(21):2421–2430, 1990.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Generalization in a Hopfield network.Journal de Physique, 51(21):2421–2430, 1990

Reference 23

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This paper cites Storage and Learning phase transitions in the Random-Features Hopfield Model.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Storage and Learning phase transitions in the Random-Features Hopfield Model

Reference 24

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This paper cites Random Features Hopfield Networks generalize retrieval to previously unseen examples.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Random Features Hopfield Networks generalize retrieval to previously unseen examples

Reference 25

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Unresolved cited work

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This paper cites A kernel theory of modern data augmentation.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits A kernel theory of modern data augmentation

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This paper cites Provably strict generalisation benefit for invariance in kernel ridge regression.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Provably strict generalisation benefit for invariance in kernel ridge regression

Reference 28

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This paper cites Gerken and Pan Kessel.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Gerken and Pan Kessel

Reference 29

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Equivariant Neural Tangent Kernels

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This paper cites The implicit bias of gradient descent on separable data.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits The implicit bias of gradient descent on separable data

Reference 31

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Risk and parameter convergence of logistic regression

Reference 32

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This paper cites Lee, Suriya Gunasekar, Pedro Henrique Pamplona Savarese, Nathan Srebro, and Daniel Soudry.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Lee, Suriya Gunasekar, Pedro Henrique Pamplona Savarese, Nathan Srebro, and Daniel Soudry

Reference 33

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Unresolved cited work

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Addison-Wesley, 1991

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Unresolved cited work

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This paper cites On the limited memory bfgs method for large scale optimization.Mathematical programming, 45(1):503–528, 1989.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits On the limited memory bfgs method for large scale optimization.Mathematical programming, 45(1):503–528, 1989

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This paper cites Battaglino, and Michael R.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Battaglino, and Michael R

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This paper cites A vector-contraction inequality for rademacher complexities.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits A vector-contraction inequality for rademacher complexities

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This paper cites The MIT Press, 2nd edition, 2018.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits The MIT Press, 2nd edition, 2018

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This paper cites Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Cambridge Studies in Advanced Mathematics

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This paper cites Hebb.The Organization of Behavior: A Neuropsychological Theory.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Hebb.The Organization of Behavior: A Neuropsychological Theory

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This paper cites Associatron-a model of associative memory.IEEE Transactions on Systems, Man, and Cybernetics, SMC-2(3):380–388, 1972.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Associatron-a model of associative memory.IEEE Transactions on Systems, Man, and Cybernetics, SMC-2(3):380–388, 1972

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This paper cites Adaptive switching circuits.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Adaptive switching circuits

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This paper cites A theory of Pavlovian conditioning.Classical conditioning, Current research and theory, 2:64–69, 1972.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits A theory of Pavlovian conditioning.Classical conditioning, Current research and theory, 2:64–69, 1972

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This paper cites Storage and retrieval capacities of associative memories.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Storage and retrieval capacities of associative memories

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Observation c29dc22d-1fc8-4752-acb0-8f740af6f682 · outbound

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Collective computational properties of neural networks: New learning mechanisms.Physical Review A, 34(5):4217–4228, 1986

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This paper cites Increasing the capacity of a hopfield network without sacrificing functionality.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Increasing the capacity of a hopfield network without sacrificing functionality

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This paper cites Storkey and R.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Storkey and R

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This paper cites Optimum bounds for the distributions of martingales in banach spaces.The Annals of Probability, 22(4):1679–1706, 1994.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Optimum bounds for the distributions of martingales in banach spaces.The Annals of Probability, 22(4):1679–1706, 1994

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Note, as θ∈Ψ(Q n) this implies bi =b π(i) =b j

Reference 52

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This paper cites Note, and again asθ∈Ψ(Q n), this impliesw ij =w π(i)π(j) =w ab.

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits Note, and again asθ∈Ψ(Q n), this impliesw ij =w π(i)π(j) =w ab

Reference 53

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Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits double ascent/descent

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