PAL uses the classical Preisach hysteresis operator with learned thresholds and an extrema stack to model sequences, proving O(1)-depth Turing completeness via two-stack PDA simulation and incomparability with standard transformers on rate-independent vs. random-access functions.
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- background Key Words:kernel Hopfield network, associative memory, storage capacity, attractor geometry, signal- to-noise ratio, exemplar-based memory 1. Introduction Associative memory, the ability to retrieve complete data patterns from partial or noisy cues, is a funda- mental mechanism in both biological and artificial neural systems. The Hopfield network [1] provides a canonical model for this process, where memories are stored as stable fixed points (attractors) of an energy landscape. While the class
- background Inceoglu et al. 2018). More recently, deep learning (Y. LeCun et al. 2015), a subfield of machine learning, has emerged as a powerful tool to predict solar eruptions. A suite of deep learning methods has been developed, ranging from recurrent neural networks, including long short-term memory and gated recurrent units, to convolutional neural networks (J. J. Hopfield 1982; S. Hochreiter & J. Schmidhuber 1997; Y. LeCun et al. 2015), to predict eruptive events (H. Liu et al. 2019; X. Li et al. 2020
- background call these outliers Correlation Traps, and track them through extended training, connecting them to overfitting in the anti-grokking phase. We note that Correlation Traps were first proposed in [14]. Self-averaging and overfitting.Our overfitting criterion connects to statistical-mechanics accounts of glassy learning, where poor generalization reflects sample-specific structure rather than a single stable rule [ 8, 1, 7, 23, 4]. The MP law gives a self-averaging baseline for randomized layer spe
- background bulk solutions. This architecture has demonstrated high- accuracy classification of image patterns by physically preventing unwanted feedback loops [44]. To process time-varying signals or solve optimization problems, architectures have incorporated feedback loops and autocatalysis. Building on the foundational associa- tive memory models proposed by Hopfield [45], DNA- based Hopfield networks utilize the energy landscape of the reaction system to store state information. Recent work demonstrate
- background One notable application in the physical sciences has been in the high-energy physics community: EBMs were used for modeling event patterns in the Large Hadron Collider (LHC) for anomaly detection and to augment a classifier [4] with success. 1.3 Introduction to energy-based models (EBMs) Energy-based models interpret a probability distribution through the lens of the Boltzmann distribution [16, 1, 20]. In the EBM formulation, the unnormalized probability density is parameterized by an energy fun
- background express optimal phenotypes even in highly variable environments. (C) Successful GRNs become highly aligned with the optimal phenotype, meaning that very few regulatory connections lead to deviations from achieving the optimal phenotype. Alignment can be seen as the GRNs developing highly robust solutions that mimic the Hopfield learning rule for storing memories [16] in an energy landscape. (D) Alignment is found to promote specific types of network motifs in the GRN, in particular coherent FFLs
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background 7representative citing papers
Langevin sampling on the modern Hopfield energy produces training-free stochastic attention that transitions from exact retrieval to generation as temperature rises, with an entropy inflection condition marking the shift.
Gradient flow on deep diagonal linear LDA networks with balanced initialization converts additive updates to multiplicative updates, automatically conserving the (2/L) quasi-norm.
DenseAMs show tradeoffs between entropy production, retrieval accuracy, and speed at intermediate loads, with a new failure mode in higher-order networks at finite temperature.
Joint training of NCA rules and SIREN pre-patterns improves robustness, encoding capacity, and symmetry breaking compared to purely self-organizing models by offloading information to initial conditions.
Random Matrix Theory detects overfitting via growing Correlation Traps in weight spectra during the anti-grokking phase of neural network training.
A single energy-based model trained on LAPD plasma data enables diagnostic reconstruction, inverse inference of probe position, conditional trend sampling, and unconditional mode reproduction for potential anomaly detection.
Geometric entropy on the N-sphere sets retrieval phase boundaries in continuous thermal dense associative memories, achieving maximum capacity α=0.5 at zero temperature with kernel-dependent critical lines separating retrieval from failure.
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
Memories of amplitude and direction in non-Brownian suspensions coexist and compete, with a specific amplitude suppressing directional memory and restoring symmetry.
Asynchronous sequential updates in KLR Hopfield networks produce statistically indistinguishable trajectories from synchronous dynamics, achieve empirical capacities near P/N=30, and converge with event counts close to initial Hamming distance.
Casimir-stabilized protocell clusters form ε-machines whose attractor states and transitions create emergent prebiotic information through physical memory rather than molecular polymers.
Hybrid neural network predicts eruptive versus confined solar flares from SDO/HMI magnetogram sequences, reports good performance, and links results to magnetic flux cancellation in polarity inversion lines.
LLM hallucinations arise from task-dependent basins in latent space, with separability varying by task and geometry-aware steering reducing their probability.
KLR Hopfield networks store up to 16-20 times their neuron count before dynamical instability from crosstalk noise causes collapse, with sharp attractor boundaries observed via morphing and SNR analysis.
Cell-to-cell variability selects for aligned, motif-enriched gene regulatory networks that are robust to developmental noise and mutations.
Spintronic CiM shows uniform temperature that increases linearly with participating memory cells and decreases linearly with array size.
Experts rate AI scenarios as more likely, less risky, more beneficial, and more valuable than the public, applying different weightings to risk versus benefit.
Non-steady-state chemical charge transport dynamics integrated into reservoir computing enable waveform recognition, voice identification, and chaos prediction, with performance governed by frequency alignment that functions as a chemically-tuned band-pass filter.
citing papers explorer
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Preisach Attention: A Hysteretic Model of Sequential Memory
PAL uses the classical Preisach hysteresis operator with learned thresholds and an extrema stack to model sequences, proving O(1)-depth Turing completeness via two-stack PDA simulation and incomparability with standard transformers on rate-independent vs. random-access functions.
-
Stochastic Attention via Langevin Dynamics on the Modern Hopfield Energy
Langevin sampling on the modern Hopfield energy produces training-free stochastic attention that transitions from exact retrieval to generation as temperature rises, with an entropy inflection condition marking the shift.
-
Implicit Bias in Deep Linear Discriminant Analysis
Gradient flow on deep diagonal linear LDA networks with balanced initialization converts additive updates to multiplicative updates, automatically conserving the (2/L) quasi-norm.
-
Stochastic Thermodynamics of Associative Memory
DenseAMs show tradeoffs between entropy production, retrieval accuracy, and speed at intermediate loads, with a new failure mode in higher-order networks at finite temperature.
-
Learning Developmental Scaffoldings to Guide Self-Organisation
Joint training of NCA rules and SIREN pre-patterns improves robustness, encoding capacity, and symmetry breaking compared to purely self-organizing models by offloading information to initial conditions.
-
Detecting overfitting in Neural Networks during long-horizon grokking using Random Matrix Theory
Random Matrix Theory detects overfitting via growing Correlation Traps in weight spectra during the anti-grokking phase of neural network training.
-
Energy-based models for diagnostic reconstruction and analysis in a laboratory plasma device
A single energy-based model trained on LAPD plasma data enables diagnostic reconstruction, inverse inference of probe position, conditional trend sampling, and unconditional mode reproduction for potential anomaly detection.
-
Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory
Geometric entropy on the N-sphere sets retrieval phase boundaries in continuous thermal dense associative memories, achieving maximum capacity α=0.5 at zero temperature with kernel-dependent critical lines separating retrieval from failure.
-
Deep sequence models tend to memorize geometrically; it is unclear why
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
-
Memories of amplitude and direction coexist and compete in non-Brownian suspensions
Memories of amplitude and direction in non-Brownian suspensions coexist and compete, with a specific amplitude suppressing directional memory and restoring symmetry.
-
Efficient event-driven retrieval in high-capacity kernel Hopfield networks
Asynchronous sequential updates in KLR Hopfield networks produce statistically indistinguishable trajectories from synchronous dynamics, achieve empirical capacities near P/N=30, and converge with event counts close to initial Hamming distance.
-
Emergent Information Formation in Prebiotic Protocell Clusters: A Computational Mechanics Framework of $\epsilon$-Machines and Attractor Memory
Casimir-stabilized protocell clusters form ε-machines whose attractor states and transitions create emergent prebiotic information through physical memory rather than molecular polymers.
-
Predicting Associations between Solar Flares and Coronal Mass Ejections Using SDO/HMI Magnetograms and a Hybrid Neural Network
Hybrid neural network predicts eruptive versus confined solar flares from SDO/HMI magnetogram sequences, reports good performance, and links results to magnetic flux cancellation in polarity inversion lines.
-
Hallucination Basins: A Dynamic Framework for Understanding and Controlling LLM Hallucinations
LLM hallucinations arise from task-dependent basins in latent space, with separability varying by task and geometry-aware steering reducing their probability.
-
Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks
KLR Hopfield networks store up to 16-20 times their neuron count before dynamical instability from crosstalk noise causes collapse, with sharp attractor boundaries observed via morphing and SNR analysis.
-
How is gene-regulatory evolution affected by cell-to-cell variability?
Cell-to-cell variability selects for aligned, motif-enriched gene regulatory networks that are robust to developmental noise and mutations.
-
Computing In Spintronic Memory: A Thermal Perspective
Spintronic CiM shows uniform temperature that increases linearly with participating memory cells and decreases linearly with array size.
-
Perception Gaps in Risk, Benefit, and Value Between Experts and Public Challenge Socially Accepted AI
Experts rate AI scenarios as more likely, less risky, more beneficial, and more valuable than the public, applying different weightings to risk versus benefit.
-
Exploring Non-Steady-State Charge Transport Dynamics in Information Processing: Insights from Reservoir Computing
Non-steady-state chemical charge transport dynamics integrated into reservoir computing enable waveform recognition, voice identification, and chaos prediction, with performance governed by frequency alignment that functions as a chemically-tuned band-pass filter.
- Beyond Silicon: Materials, Mechanisms, and Methods for Physical Neural Computing