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Artificial Kuramoto Oscillatory Neurons
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It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations. Code:https://github.com/autonomousvision/akorn Project page:https://takerum.github.io/akorn_project_page/
Forward citations
Cited by 9 Pith papers
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Global synchronization beyond dense graphs: the case of threshold graphs
Connected threshold graphs—built by repeatedly adding isolated or universal vertices—are globally synchronizing for the homogeneous Kuramoto model at any edge density.
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Understanding LoRA as Knowledge Memory: An Empirical Analysis
LoRA modules function as composable knowledge memories for LLMs with measurable storage capacity, internalization efficiency, and advantages in multi-module long-context reasoning.
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Traveling Waves Integrate Spatial Information Through Time
Wave-producing recurrent neural networks with time-series readouts outperform local feed-forward models and rival larger U-Nets on semantic segmentation.
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Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors
Splitting weight matrices into a fixed-norm direction and learnable per-row/column magnitudes improves LLM training over AdamW/Muon, removes weight decay and warmup, and transfers the optimal LR across width.
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Solving Sudoku using oscillatory neural networks
A Kuramoto oscillator network with one phase per cell can solve easy Sudoku puzzles in simulation and beats a Hopfield baseline, but fails on puzzles with many empty cells.
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Sudoku-Bench: Evaluating creative reasoning with Sudoku variants
A new 100-puzzle Sudoku-variant benchmark is hard for frontier LLMs, which solve under 15 percent unaided.
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Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networks
A Kuramoto-oscillator network with an added rule-violation repulsion term solves 4x4 Sudoku near-perfectly and 9x9 Sudoku with high accuracy at low-to-moderate unknown-digit ratios, outperforming prior HNN/ONN solvers.
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Designing learning in high dimensional oscillator networks with low dimensional read-out
A mean-field Kuramoto reservoir with only population-averaged phases as read-out can predict time series, with numerical evidence that chaotic Lorenz dynamics need at least four oscillator populations.
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GASPnet: Global Agreement to Synchronize Phases
A CNN augmented with global attention-driven phase synchronization (GASPnet) outperforms a parameter-matched CNN on noisy multi-object and superimposed-image classification.
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