SW-KAN
A Kolmogorov-Arnold Network variant based on Stieltjes-Wigert q-orthogonal polynomials. It addresses domain mismatch through an exponential-of-tanh mapping and enables efficient computation via three-term recurrence relations, with applications in image classification and function approximation tasks.
Timeline (last 90 days)
SW-KAN (Stieltjes-Wigert Kolmogorov-Arnold Network) adopts Stieltjes-Wigert q-orthogonal polynomials defined on the semi-infinite domain (0, ∞) as basis functions.
Stieltjes-Wigert polynomials carry a log-normal weight structure and a learnable q parameter.
SW-KAN introduces an exponential-of-tanh smooth mapping to stably map arbitrary real numbers to the positive half-axis while maintaining well-conditioned gradients.
Exponential-of-tanh is an element-wise smooth transformation compatible with automatic differentiation frameworks, and is more stable than truncation (which introduces non-differentiable points) and normalization (which depends on batch statistics).
SW-KAN uses a numerically stable three-term recurrence relation to complete polynomial expansion at O(N) complexity without requiring calls to special functions.
The paper conducts experiments on two types of tasks—image classification and continuous function approximation—and SW-KAN outperforms existing polynomial KAN baseline models on standard benchmarks.
In resource-constrained scenarios (low feature dimensionality, small amount of training data), the inductive bias introduced by SW-KAN's log-normal weight structure and learnable q parameter performs robustly.
SW-KAN is an arXiv preprint (arXiv:2610.00050v1) that has not yet undergone peer review.
SW-KAN is suitable for scenarios sensitive to parameter budgets that require efficient function approximation or classification capability, such as edge device deployment and few-shot learning.
All Facts (9)
SW-KAN (Stieltjes-Wigert Kolmogorov-Arnold Network) adopts Stieltjes-Wigert q-orthogonal polynomials defined on the semi-infinite domain (0, ∞) as basis functions.
50%UnverifiedStieltjes-Wigert polynomials carry a log-normal weight structure and a learnable q parameter.
50%UnverifiedSW-KAN introduces an exponential-of-tanh smooth mapping to stably map arbitrary real numbers to the positive half-axis while maintaining well-conditioned gradients.
50%UnverifiedExponential-of-tanh is an element-wise smooth transformation compatible with automatic differentiation frameworks, and is more stable than truncation (which introduces non-differentiable points) and normalization (which depends on batch statistics).
50%UnverifiedSW-KAN uses a numerically stable three-term recurrence relation to complete polynomial expansion at O(N) complexity without requiring calls to special functions.
50%UnverifiedThe paper conducts experiments on two types of tasks—image classification and continuous function approximation—and SW-KAN outperforms existing polynomial KAN baseline models on standard benchmarks.
50%UnverifiedIn resource-constrained scenarios (low feature dimensionality, small amount of training data), the inductive bias introduced by SW-KAN's log-normal weight structure and learnable q parameter performs robustly.
50%UnverifiedSW-KAN is an arXiv preprint (arXiv:2610.00050v1) that has not yet undergone peer review.
50%UnverifiedSW-KAN is suitable for scenarios sensitive to parameter budgets that require efficient function approximation or classification capability, such as edge device deployment and few-shot learning.
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