TESLA: Taylor Expansion of Sinusoidal Learnable Activations

Abstract

The parity problem—deciding whether the number of ones in a binary vector is odd or even—remains challenging for standard neural networks due to linear inseparability and the need for global interactions. We propose TESLA, an activation defined as a learnable combination of sine and cosine terms, enabling explicit control over polynomial degree and selective amplification of high-order components. Theoretically, we show that constraining TESLA’s coefficients yields Lipschitz/Rademacher complexity bounds and shapes the training dynamics to emphasize higher-frequency structure. Empirically, on parity with input length n=32, TESLA attains strong generalization with 100K training samples (≈ 0.002