${\mathrm{IC}}^3$: Input-Conditioned Complex Convolution for Natural Language Inference

We propose Input-Conditioned Complex Convolution (IC^3), an attention-free method for natural language inference. Building on a complex-valued representation that separates token and contextual information, IC^3 generates both a value sequence and a convolution kernel from each premise-hypothesis pair. The kernel determines how the values are combined across the sequence, and the real part of the complex convolution is used to update the token representations. Zero-padded Fourier transforms compute this convolution efficiently. Our analysis characterizes the resulting input-dependent operators, establishes limits on their approximation using fixed operators, and separates the effects of changes in the values and the kernel. With all models trained from scratch under a deterministic training protocol over ten random seeds, IC^3 achieves higher mean accuracy than baseline decoder architectures with comparable parameter counts on ANLI and FOLIO, with consistent gains on SNLI using reduced training data. Controlled operator comparisons and interventions further support the contributions of input conditioning and the imaginary component to predictive performance.