Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs

Convolutional Kolmogorov--Arnold Networks (KANs) replace the fixed weights of a convolutional kernel with learnable univariate functions. The dominant formulation attaches one such function to every kernel entry and lets it act on pixel values, expressive but parameter-heavy and prone to overfitting. We argue that the learnable functions are better placed in the \emph{structure} of the convolution than on each edge, and we organise the design space along a single axis: whether the function acts on the pixel \emph{values} or on the filter \emph{shape}. We study three realisations. SV-KAN applies one shared univariate function to the values and leaves the spatial filter free and static, aa classical convolution with a single learnable shared activation. AG-KAN keeps the shared value function but supplies the spatial structure through a content-adaptive Gaussian gate. RF-KAN instead moves the learnable functions onto the filter shape, building each filter from oriented ridge profiles expanded in a localised oscillatory (Morlet) wavelet basis with content-adaptive amplitudes. Under a matched four-layer protocol with in-run references and three seeds, RF-KAN and SV-KAN reach $88.47\pm0.10\%$ and $88.20\pm0.31\%$ on CIFAR-10 and $64.40\pm0.19\%$ and $64.57\pm0.30\%$ on CIFAR-100, at about $0.4$M parameters. At this matched scale the shape model and the simplest value model meet at the top, both above a plain convolution and every per-edge KAN we tested, including the official Gram variant, at roughly a fifth of the parameters. A controlled study attributes the RF-KAN gain to an intrinsically localised oscillatory basis and to content adaptivity, and an ablation that removes the learned shape entirely, leaving only the shared value function, collapses accuracy by over forty points, identifying the learned shape as the load-bearing ingredient at this scale.

Empathic Prompting: Non-Verbal Context Integration for Multimodal LLM Conversations

We present Empathic Prompting, a novel framework for multimodal human-AI interaction that enriches Large Language Model (LLM) conversations with implicit non-verbal context. The system integrates a commercial facial expression recognition service to capture users' emotional cues and embeds them as contextual signals during prompting. Unlike traditional multimodal interfaces, empathic prompting requires no explicit user control; instead, it unobtrusively augments textual input with affective information for conversational and smoothness alignment. The architecture is modular and scalable, allowing integration of additional non-verbal modules. We describe the system design, implemented through a locally deployed DeepSeek instance, and report a preliminary service and usability evaluation (N=5). Results show consistent integration of non-verbal input into coherent LLM outputs, with participants highlighting conversational fluidity. Beyond this proof of concept, empathic prompting points to applications in chatbot-mediated communication, particularly in domains like healthcare or education, where users' emotional signals are critical yet often opaque in verbal exchanges.