Carlos T. Calafate

I. de ZarzÃ, J. de Curtò, Jordi Cabot et al.

Large Language Models (LLMs) increasingly serve as autonomous reasoning agents in decision support, scientific problem-solving, and multi-agent coordination systems. However, deploying LLM agents in consequential applications requires assurance that their reasoning remains stable under semantically equivalent input variations, a property we term semantic invariance. Standard benchmark evaluations, which assess accuracy on fixed, canonical problem formulations, fail to capture this critical reliability dimension. To address this shortcoming, in this paper we present a metamorphic testing framework for systematically assessing the robustness of LLM reasoning agents, applying eight semantic-preserving transformations (identity, paraphrase, fact reordering, expansion, contraction, academic context, business context, and contrastive formulation) across seven foundation models spanning four distinct architectural families: Hermes (70B, 405B), Qwen3 (30B-A3B, 235B-A22B), DeepSeek-R1, and gpt-oss (20B, 120B). Our evaluation encompasses 19 multi-step reasoning problems across eight scientific domains. The results reveal that model scale does not predict robustness: the smaller Qwen3-30B-A3B achieves the highest stability (79.6% invariant responses, semantic similarity 0.91), while larger models exhibit greater fragility.

J. de Curtò, I. de Zarzà, Hong Yan et al.

In this work we investigate the use of the Signature Transform in the context of Learning. Under this assumption, we advance a supervised framework that potentially provides state-of-the-art classification accuracy with the use of few labels without the need of credit assignment and with minimal or no overfitting. We leverage tools from harmonic analysis by the use of the signature and log-signature, and use as a score function RMSE and MAE Signature and log-signature. We develop a closed-form equation to compute probably good optimal scale factors, as well as the formulation to obtain them by optimization. Techniques of Signal Processing are addressed to further characterize the problem. Classification is performed at the CPU level orders of magnitude faster than other methods. We report results on AFHQ, MNIST and CIFAR10, achieving 100% accuracy on all tasks assuming we can determine at test time which probably good optimal scale factor to use for each category.