Al Kari

Al Kari

The Cognitive Categorical Transformer (CCT) is a 306M-parameter architecture that augments a pretrained GPT-2 Small backbone with cognitively grounded components derived from category theory and several inspirations from cognitive science. Under a matched-step protocol (215,000 optimizer steps, matched data, matched optimizer and schedule) on WikiText-103, CCT reaches 21.27 validation perplexity, compared with 24.19 for an identically fine-tuned GPT-2 Small baseline. The architecture therefore contributes a 2.92 PPL (12% relative) reduction beyond what in-domain fine-tuning alone provides. A retrain-from-scratch ablation that holds GT-Full simplicial message passing bypassed across the entire seven-phase activation schedule reaches 23.72 PPL, localizing 84% of the architectural improvement (2.45 of 2.92 PPL) to GT-Full. We present the first ablation-validated evidence that simplicial message passing improves language-model perplexity at the 306M-parameter scale on WikiText-103. Published GPT-2 Large reaches 22.05 zero-shot PPL on WikiText-103 with 6.2x more parameters than GPT-2 Small; this paper treats that number as an external published reference, not as the architectural benchmark. Three negative results on consistency-style categorical priors (sheaf smoothing, adjunction round-trip, curvature regularization) and the joint structural-prior result for GT-Full and PrecisionWeightedPP together support an empirical pattern termed the *structure/consistency distinction*, in which categorical priors that add new topology improve language modeling and those that enforce a consistency identity do not.

Al Kari

The proliferation of Large Language Model (LLM) architectures presents a fundamental challenge: valuable, task-specific behaviors learned through fine-tuning methods like Low-Rank Adaptation (LoRA) are effectively trapped within their source model's architecture, herein referred to architectural lock-in. Existing transfer methods attempt to bridge this gap by aligning the static weight spaces of models, a brittle and indirect approach that relies on tenuous correlations between parameter geometries. This paper introduces a fundamentally different and more direct paradigm: the Cartridge Activation Space Transfer (CAST), a novel framework that liberates LoRA-encoded behaviors by learning a direct, nonlinear mapping between the activation manifolds, the geometric structures formed by the model's internal neuron activations, of two distinct LLM architectures. CAST treats a pre-trained LoRA as a frozen "behavioral kernel." It learns a set of lightweight, bidirectional projection heads that translate the target model's activation stream into the source model's latent space, apply the frozen kernel, and project the result back. This process, trained on a general text corpus without any task-specific data, effectively decouples the learned skill from the source architecture. We demonstrate that CAST enables true "zero-shot" translation of any standard LoRA adapter. Our experiments, including transfers between heterogeneous model families like Llama-2 and Mistral, show that CAST-translated adapters achieve 85-95\% of the performance of a LoRA fully retrained on the target model, quantitatively outperforming current weight-space transfer techniques and establishing a new state-of-the-art in model interoperability.