arXiv:2601.21601v2 Announce Type: replace-cross Abstract: Neural networks adapt through first-order parameter updates, yet it remains unclear whether such updates preserve logical coherence. We investigate the geometric limits of the Linear Propagation Assumption (LPA), the premise that local updates coherently propagate to logical consequences. To formalize this, we adopt relation algebra and study three core operations on relations: negation flips truth values, converse swaps argument order, and composition chains relations. For negation and converse, we prove that guaranteeing direction-agnostic first-order propagation necessitates a tensor factorization separating entity-pair context from relation content. However, for composition, we identify a fundamental obstruction. We show that composition reduces to conjunction, and prove that any conjunction well-defined on linear features must be bilinear. Since bilinearity is incompatible with negation, this forces the feature map to collapse. These results suggest that failures in knowledge editing, the reversal curse, and multi-hop reasoning may stem from common structural limitations inherent to the LPA.

arXiv:2602.14761v1 Announce Type: cross Abstract: Current meta-learning methods are constrained to narrow task distributions with fixed feature and label spaces, limiting applicability. Moreover, the current meta-learning literature uses key terms like "universal" and "general-purpose" inconsistently and lacks precise definitions, hindering comparability. We introduce a theoretical framework for meta-learning which formally defines practical universality and introduces a distinction between algorithm-explicit and algorithm-implicit learning, providing a principled vocabulary for reasoning about universal meta-learning methods. Guided by this framework, we present TAIL, a transformer-based algorithm-implicit meta-learner that functions across tasks with varying domains, modalities, and label configurations. TAIL features three innovations over prior transformer-based meta-learners: random projections for cross-modal feature encoding, random injection label embeddings that extrapolate to larger label spaces, and efficient inline query processing. TAIL achieves state-of-the-art performance on standard few-shot benchmarks while generalizing to unseen domains. Unlike other meta-learning methods, it also generalizes to unseen modalities, solving text classification tasks despite training exclusively on images, handles tasks with up to 20$\times$ more classes than seen during training, and provides orders-of-magnitude computational savings over prior transformer-based approaches.