Cognitive Schemas, Laws and Tasks
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The paper proposes a minimal structural framework for cognitive representation and problem solving, emphasizing the role of context, invariance recognition, and representative selection. It introduces a Knowledge Space composed of a Concept Graph and a Procedure Graph to formalize these operations without relying on complex inference or learning mechanisms. Illustrative examples and a weak-solver demonstration show how proper representational organization can simplify problem solving and delineate success and failure conditions.
The paper introduces a multi-stage rule‑chaining framework for the Abstraction and Reasoning Corpus (ARC), aiming to model cognitive generalization by inferring abstract rules from few examples. It combines three solvers—a deterministic rule discovery module, a pattern‑composition engine, and a structural abstraction layer—executed sequentially in a fallback hierarchy that reuses earlier reasoning traces to improve interpretability and generalization. The system achieved over 95% accuracy on ARC tasks, demonstrating strong performance across deterministic, compositional, and abstract categories.
arXiv:2605.11388v2 Announce Type: replace Abstract: Humans intuitively solve complex problems by flexibly shifting among reasoning modes: they plan, execute, revise intermediate goals, resolve ambigu...
ConceptARC at Scale introduces a generator that produces thousands of ARC-style tasks focused on specific spatial and semantic concepts, expanding the original benchmark by tenfold. The new dataset, ConceptARC-100, contains 1,600 manually reviewed tasks across 16 concepts, each with 100 tasks. Evaluation of large reasoning models on this dataset reveals that they reliably solve certain concepts, struggle with others, and develop internal representations that cluster by transformation operations such as recoloring, removal, or translation.
The paper introduces a self-demonstration-driven method for mapping relational database schemas to ontologies, addressing challenges such as semantic heterogeneity and cryptic schema naming. It combines neuro-symbolic task decomposition with pattern-guided, dependency-aware demonstrations to improve LLM performance on schema-ontology mapping. Experiments on the RODI benchmark show state‑of‑the‑art results, outperforming existing methods by up to 25 percentage points in F1 score.
arXiv:2607. 20520v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly evaluated on mathematical problem solving, yet prior work often treats representationally equivalent formulations as interchangeable and conflates reasoning errors with interface failures.