In this paper, we show the possibility of a direct injection of algorithms into neural network architecture. We focus on a complex algorithm, that is, Cocke-Youger-Kasami (CYK) for parsing context-free grammars in Chomsky Normal Form and we propose CYKNN, a simple recurrent neural network architecture for encoding the CYK algorithm in trainable matrix-vector multiplications.We experimented with a very simple grammar with 4 variations showing that our approach outperforms existing LLMs with more than 20B parameters with an in-context learning setting and smaller LLMs of the Qwen family fine-tuned with LoRA. Our attempt paves the way to a different approach to neuro-symbolic methodologies.
Can syntactic processing emerge spontaneously from purely local interaction? We present a concrete instance on a minimal system: an 18,658-parameter two-dimensional neural cellular automaton (NCA), supervised by nothing more than a 1-bit boundary signal, is trained on the membership problem of an arithmetic-expression grammar. After training, its internal L×L grid spontaneously self-organizes into an ordered, spatially extended representation that we name Proto-CKY. This representation satisfies three operational criteria for syntactic processing: expressive power beyond the regular languages, structural generalization beyond the training distribution, and an internal organization quantitatively aligned with grammatical structure (Pearson r≈0.71). It emerges independently on four context-free grammars and regenerates spontaneously after perturbation. Proto-CKY is functionally aligned with the CKY algorithm but formally distinct from it: it is a physical prototype, a concrete instantiation of a mathematical ideal on a physical substrate, and the systematic distance between the two carries information about the substrate itself.
Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.
Large language models (LLMs) generate fluent text by incrementally predicting the next token from a prefix. Critics in the generative tradition argue that such systems lack genuine grammar; influential replies from the dependency-grammar perspective hold that LLM behavior is well described by local head-dependent structure built word by word. We argue that a sharper observation has been overlooked: the prefix-driven, type-completing dynamics of autoregressive generation align closely with the incremental processing model that Combinatory Categorial Grammar (CCG) was originally designed to support. On this basis we propose a neurosymbolic framework in which LLM outputs are lifted into typed compositional derivations -- not claiming that LLMs implement CCG internally, but that their outputs admit a principled, incremental, and auditable CCG reconstruction. Two consequences follow. First, through the Curry-Howard correspondence the lifting extends beyond natural language to the formal languages LLMs also produce -- programming languages such as Solidity, description-logic and query languages such as OWL and SQL -- with the type system varying and the architecture held fixed. Second, the lifting supports two layers of checking: a compositional layer that catches structural failures directly, and a content layer that checks the lifted structure against external knowledge sources, enabling the earliest possible flagging of hallucinated content. The account thereby requires of a producer not cognition but a prefix-driven generative profile. We close with a sketch of synchronous LLM-CCG coupling as one direction the framework opens.