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We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a…
Compositional generalization is a basic mechanism in human language learning, but current neural networks lack such ability. In this paper, we conduct fundamental research for encoding compositionality in neural networks. Conventional…
Bernard Lang defines parsing as the calculation of the intersection of a FSA (the input) and a CFG. Viewing the input for parsing as a FSA rather than as a string combines well with some approaches in speech understanding systems, in which…
Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
Humans excel at applying learned behavior to unlearned situations. A crucial component of this generalization behavior is our ability to compose/decompose a whole into reusable parts, an attribute known as compositionality. One of the…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…
The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
We introduce flat automata for automatic generation of tokenizers. Flat automata are a simple representation of standard finite automata. Using the flat representation, automata can be easily constructed, combined and printed. Due to the…
This paper establishes a theoretical framework connecting neural network learning with abstract algebraic structures. We first present a minimal counterexample demonstrating that standard neural networks completely fail on compositional…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
We study deterministic tree-walking-storage automata, which are finite-state devices equipped with a tree-like storage. These automata are generalized stack automata, where the linear stack storage is replaced by a non-linear tree-like…
Compositional generalization is a key ability of humans that enables us to learn new concepts from only a handful examples. Neural machine learning models, including the now ubiquitous Transformers, struggle to generalize in this way, and…
In GFG automata, it is possible to resolve nondeterminism in a way that only depends on the past and still accepts all the words in the language. The motivation for GFG automata comes from their adequacy for games and synthesis, wherein…
Mechanistic interpretability has transformed the analysis of transformer circuits by decomposing model behavior into competing algorithms, identifying phase transitions during training, and deriving closed-form predictions for when and why…
We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a…