相关论文: Ternary Gamma Semirings: From Neural Implementatio…
Binary semirings such as the tropical, log, and probability semirings form a core algebraic tool in classical and modern neural inference systems, supporting tasks like Viterbi decoding, dynamic programming, and probabilistic reasoning.…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…
Binary idempotent semirings govern classical path algebras. Their multiplicative structure is dyadic. We examine whether this restriction is structural or accidental. We define ternary idempotent $\Gamma$-semirings as higher-arity ordered…
Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…
We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism,…
The theory of ternary $\Gamma$-semirings extends classical ring and semiring frameworks by introducing a ternary product controlled by a parameter set $\Gamma$. Building on the foundational axioms recently established by Rao, Rani, and…
Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
This paper develops the algebraic foundation required to build a Zariski-type geometry for \emph{commutative ternary $\Gamma$-semirings}, where multiplication is an inherently triadic, multi-parametric interaction…
Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…
Compositional generalization is a crucial property in artificial intelligence, enabling models to handle novel combinations of known components. While most deep learning models lack this capability, certain models succeed in specific tasks,…
One of the hallmarks of human intelligence is the ability to compose learned knowledge into novel concepts which can be recognized without a single training example. In contrast, current state-of-the-art methods require hundreds of training…
This paper establishes the homological and geometric foundations of non-commutative n-ary Gamma-semirings, unifying two previously distinct directions in Gamma-algebra: the derived Gamma-geometry developed for the commutative ternary case…
Model miscalibration has been frequently identified in modern deep neural networks. Recent work aims to improve model calibration directly through a differentiable calibration proxy. However, the calibration produced is often biased due to…
Neural sequence models exhibit limited compositional generalization ability in semantic parsing tasks. Compositional generalization requires algebraic recombination, i.e., dynamically recombining structured expressions in a recursive…
Sequence-to-sequence learning with neural networks has become the de facto standard for sequence prediction tasks. This approach typically models the local distribution over the next word with a powerful neural network that can condition on…
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…
Graph-based semi-supervised learning has been shown to be one of the most effective approaches for classification tasks from a wide range of domains, such as image classification and text classification, as they can exploit the connectivity…
The use of deep neural networks in edge computing devices hinges on the balance between accuracy and complexity of computations. Ternary Connect (TC) \cite{lin2015neural} addresses this issue by restricting the parameters to three levels…
In this work, we build a generic architecture of Convolutional Neural Networks to discover empirical properties of neural networks. Our first contribution is to introduce a state-of-the-art framework that depends upon few hyper parameters…