Related papers: The Heap Lambda Machine
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
We describe an efficient hierarchical method to compute attention in the Transformer architecture. The proposed attention mechanism exploits a matrix structure similar to the Hierarchical Matrix (H-Matrix) developed by the numerical…
Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…
The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…
In implementing evaluation strategies of the lambda-calculus, both correctness and efficiency of implementation are valid concerns. While the notion of correctness is determined by the evaluation strategy, regarding efficiency there is a…
We present a call-by-need $\lambda$-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit…
We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge…
This paper demonstrates the use of neural networks for developing a system that can recognize hand-written English alphabets. In this system, each English alphabet is represented by binary values that are used as input to a simple feature…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
We propose a new step-wise approach to proving observational equivalence, and in particular reasoning about fragility of observational equivalence. Our approach is based on what we call local reasoning. The local reasoning exploits the…
This paper describes an architecture for robots that combines the complementary strengths of probabilistic graphical models and declarative programming to represent and reason with logic-based and probabilistic descriptions of uncertainty…
Since language processing systems generally allocate/discard memory with complex reference relationships, including circular and indirect references, their implementation is often not trivial. Here, the allocated memory and the references…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a…
Strategies for partially observable Markov decision processes (POMDP) typically require memory. One way to represent this memory is via automata. We present a method to learn an automaton representation of a strategy using a modification of…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…
Most existing Neural Machine Translation models use groups of characters or whole words as their unit of input and output. We propose a model with a hierarchical char2word encoder, that takes individual characters both as input and output.…
The image classification machine learning model was trained with the intention to predict the category of the input image. While multiple state-of-the-art ensemble model methodologies are openly available, this paper evaluates the…
We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…