Related papers: Higher-order Cons-free Interpreters
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
Many NLP applications require models to be interpretable. However, many successful neural architectures, including transformers, still lack effective interpretation methods. A possible solution could rely on building explanations from…
Transforming constraint models is an important task in re- cent constraint programming systems. User-understandable models are defined during the modeling phase but rewriting or tuning them is manda- tory to get solving-efficient models. We…
Several authors devised type-based termination criteria for ML-like languages allowing non-structural recursive calls. We extend these works to general rewriting and dependent types, hence providing a powerful termination criterion for the…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such…
A set is autoreducible if it can be reduced to itself by a Turing machine that does not ask its own input to the oracle. We use autoreducibility to separate the polynomial-time hierarchy from polynomial space by showing that all…
We consider the language of $\Delta_0$-formulas with list terms interpreted over hereditarily finite list superstructures. We study the complexity of reasoning in extensions of the language of $\Delta_0$-formulas with non-standard list…
For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…
For any group $G$ with subgroup $H$ and a set of representatives $T$ from the set of cosets $G/H$, we develop a rewriting system from $G$ that bequeaths a product into the set decomposition $T\times H$ of $G$, converting it into a group. In…
There is a growing concern about typically opaque decision-making with high-performance machine learning algorithms. Providing an explanation of the reasoning process in domain-specific terms can be crucial for adoption in risk-sensitive…
The advent of recurrent neural networks for handwriting recognition marked an important milestone reaching impressive recognition accuracies despite the great variability that we observe across different writing styles. Sequential…
Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we set out to characterise the hierarchy NP $\subseteq$ NEXP $\subseteq$ NEXP$^{(2)}$ $\subseteq \cdots \subseteq$…
We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative…
Large language models often respond to ambiguous requests by implicitly committing to one interpretation, frustrating users and creating safety risks when that interpretation is wrong. We propose generating a single structured response that…
Although there are several systems that successfully generate construction steps for ruler and compass construction problems, none of them provides readable synthetic correctness proofs for generated constructions. In the present work, we…