Related papers: Parametrised Functional Interpretations
We discuss a new approach to functional interpretations based on uniform quantification and relativization. The uniform quantification in the background permits a more penetrating analysis of principles related to collection and…
This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…
We present a conceptual framework that unifies a variety of evaluation metrics for different structured prediction tasks (e.g. event and relation extraction, syntactic and semantic parsing). Our framework requires representing the outputs…
During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with…
We show that the types of the witnesses in the Herbrand functional interpretation can be simplified, avoiding the use of "sets of functionals" in the interpretation of implication and universal quantification. This is done by presenting an…
This technical report presents a general framework for parsing a variety of grammar formalisms. We develop a grammar formalism, called an Abstract Grammar, which is general enough to represent grammars at many levels of the hierarchy,…
Improving the interpretability of brain decoding approaches is of primary interest in many neuroimaging studies. Despite extensive studies of this type, at present, there is no formal definition for interpretability of brain decoding…
This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
To tackle interpretability in deep learning, we present a novel framework to jointly learn a predictive model and its associated interpretation model. The interpreter provides both local and global interpretability about the predictive…
Understanding Transformer-based models has attracted significant attention, as they lie at the heart of recent technological advances across machine learning. While most interpretability methods rely on running models over inputs, recent…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
This paper introduces function alignment, a novel theory of mind and intelligence that is both intuitively compelling and structurally grounded. It explicitly models how meaning, interpretation, and analogy emerge from interactions among…
We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and…
There is an overwhelmingly large literature and algorithms already available on `large scale inference problems' based on different modeling techniques and cultures. Our primary goal in this paper is \emph{not to add one more new…
The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
In many real-world applications, the reward function is too complex to be manually specified. In such cases, reward functions must instead be learned from human feedback. Since the learned reward may fail to represent user preferences, it…