Related papers: Cost-Aware Type Theory
Latent Chain-of-Thought (Latent CoT) models promise efficient reasoning via continuous representations, yet exhibit puzzling performance inconsistencies: excelling at exploration (ProsQA: 97.0%) but failing at computation (GSM8K: 34.1%). We…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a…
Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of…
Reasoning about the cost of executing programs is one of the fundamental questions in computer science. In the context of programming with probabilities, however, the notion of cost stops being deterministic, since it depends on the…
In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Multi-context systems provide a powerful framework for modelling information-aggregation systems featuring heterogeneous reasoning components. Their execution can, however, incur non-negligible cost. Here, we focus on cost-complexity of…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
Concept learning is a form of supervised machine learning that operates on knowledge bases in description logics. State-of-the-art concept learners often rely on an iterative search through a countably infinite concept space. In each…
One of the key factors in language productivity and human cognition is the ability of systematic compositionality, which refers to understanding composed unseen examples of seen primitives. However, recent evidence reveals that the…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…
The vast growth of data has rendered traditional manual inspection infeasible, necessitating the adoption of computational methods for efficient data exploration. Topic modeling has emerged as a powerful tool for analyzing large-scale…
Two novel descriptions of weak {\omega}-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are {\omega}-categories. The second is a recursive description of a…
Most neural networks utilize the same amount of compute for every example independent of the inherent complexity of the input. Further, methods that adapt the amount of computation to the example focus on finding a fixed inference-time…
We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…