Related papers: Sophistication vs Logical Depth
Code Sensitivity refers to the ability of Code LLMs to recognize and respond to details changes in problem descriptions. While current code benchmarks and instruction data focus on difficulty and diversity, sensitivity is overlooked. We…
Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
Two different definitions of the Artificial Intelligence concept have been proposed in papers [1] and [2]. The first definition is informal. It says that any program that is cleverer than a human being, is acknowledged as Artificial…
Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as…
Logical reasoning is a core capability for large language models (LLMs), yet existing benchmarks that rely solely on final-answer accuracy fail to capture the quality of the reasoning process. To address this, we introduce FineLogic, a…
We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any…
Large Language Models increasingly rely on self-explanations, such as chain of thought reasoning, to improve performance on multi step question answering. While these explanations enhance accuracy, they are often verbose and costly to…
The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary…
We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
What is the relationship between the complexity of a learner and the randomness of his mistakes? This question was posed in \cite{rat0903} who showed that the more complex the learner the higher the possibility that his mistakes deviate…
Cognitive science and theoretical computer science both seek to classify and explain the difficulty of tasks. Mechanisms of intelligence are those that reduce task difficulty. Here we map concepts from the computational complexity of a…
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…
Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
Learned Bloom Filters, i.e., models induced from data via machine learning techniques and solving the approximate set membership problem, have recently been introduced with the aim of enhancing the performance of standard Bloom Filters,…
We introduce a new notion of complexity of functions and we show that it has the following properties: (i) it governs a PAC Bayes-like generalization bound, (ii) for neural networks it relates to natural notions of complexity of functions…
HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking.…