Related papers: Relativity of Depth and Sophistication
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…
In this paper, we investigate how to measure the intelligence of systems under specific structures. Two indicators are adopted to characterize the intelligence of a given structure, namely the function diversity of the structure, and the…
Large Language Models (LLMs) changed the way we design and interact with software systems. Their ability to process and extract information from text has drastically improved productivity in a number of routine tasks. Developers that want…
The complexity of modern software systems entails the need for reconfiguration mechanisms gov- erning the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally,…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and…
We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system…
The reasoning capabilities of Large Language Models (LLMs) are increasingly attributed to training data quality rather than mere parameter scaling. However, existing data-centric paradigms often equate quality with factuality or diversity…
The leaderboard of Large Language Models (LLMs) in mathematical tasks has been continuously updated. However, the majority of evaluations focus solely on the final results, neglecting the quality of the intermediate steps. This oversight…
Asking questions is a pervasive human activity, but little is understood about what makes them difficult to answer. An analysis of a pair of large databases, of New York Times crosswords and questions from the quiz-show Jeopardy,…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same…
Large language models (LLMs) have become capable mathematical problem-solvers, often producing correct proofs for challenging problems. However, correctness alone is not sufficient: mathematical proofs should also be clear, concise,…
For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…
Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…
We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs…
The estimation of depth in two-dimensional images has long been a challenging and extensively studied subject in computer vision. Recently, significant progress has been made with the emergence of Deep Learning-based approaches, which have…