13 papers · ranked by Valyu relevance
Zoe Leyva-Acosta, Eduardo Acuña Yeomans, Francisco Hernández-Quiroz, Ming Li
Algorithmic complexity is a foundational notion in theoretical computer science, but its incomputability has led to two families of practical estimators: compression-based and program-execution-based (e.g., the Coding Theorem Method, CTM). Despite widespread use, the correspondence between these paradigms remains…
Eduardo Y. Sakabe, Felipe S. Abrahão, Alexandre Simões, Esther Colombini + 3 more
Understanding and controlling the complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based loss functions and statistical metrics, these measures often fail to capture deeper, causally…
Jeff Edmonds, Ming Li
This paper does not aim to prove new mathematical theorems or claim a fundamental unification of physics and information, but rather to provide a new pedagogical framework for interpreting foundational results in algorithmic information theory. Our focus is on understanding the profound connection between entropy and…
Milan Lopuhaä-Zwakenberg
Quantitative analysis of risk models is essential to ensure the resilience of complex systems. Fault trees (FTs) form a ubiquitous prominent risk model, and unreliability is its key safety metric. As complex systems have larger and larger models, the complexity of algorithms computing unreliability is a pressing…
Boumediene Hamzi, Marianne Clausel, Kamal Dingle, Marcus Hutter + 2 more
Spurious correlations between time series are a persistent problem: simple, low-complexity patterns are abundant, so unrelated series can easily exhibit high Pearson correlation. We argue that Kolmogorov complexity-a series’ resistance to compression-provides a principled diagnostic for flagging such cases. We prove an…
Giulio Ruffini, Ming Li
The regulator theorem states that, under certain conditions, any optimal controller must embody a model of the system it regulates, grounding the idea that controllers embed, explicitly or implicitly, internal models of the controlled. This principle underpins neuroscience and predictive brain theories like the…
Mohammad Abdur Rob, Md. Zakir Hossen, Md. Kamal Hossen, Md. Mithun Ali + 2 more
Sorting algorithms play a crucial role in computing, but most are designed with rigid structure that are only efficient under certain conditions. Although some sorting algorithms perform well in some circumstances, they do not perform well on some resistant platforms. This study introduces Wall-L Merge Sort, which…
Zhengmian Hu, Boris Ryabko
Can artificial intelligence discover, from raw experience and without human supervision, concepts that humans have discovered? One challenge is that human concepts themselves are fluid: conceptual boundaries can shift, split, and merge as inquiry progresses (e.g., Pluto is no longer considered a planet). To make…
Mengqi Zhang, Guangqiang Teng, Xiaoyu Lei, Boris Ryabko
Lei proposed an algorithm Algorithm $A_{3}$ in 2023 to generate an exact discrete uniform distribution from an unknown biased Bernoulli source. The present paper does not claim a new extraction algorithm. Its contributions are analytical: first, we provide a Fourier-analytic proof of the uniformity mechanism based on…
Ran Wang, Weiquan Huang, Junyu Wu, Chen Chen + 3 more
To address the rapid population diversity loss and premature convergence of the Artificial Lemming Algorithm (ALA) in complex optimization problems, this paper proposes an Improved Artificial Lemming Algorithm (IALA) with multi-strategy enhancements inspired by lemming behavior. First, a non-uniform mutation operator…
Chandrajit Bajaj, Ming Li
Real-world autonomous agents learn under nonstationarity, safety constraints, and finite energetic budgets. We develop a framework for perennial learning-agents that continuously refine their models while provably controlling the cost of forgetting-by unifying three classical pillars: Kolmogorov complexity, which…
Alessandro Achille, Stefano Soatto, Ming Li
We describe AI agents as stochastic dynamical systems and frame the problem of learning to reason as in transductive inference: Rather than approximating the distribution of past data as in classical induction, the objective is to capture its algorithmic structure so as to reduce the time needed to solve new tasks. In…
Xin Li
Computation separates time from space: nondeterministic problems are exponential in time (the “Time Dragon”) but polynomially simulable in space (the “Space Dragon”), as formalized by Savitch's theorem (NPSPACE⊆PSPACE). We propose that the brain physically instantiates this theorem through Recursive Condensation, a…