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arXiv 2025年

作者： Hernández-Espinosa, Alberto Ozelim, Luan Abrahão, Felipe S. Zenil, Hector Oxford Immune Algorithmics Oxford University Innovation London Institute for Healthcare Engineering United Kingdom Algorithmic Dynamics Lab Center of Molecular Medicine Karolinska Institute & King’s College London United Kingdom Brazil Brazil Department of Biomedical Computing Department of Digital Twins School of Biomedical Engineering and Imaging Sciences United Kingdom King’s Institute for Artificial Intelligence King’s College London United Kingdom

We introduce an open-ended test grounded in algorithmic probability that can avoid benchmark contamination in the quantitative evaluation of frontier models in the context of their Artificial General Intelligence (AGI) and Superintelligence (ASI) claims. Unlike other tests, this test does not rely on statistical compression methods (such as GZIP or LZW), which are more closely related to Shannon entropy than to Kolmogorov complexity. The test challenges aspects related to features of intelligence of fundamental nature such as synthesis and model creation in the context of inverse problems (generating new knowledge from observation). We argue that metrics based on model abstraction and optimal Bayesian inference for planning can provide a robust framework for testing intelligence, including natural intelligence (human and animal), narrow AI, AGI, and ASI. Our results show no clear evidence of LLM convergence towards a defined level of intelligence, particularly AGI or ASI. We found that LLM model versions tend to be fragile and incremental, as new versions may perform worse than older ones, with progress largely driven by the size of training data. The results were compared with a hybrid neurosymbolic approach that theoretically guarantees model convergence from optimal inference based on the principles of algorithmic probability and Kolmogorov complexity. The method outperforms LLMs in a proof-of-concept on short binary sequences. Our findings confirm suspicions regarding the fundamental limitations of LLMs, exposing them as systems optimised for the perception of mastery over human language. Progress among different LLM versions from the same developers was found to be inconsistent and limited, particularly in the absence of a solid symbolic counterpart. Copyright © 2025, The Authors. All rights reserved.

关键词： Inverse problems

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A review of methods for estimating algorithmic complexity: Options, challenges, and new directions

arXiv

引用

arXiv 2020年

作者： Zenil, Hector Algorithmic Dynamics Lab Karolinska Institute Stockholm Sweden Oxford Immune Algorithmics Reading United Kingdom Algorithmic Nature Group LABORES Paris France

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression to newer approaches that advance, complement and also pose new challenges and may exhibit their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented and despite their many challenges, some of these methods can be better motivated by and better grounded in the principles of algorithmic information theory. It will be explained how different approaches to algorithmic complexity can explore the relaxation of different necessary and sufficient conditions in their pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance. We conclude with a discussion of possible directions that may or should be taken into consideration to advance the field and encourage methodological innovation, but more importantly, to contribute to scientific discovery. This paper also serves as a rebuttal of claims made in a previously published minireview by another author, and offers an alternative account. Copyright © 2020, The Authors. All rights reserved.

关键词： Computational complexity

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Evolving neural networks through a Reverse Encoding Tree

arXiv

引用

arXiv 2020年

作者： Zhang, Haoling Yang, Chao-Han Huck Zenil, Hector Kiani, Narsis A. Shen, Yue Tegner, Jesper N. Institute of Biochemistry BGI-Shenzhen Shenzhen Guangdong China School of ECE Georgia Institute of Technology AtlantaGA United States Algorithmic Dynamics Lab Oxford Immune Algorithmics United Kingdom Algorithmic Dynamics Lab Oxford Immune Algorithmics Sweden Algorithmic Dynamics Lab Karolinska Institute Stockholm Sweden Living Systems Lab BESE CEMSE King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

NeuroEvolution is one of the most competitive evolutionary learning strategies for designing novel neural networks for use in specific tasks, such as logic circuit design and digital gaming. However, the application of benchmark methods such as the NeuroEvolution of Augmenting Topologies (NEAT) remains a challenge, in terms of their computational cost and search time inefficiency. This paper advances a method which incorporates a type of topological edge coding, named Reverse Encoding Tree (RET), for evolving scalable neural networks efficiently. Using RET, two types of approaches - NEAT with Binary search encoding (Bi-NEAT) and NEAT with Golden-Section search encoding (GS-NEAT) - have been designed to solve problems in benchmark continuous learning environments such as logic gates, Cartpole, and Lunar Lander, and tested against classical NEAT and FS-NEAT as baselines. Additionally, we conduct a robustness test to evaluate the resilience of the proposed NEAT approaches. The results show that the two proposed approaches deliver an improved performance, characterized by (1) a higher accumulated reward within a finite number of time steps;(2) using fewer episodes to solve problems in targeted environments, and (3) maintaining adaptive robustness under noisy perturbations, which outperform the baselines in all tested cases. Our analysis also demonstrates that RET expends potential future research directions in dynamic environments. Code is available from https://***/HaolingZHANG/ReverseEncodingTree. © 2020, CC BY.

关键词： Evolutionary algorithms

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Compression is comprehension, and the unreasonable effectiveness of digital computation in the natural world

arXiv

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arXiv 2019年

作者： Zenil, Hector Oxford Immune Algorithmics Oxford University Innovation Oxford United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Center for Molecular Medicine Karolinska Institute Stockholm Sweden Algorithmic Nature Group LABORES for the Natural and Digital Sciences Paris France

Chaitin’s work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to justify and quantify what I think is clear evidence of the algorithmic nature of the world. To illustrate the concept I will establish novel upper bounds of algorithmic randomness for elementary cellular automata. I will discuss how the practice of science consists in conceiving a model that starts from certain initial values, running a computable instantiation, and awaiting a result in order to determine where the system may be in a future state—in a shorter time than the time taken by the actual unfolding of the phenomenon in question. If a model does not comply with all or some of these requirements it is traditionally considered useless or even unscientific, so the more precise and faster the better. A model is thus better if it can explain more with less, which is at the core of Chaitin’s "compression is comprehension". I will pursue these questions related to the random versus possibly algorithmic nature of the world in two directions, drawing heavily on the work of Chaitin. I will also discuss how the algorithmic approach is related to the success of science at producing models of the world, allowing computer simulations to better understand it and make more accurate predictions and interventions. Copyright © 2019, The Authors. All rights reserved.

关键词： Philosophical aspects

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The Thermodynamics of Network Coding, and an algorithmic Refinement of the Principle of Maximum Entropy

arXiv

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arXiv 2018年

作者： Zenil, Hector Kiani, Narsis A. Tegnér, Jesper Algorithmic Dynamics Lab2 Unit of Computational Medicine Center for Molecular Medicine Department of Medicine Solna Karolinska Institute Stockholm Sweden Natural and Digital Sciences Paris France Oxford Immune Algorithmics Oxford University Innovation Oxford United Kingdom Saudi Arabia

The principle of maximum entropy (Maxent) suggests to select the distribution with maximal entropy. While this has served the community as a useful tool it has recently become clear that distributions with high entropy may indeed be produced by short generative programs. Here we refine the principle by considering recursive (computable) generative programs as a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code to produce an output with a different algorithmic probability. Using the distinction between computable and algorithmic randomness we quantify the cost in informa- tion loss associated with reprogramming. To illustrate this we construct reference graphs reversing the same algorithmic calculus and introduce a Maximal algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. Using MARPA and reprogrammability we refine Maxent by quantifying the algorithmic typicality of an object based on a combined distance from algorithmic randomness. Classical entropy-based Maxent collapse all random-looking cases despite the generating mechanism thereby confounding all distinct degrees of randomness and pseudo-randomness. We discuss practi- cal implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation. Copyright © 2018, The Authors. All rights reserved.

关键词： Random processes

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Evolving Neural Networks through a Reverse Encoding Tree

Evolving Neural Networks through a Reverse Encoding Tree

引用

Congress on Evolutionary Computation

作者： Haoling Zhang Chao-Han Huck Yang Hector Zenil Narsis A. Kiani Yue Shen Jesper N. Tegner BGI-Shenzhen Institute of Biochemistry Shenzhen Guangdong China School of ECE Georgia Institute of Technology Atlanta GA USA Algorithmic Dynamics Lab & Oxford Immune Algorithmics U.K. & Sweden Algorithmic Dynamics Lab Karolinska Institute Stockholm Sweden Living Systems Lab BESE CEMSE King Abdullah University of Science and Technology Thuwal Saudi Arabia

ISBN: (数字)9781728169293

ISBN: (纸本)9781728169309

NeuroEvolution is one of the most competitive evolutionary learning strategies for designing novel neural networks for use in specific tasks, such as logic circuit design and digital gaming. However, the application of benchmark methods such as the NeuroEvolution of Augmenting Topologies (NEAT) remains a challenge, in terms of their computational cost and search time inefficiency. This paper advances a method which incorporates a type of topological edge coding, named Reverse Encoding Tree (RET), for evolving scalable neural networks efficiently. Using RET, two types of approaches - NEAT with Binary search encoding (Bi-NEAT) and NEAT with Golden-Section search encoding (GS-NEAT) - have been designed to solve problems in benchmark continuous learning environments such as logic gates, Cartpole, and Lunar Lander, and tested against classical NEAT and FS-NEAT as baselines. Additionally, we conduct a robustness test to evaluate the resilience of the proposed NEAT approaches. The results show that the two proposed approaches deliver improved performance, characterized by (1) a higher accumulated reward within a finite number of time steps; (2) using fewer episodes to solve problems in targeted environments, and (3) maintaining adaptive robustness under noisy perturbations, which outperform the baselines in all tested cases. Our analysis also demonstrates that RET expends potential future research directions in dynamic environments. Code is available from https://***/HaolingZHANG/ReverseEncodingTree.

关键词： Encoding Neural networks Sociology Statistics Network topology Topology Search methods

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algorithmic probability-guided supervised machine learning on non-differentiable spaces

arXiv

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arXiv 2019年

作者： Hernández-Orozco, Santiago Zenil, Hector Riedel, Jürgen Uccello, Adam Kiani, Narsis A. Tegnér, Jesper Facultad de Ciencias Universidad Nacional Autónoma de México Mexico City Mexico Oxford Immune Algorithmics Oxford United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Karolinska Institutet Sweden Algorithmic Nature Group LABORES Paris France Computer Electrical and Mathematical Sciences and Engineering Saudi Arabia

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows greater resilience to random attacks. We investigate the shape of the discrete algorithmic space when performing regression or classification using a loss function parametrized by algorithmic complexity, demonstrating that the property of differentiation is not necessary to achieve results similar to those obtained using differentiable programming approaches such as deep learning. In doing so we use examples which enable the two approaches to be compared (small, given the computational power required for estimations of algorithmic complexity). We find and report that (i) machine learning can successfully be performed on a non-smooth surface using algorithmic complexity;(ii) that parameter solutions can be found using an algorithmic-probability classifier, establishing a bridge between a fundamentally discrete theory of computability and a fundamentally continuous mathematical theory of optimization methods;(iii) a formulation of an algorithmically directed search technique in non-smooth manifolds can be defined and conducted;(iv) exploitation techniques and numerical methods for algorithmic search to navigate these discrete non-differentiable spaces can be performed;in application of the (a) identification of generative rules from data observations;(b) solutions to image classification problems more resilient against pixel attacks compared to neural networks;(c) identification of equation parameters from a small data-set in the presence of noise in continuous ODE system problem, (d) classification of Boolean NK networks by (1) network topology, (2) underlying Boolean function, and (3) number of incoming edges. Copyright © 2019, The Authors. All rights reserved.

关键词： Computational complexity

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A computable piece of uncomputable art whose expansion may explain the universe in software space

arXiv

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arXiv 2021年

作者： Zenil, Hector Oxford Immune Algorithmics Reading United Kingdom The Alan Turing Institute British Library London United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Center for Molecular Medicine Karolinska Institute Stockholm Sweden Algorithmic Nature Group LABORES for the Natural and Digital Sciences Paris France

At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find a most exciting and promising areas of science related to causation with an alternative, possibly best possible, solution to the challenge of the inverse problem. That is, the problem of finding the possible causes, mechanistic origins, first principles, and generative models of a piece of data from a physical phenomenon. Here we explain how generating and exploring software space following the framework of algorithmic Information dynamics, it is possible to find small models and learn to navigate a sci-fi-looking space that can advance the field of scientific discovery with complementary tools to offer an opportunity to advance science itself. Copyright © 2021, The Authors. All rights reserved.

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Methods and Applications of algorithmic Complexity 1

引用

丛书名： Emergence, Complexity and Computation

1000年

作者： Hector Zenil Fernando Soler Toscano Nicolas Gauvrit

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ON SEQUENTIAL STRUCTURES IN INCOMPRESSIBLE MULTIDIMENSIONAL NETWORKS

arXiv

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arXiv 2018年

作者： Abrahão, Felipe S. Wehmuth, Klaus Zenil, Hector Ziviani, Artur Petrópolis Brazil Brazil Oxford Immune Algorithmics Oxford University Innovation Oxford United States Algorithmic Dynamics Lab School of Biomedical Engineering and Imaging Sciences King’s Institute for Artificial Intelligence King’s College London United States The Alan Turing Institute British Library London United States

MSC Codes 05C82, 68Q30, 03D32, 05C80, 68P30, 94A29, 68R10, 05C60, 05C75, 94A16, 68T09,In order to deal with multidimensional structure representations of real-world networks, as well as with their worst-case irreducible information content analysis, the demand for new graph abstractions increases. This article investigates incompressible multidimensional networks defined by generalized graph representations. In particular, we mathematically study the lossless incompressibility of snapshot-dynamic networks and multiplex networks in comparison to the lossless incompressibility of more general forms of dynamic networks and multilayer networks, from which snapshot-dynamic networks or multiplex networks are particular cases. Our theoretical investigation first explores fundamental and basic conditions for connecting the sequential growth of information with sequential interdimensional structures such as time in dynamic networks, and secondly it presents open problems demanding future investigation. Although there may be a dissonance between sequential information dynamics and sequential topology in the general case, we demonstrate that incompressibility (or algorithmic randomness) dissolves it, preventing both the algorithmic dynamics and the interdimensional structure of multidimensional networks from displaying a snapshot-like behavior (as characterized by any arbitrary mathematical theory). Thus, beyond methods based on statistics or probability as traditionally seen in random graphs and complex networks models, representational incompressibility implies a necessary underlying constraint in the multidimensional network topology. We argue that the study of how isomorphic transformations and their respective algorithmic information distortions can characterize sequential interdimensional structures in (multidimensional) networks helps the analysis of network topological properties while being agnostic to the chosen theory, algorithm, computation model, and programming l

关键词： Network topology

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