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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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Non-Random Data Encodes Its Geometric and Topological Dimensions

arXiv

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arXiv 2024年

作者： Zenil, Hector Abrahão, Felipe S. Ozelim, Luan School of Biomedical Engineering and Imaging Sciences King’s College London United Kingdom The Alan Turing Institute British Library United Kingdom King’s Institute for Artificial Intelligence King’s College London United Kingdom The Arrival Institute United Kingdom Oxford Immune Algorithmics Oxford University Innovation United Kingdom Algorithmic Dynamics Lab Center for Molecular Medicine Karolinska Institutet Sweden Brazil Brazil

Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages (i.e., objects embedded into multidimensional spaces) from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. Our multidimensional space reconstruction method from an arbitrary received signal is proven to be agnostic vis-à-vis the encoding-decoding scheme, computation model, programming language, formal theory, the computable (or semi-computable) method of approximation to algorithmic complexity, and any arbitrarily chosen (computable) probability measure. The method derives from the principles of an approach to Artificial General Intelligence (AGI) capable of building a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We argue that this optimal and universal method of decoding non-random data has applications to signal processing, causal deconvolution, topological and geometric properties encoding, cryptography, and bio- and technosignature detection. Copyright © 2024, The Authors. All rights reserved.

关键词： Topology

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A REVIEW OF MATHEMATICAL AND COMPUTATIONAL METHODS IN CANCER dynamics

arXiv

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arXiv 2022年

作者： Uthamacumaran, Abicumaran Zenil, Hector MontrealQC Canada The Alan Turing Institute British Library LondonNW1 2DB United Kingdom Oxford Immune Algorithmics ReadingRG30 1EU United Kingdom Algorithmic Dynamics Lab Karolinska Institute Stockholm171 77 Sweden Algorithmic Nature Group LABORES Paris76006 France

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multicellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored. © 2022, CC BY-SA.

关键词： Complex networks

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Assembly Theory is an approximation to algorithmic complexity based on LZ compression that does not explain selection or evolution

arXiv

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arXiv 2024年

作者： Abrahão, Felipe S. Hernández-Orozco, Santiago Kiani, Narsis A. Tegnér, Jesper Zenil, Hector Oxford Immune Algorithmics Reading United Kingdom Center for Logic Epistemology and the History of Science University of Campinas Brazil DEXL National Laboratory for Scientific Computing Brazil Department of Oncology-Pathology Center for Molecular Medicine Karolinska Institutet Sweden Algorithmic Dynamics Lab Center for Molecular Medicine Karolinska Institutet Sweden Living Systems Lab KAUST Thuwal Saudi Arabia The Alan Turing Institute British Library London United Kingdom School of Biomedical Engineering and Imaging Sciences King’s College London Saudi Arabia

We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed ‘assembly index’ that belongs to the LZ family of popular compression algorithms (ZIP, GZIP, JPEG). Such popular algorithms have been shown to empirically reproduce the results of AT, results that have also been reported before in successful applications to separating organic from non-organic molecules and in the context of the study of selection and evolution. We show that the assembly index value is equivalent to the size of a minimal context-free grammar. The statistical compressibility of such a method is bounded by Shannon Entropy and other equivalent traditional LZ compression schemes, such as LZ77, LZ78, or LZW. In addition, we demonstrate that AT, and the algorithms supporting its pathway complexity, assembly index, and assembly number, define compression schemes and methods that are subsumed into the theory of algorithmic (Kolmogorov-Solomonoff-Chaitin) complexity. Due to AT’s current lack of logical consistency in defining causality for non-stochastic processes and the lack of empirical evidence that it outperforms other complexity measures found in the literature capable of explaining the same phenomena, we conclude that the assembly index and the assembly number do not lead to an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by (abiotic or Darwinian) selection and evolution, that could not have been arrived at using Shannon Entropy or that have not been reported before using classical information theory or algorithmic complexity. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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

arXiv

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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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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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Assembly Theory Reduced to Shannon entropy and Rendered Redundant by Naive Statistical Algorithms

arXiv

引用

arXiv 2024年

作者： Ozelim, Luan Uthamacumaran, Abicumaran Abrahão, Felipe S. Hernández-Orozco, Santiago Kiani, Narsis A. Tegnér, Jesper Zenil, Hector Oxford Immune Algorithmics Oxford University Innovation United Kingdom Center for Logic Epistemology and The History of Science University of Campinas Brazil DEXL National Laboratory for Scientific Computing Brazil Department of Oncology-Pathology Center for Molecular Medicine Karolinska Institutet Sweden Algorithmic Dynamics Lab Karolinska Institutet Sweden King’s College London United Kingdom Dept. Physics and Psychology Concordia University Canada McGill University Neurosurgical Simulation and Artificial Intelligence Learning Centre Canada Living Systems Lab KAUST Saudi Arabia School of Biomedical Engineering and Imaging Sciences King’s Institute for Artificial Intelligence King’s College London United Kingdom

We respond to arguments against our critique of Assembly Theory that claim to show its divergence from popular compression. We have proven that any implementation of the concept of ‘copy number’ underlying Assembly Theory (AT) and its assembly index (Ai) is equivalent to Shannon entropy, and not fundamentally or methodologically different from algorithms like ZIP compression. Here we show that the weak empirical correlation between Ai and LZW, which the authors have offered as a defence is based on an incomplete and misleading experiment. When the experiment is completed, the fast asymptotic convergence to LZ compression and Shannon entropy is undeniable, just as their mathematical proof of equivalence remains undisputed. This contribution completes the theoretical and empirical demonstration that any variation of the copy-number concept underlying AT, which entails counting the number of object repetitions ‘to arrive at a measure for life,’ is equivalent to statistical compression and Shannon entropy. We demonstrate that the authors’ ‘we-are-better-because-we-are-worse’ argument against compression does not withstand basic scrutiny, and that their empirical results separating organic from inorganic compounds have not only been previously reported, sans claims to unify physics and biology, but are driven solely by molecular length– which they did not control for– rather than by any particular feature of life captured by Assembly Theory or their index. Finally, we show that Ai is a particular case of our Block Decomposition Method, introduced almost a decade earlier, and that arguments attributing special stochastic properties to Ai are misleading, since the properties of Ai are not unique, but rather exactly the same as those that Shannon entropy possesses and for which it was designed in the first place–for the quantification of uncertainty–and which we have proven to be equivalent to Ai. Shannon entropy is already not only equipped with stochasticity but was desig

关键词： Stochastic systems

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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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A SIMPLICITY BUBBLE PROBLEM IN FORMAL-THEORETIC LEARNING SYSTEMS

arXiv

引用

arXiv 2021年

作者： Abrahão, Felipe S. Zenil, Hector Porto, Fabio Winter, Michael Wehmuth, Klaus D'Ottaviano, Itala M.L. Brazil RJ Petropolis Brazil for the Natural and Digital Sciences Paris France Machine Learning Group Department of Chemical Engineering and Biotechnology The University of Cambridge United Kingdom Oxford Immune Algorithmics England United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Department of Medicine Solna Center for Molecular Medicine Karolinska Institute Stockholm Sweden

When mining large datasets in order to predict new data, limitations of the principles behind statistical machine learning pose a serious challenge not only to the Big Data deluge, but also to the traditional assumptions that data generating processes are biased toward low algorithmic complexity. Even when one assumes an underlying algorithmic-informational bias toward simplicity in finite dataset generators, we show that current approaches to machine learning (including deep learning, or any formal-theoretic hybrid mix of top-down AI and statistical machine learning approaches), can always be deceived, naturally or artificially, by sufficiently large datasets. In particular, we demonstrate that, for every learning algorithm (with or without access to a formal theory), there is a sufficiently large dataset size above which the algorithmic probability of an unpredictable deceiver is an upper bound (up to a multiplicative constant that only depends on the learning algorithm) for the algorithmic probability of any other larger dataset. In other words, very large and complex datasets can deceive learning algorithms into a "simplicity bubble" as likely as any other particular non-deceiving dataset. These deceiving datasets guarantee that any prediction effected by the learning algorithm will unpredictably diverge from the high-algorithmic-complexity globally optimal solution while converging toward the low-algorithmic-complexity locally optimal solution, although the latter is deemed a global one by the learning algorithm. We discuss the framework and additional empirical conditions to be met in order to circumvent this deceptive phenomenon, moving away from statistical machine learning towards a stronger type of machine learning based on, and motivated by, the intrinsic power of algorithmic information theory and computability theory. Copyright © 2021, The Authors. All rights reserved.

关键词： Large dataset

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algorithmic Information dynamics of Cellular Automata

arXiv

引用

arXiv 2021年

作者： Zenil, Hector Adams, Alyssa Oxford Immune Algorithmics ReadingRG30 1EU United Kingdom Alan Turing Institute British Library LondonNW1 2DB United Kingdom Algorithmic Dynamics Lab Karolinska Institute Stockholm171 77 Sweden Algorithmic Nature Group Labores Paris76006 France Morgridge Institute of Research Department of Bacteriology University of Wisconsin-Madison MadisonWI53706 United States

We illustrate an application of algorithmic Information dynamics (AID) to Cellular Automata (CA) demonstrating how this digital calculus is able to quantify change in discrete dynamical systems. We demonstrate the sensitivity of the Block Decomposition Method on 1D and 2D CA, including Conway's Game of Life, against measures of statistical nature such as compression (such as Lempel-Ziv-Welch) and Shannon Entropy in two different contexts (1) perturbation analysis and (2) dynamic-state colliding CA. The approach is interesting because it analyses a quintessential object native to software space (CA) in software space itself by using algorithmic information dynamics through a model-driven universal search instead of a traditional statistical approach e.g. LZW compression or Shannon entropy. The colliding example of two state-independent (if not three as one is regulating the collision itself) discrete dynamical systems offers a potential proof of concept for the development of a multivariate version of the AID calculus. Copyright © 2021, The Authors. All rights reserved.

关键词： Computational complexity

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