Get our free extension to see links to code for papers anywhere online!Free add-on: code for papers everywhere!Free add-on: See code for papers anywhere!

Hector Zenil, Felipe S. Abrahão

Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a univariate 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 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-a-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 of the events. The method derives from the principles of an approach to Artificial General Intelligence 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.

Via

Hector Zenil, Jesper Tegnér, Felipe S. Abrahão, Alexander Lavin, Vipin Kumar, Jeremy G. Frey, Adrian Weller, Larisa Soldatova, Alan R. Bundy, Nicholas R. Jennings, Koichi Takahashi, Lawrence Hunter, Saso Dzeroski, Andrew Briggs, Frederick D. Gregory, Carla P. Gomes, Christopher K. I. Williams, Jon Rowe, James Evans, Hiroaki Kitano, Joshua B. Tenenbaum, Ross King

Recent advances in machine learning and AI, including Generative AI and LLMs, are disrupting technological innovation, product development, and society as a whole. AI's contribution to technology can come from multiple approaches that require access to large training data sets and clear performance evaluation criteria, ranging from pattern recognition and classification to generative models. Yet, AI has contributed less to fundamental science in part because large data sets of high-quality data for scientific practice and model discovery are more difficult to access. Generative AI, in general, and Large Language Models in particular, may represent an opportunity to augment and accelerate the scientific discovery of fundamental deep science with quantitative models. Here we explore and investigate aspects of an AI-driven, automated, closed-loop approach to scientific discovery, including self-driven hypothesis generation and open-ended autonomous exploration of the hypothesis space. Integrating AI-driven automation into the practice of science would mitigate current problems, including the replication of findings, systematic production of data, and ultimately democratisation of the scientific process. Realising these possibilities requires a vision for augmented AI coupled with a diversity of AI approaches able to deal with fundamental aspects of causality analysis and model discovery while enabling unbiased search across the space of putative explanations. These advances hold the promise to unleash AI's potential for searching and discovering the fundamental structure of our world beyond what human scientists have been able to achieve. Such a vision would push the boundaries of new fundamental science rather than automatize current workflows and instead open doors for technological innovation to tackle some of the greatest challenges facing humanity today.

Via

Hector Zenil, Alyssa Adams, Felipe S. Abrahão

We introduce a general-purpose univariate signal deconvolution method based on the principles of an approach to Artificial General Intelligence. This approach is based on a generative model that combines information theory and algorithmic probability that required a large calculation of an estimation of a `universal distribution' to build a general-purpose model of models independent of probability distributions. This was used to investigate how non-random data may encode information about the physical properties such as dimension and length scales in which a signal or message may have been originally encoded, embedded, or generated. This multidimensional space reconstruction method is based on information theory and algorithmic probability, and it is agnostic, but not independent, with respect to the chosen computable or semi-computable approximation method or encoding-decoding scheme. The results presented in this paper are useful for applications in coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages sent by generating sources of unknown nature for which no prior knowledge is available. We argue that this can have strong potential for cryptography, signal processing, causal deconvolution, life, and techno signature detection.

Via

Felipe S. Abrahão, Hector Zenil, Fabio Porto, Klaus Wehmuth

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 fully automated, with or without access to pseudo-random generators, computable learning algorithms, in particular those of statistical nature used in current approaches to machine learning (including deep learning), can always be deceived, naturally or artificially, by sufficiently large datasets. In particular, we demonstrate that, for every finite learning algorithm, 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 are as likely to deceive learning algorithms into a "simplicity bubble" as any other particular dataset. These deceiving datasets guarantee that any prediction will diverge from the high-algorithmic-complexity globally optimal solution while converging toward the low-algorithmic-complexity locally optimal solution. We discuss the framework and empirical conditions for circumventing this deceptive phenomenon, moving away from statistical machine learning towards a stronger type of machine learning based on, or motivated by, the intrinsic power of algorithmic information theory and computability theory.

Via

Alexander Lavin, Hector Zenil, Brooks Paige, David Krakauer, Justin Gottschlich, Tim Mattson, Anima Anandkumar, Sanjay Choudry, Kamil Rocki, Atılım Güneş Baydin, Carina Prunkl, Olexandr Isayev, Erik Peterson, Peter L. McMahon, Jakob Macke, Kyle Cranmer, Jiaxin Zhang, Haruko Wainwright, Adi Hanuka, Manuela Veloso, Samuel Assefa, Stephan Zheng, Avi Pfeffer

The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of Simulation Intelligence", a roadmap for the development and integration of the essential algorithms necessary for a merger of scientific computing, scientific simulation, and artificial intelligence. We call this merger simulation intelligence (SI), for short. We argue the motifs of simulation intelligence are interconnected and interdependent, much like the components within the layers of an operating system. Using this metaphor, we explore the nature of each layer of the simulation intelligence operating system stack (SI-stack) and the motifs therein: (1) Multi-physics and multi-scale modeling; (2) Surrogate modeling and emulation; (3) Simulation-based inference; (4) Causal modeling and inference; (5) Agent-based modeling; (6) Probabilistic programming; (7) Differentiable programming; (8) Open-ended optimization; (9) Machine programming. We believe coordinated efforts between motifs offers immense opportunity to accelerate scientific discovery, from solving inverse problems in synthetic biology and climate science, to directing nuclear energy experiments and predicting emergent behavior in socioeconomic settings. We elaborate on each layer of the SI-stack, detailing the state-of-art methods, presenting examples to highlight challenges and opportunities, and advocating for specific ways to advance the motifs and the synergies from their combinations. Advancing and integrating these technologies can enable a robust and efficient hypothesis-simulation-analysis type of scientific method, which we introduce with several use-cases for human-machine teaming and automated science.

Via

Hector Zenil

At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find an exciting and promising area 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.

Via

Haoling Zhang, Chao-Han Huck Yang, Hector Zenil, Narsis A. Kiani, Yue Shen, Jesper N. Tegner

NeuroEvolution is one of the most competitive evolutionary learning frameworks 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 algorithms. The results show that the two proposed strategies 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://github.com/HaolingZHANG/ReverseEncodingTree.

Via

Santiago Hernández-Orozco, Hector Zenil, Jürgen Riedel, Adam Uccello, Narsis A. Kiani, Jesper Tegnér

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.

Via

Rise Ooi, C. -H. Huck Yang, Pin-Yu Chen, Vìctor Eguìluz, Narsis Kiani, Hector Zenil, David Gomez-Cabrero, Jesper Tegnèr

Networks are fundamental building blocks for representing data, and computations. Remarkable progress in learning in structurally defined (shallow or deep) networks has recently been achieved. Here we introduce evolutionary exploratory search and learning method of topologically flexible networks under the constraint of producing elementary computational steady-state input-output operations. Our results include; (1) the identification of networks, over four orders of magnitude, implementing computation of steady-state input-output functions, such as a band-pass filter, a threshold function, and an inverse band-pass function. Next, (2) the learned networks are technically controllable as only a small number of driver nodes are required to move the system to a new state. Furthermore, we find that the fraction of required driver nodes is constant during evolutionary learning, suggesting a stable system design. (3), our framework allows multiplexing of different computations using the same network. For example, using a binary representation of the inputs, the network can readily compute three different input-output functions. Finally, (4) the proposed evolutionary learning demonstrates transfer learning. If the system learns one function A, then learning B requires on average less number of steps as compared to learning B from tabula rasa. We conclude that the constrained evolutionary learning produces large robust controllable circuits, capable of multiplexing and transfer learning. Our study suggests that network-based computations of steady-state functions, representing either cellular modules of cell-to-cell communication networks or internal molecular circuits communicating within a cell, could be a powerful model for biologically inspired computing. This complements conceptualizations such as attractor based models, or reservoir computing.

Via

Hector Zenil, Narsis A. Kiani, Allan A. Zea, Jesper Tegnér

Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic probability, that decomposes an observation into its most likely algorithmic generative sources. Our approach uses a causal calculus to infer model representations. We demonstrate its ability to deconvolve interacting mechanisms regardless of whether the resultant objects are strings, space-time evolution diagrams, images or networks. While this is mostly a conceptual contribution and a novel framework, we provide numerical evidence evaluating the ability of our methods to separate data from observations produced by discrete dynamical systems such as cellular automata and complex networks. We think that these separating techniques can contribute to tackling the challenge of causation, thus complementing other statistically oriented approaches.

Via