Felipe S Abrahão

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- Research Statement:
Computation, information, and networks are three concepts of major importance in computer science and complexity science.
As society becomes more digitally-intermediated, the impact of the fundamental properties and limits of these three underpinnings on both societal and technological aspects of our current society becomes more evinced.
In this sense, grounded on theoretical computer science, mathematical logic, information theory, network science, and complex systems science, my research is motivated by the investigation of those fundamental properties and limitations that play a major role in formal knowledge, foundational mathematics, data science, artificial intelligence, and networked complex systems.

For example, I am interested in developing: new unifying theories for formal knowledge construction and discovery from complex systems and cybernetics; the creation of new distributed computation models and architectures; and the development of new methods in computational analysis of arbitrarily large data sets.

Other interests of mine include applying those results to decentralized autonomous organizations, e.g., social networks policies and cryptocurrency architectures and protocols, so as to monitor and quantify meta-relational structures of dominance and biases.

- Main areas of expertise:
Theory of computation, Mathematical logic, Information theories, Complex systems science, Complex networks theory, Epistemology.

Secondary fields: Philosophy of mathematics, artificial intelligence, and biology.

- Education:
Bachelor degree in Mathematics at the Federal University of Rio de Janeiro (UFRJ), Brazil. Doctorate and Master's in the interdisciplinary graduate program of Sciences, History of Sciences and of Techniques and Epistemology (HCTE) in the Center of Mathematical and Natural Sciences (CCMN), UFRJ.

- Supervisors:
Hector Zenil (Academic visitor at Oxford Immune Algorithmics, UK;
Ítala Maria Loffredo D'Ottaviano (postdoc at UNICAMP);
Artur Ziviani (postdoc at LNCC);
Gregory Chaitin (doctorate at UFRJ);
Francisco Antônio Dória (masters and doctorate at UFRJ), and
Adilson Gonçalves (bachelor degree at UFRJ).

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Talks and dissemination by Felipe S Abrahão

Interview with Felipe Sobreira Abrahão by Andrea Naccache on Regulation of AI algorithms

Institute of Advanced Studies (IEA) at the University of São Paulo (USP), 2024

Journal Articles by Felipe S Abrahão

On Sequential Structures in Incompressible Multidimensional Networks

Parallel Processing Letters, 2024

In order to deal with multidimensional structure representations of real-world networks, as well ... more 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 language.

Algorithmic Information Dynamics

Scholarpedia, 2020

Algorithmic Information Dynamics (AID) is an algorithmic probabilistic framework for causal disco... more Algorithmic Information Dynamics (AID) is an algorithmic probabilistic framework for causal discovery and causal analysis. It enables a numerical solution to inverse problems based or motivated on principles of algorithmic probability. AID studies dynamical systems in software space where all possible computable models can be found or approximated under the assumption that discrete longitudinal data such as particle orbits in state and phase space can approximate continuous systems by Turing-computable means. AID combines perturbation analysis and algorithmic information theory to guide a search for sets of models compatible with observations and to precompute and exploit those models as testable generative mechanisms and causal first principles underlying data and systems. AID is an alternative or a complement to other approaches and methods of experimental inference, such as statistical machine learning and classical information theory.

AID connects with and across other parallel fields of active research such as logical inference, causal reasoning, and neuro-symbolic computation. AID studies how candidate discrete computable equations as generating mechanisms are affected by changes in observed phenomena over time as a result of a system evolving (e.g. under the influence of noise) or being externally perturbed.

AID is related to other areas such as computational mechanics and program synthesis. However, unlike methods such as Bayesian networks, AID does not rely on graphical models or the (often inaccessible) empirical estimation of mass probability distributions. AID encompasses the foundations and methods that make the area of algorithmic information and algorithmic complexity more relevant to scientific discovery and causal analysis.

Emergence and algorithmic information dynamics of systems and observers

Philosophical Transactions of the Royal Society A: mathematical, physical and engineering sciences , 2022

Previous work has shown that perturbation analysis in software space can produce candidate comput... more Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole.
One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible.
By formalising the act of observing as mutual perturbations between dynamical systems,
we demonstrate that emergence of algorithmic information do depend on the observer's formal knowledge, while robust to other subjective factors, particularly: the choice of the programming language and the measurement method; errors or distortions during the information acquisition; and the informational cost of processing.
This is called observer-dependent emergence (ODE).
In addition, we demonstrate that the unbounded and fast increase of emergent algorithmic information implies asymptotically observer-independent emergence (AOIE).
Unlike ODE, AOIE is a type of emergence for which emergent phenomena will remain considered to be emergent for every formal theory that any observer might devise.
We demonstrate the existence of an evolutionary model that displays the diachronic variant of AOIE and a network model that displays the holistic variant of AOIE.
Our results show that, restricted to the context of finite discrete deterministic dynamical systems, computable systems, and irreducible information content measures, AOIE is the strongest form of emergence that formal theories can attain.

Felipe S Abrahão

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