Felipe S. Abrahão

Hector Zenil, Jesper Tegnér, Felipe S. Abrahão et al. · cambridge

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.

Hector Zenil, Alyssa Adams, Felipe S. Abrahão et al.

We present an agnostic signal reconstruction method for zero-knowledge one-way communication channels in which a receiver aims to interpret a message sent by an unknown source about which no prior knowledge is available and to which no return message can be sent. Our reconstruction method is agnostic vis-à-vis the arbitrarily chosen encoding-decoding scheme and other observer-dependent characteristics, such as the arbitrarily chosen computational model, probability distributions, or underlying mathematical theory. We investigate how non-random messages encode information about their intended physical properties, such as dimension and length scales of the space in which a signal or message may have been originally encoded, embedded, or generated. We focus on image data as a first illustration of the capabilities of the new method. We argue that our results have applications to life and technosignature detection, and to coding theory in general.

Alberto Hernández-Espinosa, Luan Ozelim, Felipe S. Abrahão et al.

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 and are not able to test beyond simple pattern matching. The test challenges aspects of AI, in particular LLMs, 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 abduction (optimal Bayesian `inference') for predictive `planning' can provide a robust framework for testing intelligence, including natural intelligence (human and animal), narrow AI, AGI, and ASI. We found that LLM model versions tend to be fragile and incremental as a result of memorisation only with progress likely driven by the size of training data. The results were compared with a hybrid neurosymbolic approach that theoretically guarantees universal intelligence based on the principles of algorithmic probability and Kolmogorov complexity. The method outperforms LLMs in a proof-of-concept on short binary sequences. We prove that compression is equivalent and directly proportional to a system's predictive power and vice versa. That is, if a system can better predict it can better compress, and if it can better compress, then it can better predict. Our findings strengthen the suspicion regarding the fundamental limitations of LLMs, exposing them as systems optimised for the perception of mastery over human language.

Hector Zenil, Felipe S. Abrahão, Luan C. S. M. Ozelim

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.

Eduardo Y. Sakabe, Felipe S. Abrahão, Alexandre Simões et al.

Understanding and controlling the informational 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 relevant algorithmic regularities embedded in network structure. We propose a shift toward algorithmic information theory, using Binarized Neural Networks (BNNs) as a first proxy. Grounded in algorithmic probability (AP) and the universal distribution it defines, our approach characterizes learning dynamics through a formal, causally grounded lens. We apply the Block Decomposition Method (BDM) -- a scalable approximation of algorithmic complexity based on AP -- and demonstrate that it more closely tracks structural changes during training than entropy, consistently exhibiting stronger correlations with training loss across varying model sizes and randomized training runs. These results support the view of training as a process of algorithmic compression, where learning corresponds to the progressive internalization of structured regularities. In doing so, our work offers a principled estimate of learning progression and suggests a framework for complexity-aware learning and regularization, grounded in first principles from information theory, complexity, and computability.

Alberto Hernández-Espinosa, Felipe S. Abrahão, Olaf Witkowski et al.

The AI alignment problem, which focusses on ensuring that artificial intelligence (AI), including AGI and ASI, systems act according to human values, presents profound challenges. With the progression from narrow AI to Artificial General Intelligence (AGI) and Superintelligence, fears about control and existential risk have escalated. Here, we investigate whether embracing inevitable AI misalignment can be a contingent strategy to foster a dynamic ecosystem of competing agents as a viable path to steer them in more human-aligned trends and mitigate risks. We explore how misalignment may serve and should be promoted as a counterbalancing mechanism to team up with whichever agents are most aligned to human interests, ensuring that no single system dominates destructively. The main premise of our contribution is that misalignment is inevitable because full AI-human alignment is a mathematical impossibility from Turing-complete systems, which we also offer as a proof in this contribution, a feature then inherited to AGI and ASI systems. We introduce a change-of-opinion attack test based on perturbation and intervention analysis to study how humans and agents may change or neutralise friendly and unfriendly AIs through cooperation and competition. We show that open models are more diverse and that most likely guardrails implemented in proprietary models are successful at controlling some of the agents' range of behaviour with positive and negative consequences while closed systems are more steerable and can also be used against proprietary AI systems. We also show that human and AI intervention has different effects hence suggesting multiple strategies.

Felipe S. Abrahão, Hector Zenil, Fabio Porto et al.

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.