arXiv subjects

Luan Ozelim

Publications and source records attributed to Luan Ozelim.

5 recordsLinked to original sources

arXiv2026

Measuring in-context algorithmic reasoning in language models against an exact Bayes-optimal reference

Whether large language models perform algorithmic inference or pattern completion is hard to test, because most benchmarks supply answers but no distributional reference for what the shown evidence licenses. F-ICL supplies one exactly: we exhaustively enumerate the 86 million valid programs of length at most 13 on a Turing-complete machine F, complement-symmetrised to remove output-polarity bias, and compute the exact posterior under a declared bounded Levin--Solomonoff prior. It is Bayes-optimal for that stated prior rather than universal, and models are never told it exists, so the score reads the inductive prior their served distribution already encodes. Across 105 serving configurations spanning open models from 0.8B to 675B and frontier systems, models answer up to 92% of queries correctly, yet 45 of the 46 exposing distributions sit farther from the F reference than a keystroke reference. This is not an artefact of task selection: on the bit coordinate, the half the length quota cannot distort, 69 of 80 runs stay below the anchor. Fidelity is inert to scale, which accuracy tracks; continuation improves late without converging; and models un-solve a solved task once per two gains, where the F reference does so once per nine and always repairs it. Because absolute distances are reference-dependent, we prove sequential bounds holding for rival priors: any predictor whose prior gives the reference positive weight has bounded cumulative excess loss, and, in a loss never invoking the reference, any Bayesian mixture giving the realised truth positive mass has a bounded truth-loss budget. On 23,998 trajectories, 86.7% already spend over 10 bits of it. Sequences ending by position nine cannot exclude an arbitrarily large finite constant, so these are lower bounds on what a rival prior must already pay. F-ICL is an open benchmark and toolkit.

cs.LG↗

arXiv2025

Can Complexity and Uncomputability Explain Intelligence? SuperARC: A Test for Artificial Super Intelligence Based on Recursive Compression

We introduce an increasing-complexity, open-ended, and human-agnostic metric to evaluate foundational and frontier AI models in the context of Artificial General Intelligence (AGI) and Artificial Super Intelligence (ASI) claims. Unlike other tests that rely on human-centric questions and expected answers, or on pattern-matching methods, the test here introduced is grounded on fundamental mathematical areas of randomness and optimal inference. We argue that human-agnostic metrics based on the universal principles established by Algorithmic Information Theory (AIT) formally framing the concepts of model abstraction and prediction offer a powerful metrological framework. When applied to frontiers models, the leading LLMs outperform most others in multiple tasks, but they do not always do so with their latest model versions, which often regress and appear far from any global maximum or target estimated using the principles of AIT defining a Universal Intelligence (UAI) point and trend in the benchmarking. Conversely, a hybrid neuro-symbolic approach to UAI based on the same principles is shown to outperform frontier specialised prediction models in a simplified but relevant example related to compression-based model abstraction and sequence prediction. Finally, we prove and conclude that predictive power through arbitrary formal theories is directly proportional to compression over the algorithmic space, not the statistical space, and so further AI models' progress can only be achieved in combination with symbolic approaches that LLMs developers are adopting often without acknowledgement or realisation.

cs.AI↗

arXiv2025

An Optimal, Universal and Agnostic Decoding Method for Message Reconstruction, Bio and Technosignature Detection

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.

cs.IT↗

arXiv2024

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

Assembly Theory (AT) and its central measure, the assembly index (Ai), represent an invaluable opportunity to address some of the most persistent and widespread conflations and misconceptions about computability and complexity theory in science. The AT defence embodies several common concurrent misconceptions that pile on each other: the belief that Turing machines impose artefactual constraints, the mischaracterisation of Kolmogorov complexity as inapplicable, and the claims around Ai as different from Shannon entropy or compression algorithms. Here we show that the new arguments advanced by the AT group in their defence, are based on misleading and incomplete experiments that, when completed, show the extent of the correlations and overlapping with popular statistical compression algorithms, conforming with the mathematical equivalence to Shannon entropy previously mathematically proved and reported, which remains undisputed. Through theoretical and empirical analysis, we show that Ai does not offer a path towards fundamental novel causal or informational insights beyond what existing statistical frameworks already offer. Rather than offering a unifying theory of life as the AT authors suggest, we argue that AT obfuscates the field and provides a cautionary example of how the accumulation of conceptual mistakes can lead to a misleading theory. Finally, we show that Ai is a particular limited case of another complexity metric based on algorithmic (Kolmogorov) complexity, consisting of decomposing an object into its causal blocks that goes beyond, and outperforms, AT.

cs.IT↗

arXiv2018

Minimal Algorithmic Information Loss Methods for Dimension Reduction, Feature Selection and Network Sparsification

We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of generality, we focus on addressing the challenge of reducing certain dimensionality aspects, such as the number of edges in a network, while retaining essential features of interest. These features include preserving crucial network properties like degree distribution, clustering coefficient, edge betweenness, and degree and eigenvector centralities but can also go beyond edges to nodes and weights for network pruning and trimming. Our approach outperforms classical statistical Machine Learning techniques and state-of-the-art dimensionality reduction algorithms by preserving a greater number of data features that statistical algorithms would miss, particularly nonlinear patterns stemming from deterministic recursive processes that may look statistically random but are not. Moreover, previous approaches heavily rely on a priori feature selection, which requires constant supervision. Our findings demonstrate the effectiveness of the algorithms in overcoming some of these limitations while maintaining a time-efficient computational profile. Our approach not only matches, but also exceeds, the performance of established and state-of-the-art dimensionality reduction algorithms. We extend the applicability of our method to lossy compression tasks involving images and any multi-dimensional data. This highlights the versatility and broad utility of the approach in multiple domains.

cs.DS↗