Continual learning is often motivated by the idea, known as the big world hypothesis, that "the world is bigger" than the agent. Recent problem formulations capture this idea by explicitly constraining an agent relative to the environment. These constraints lead to solutions in which the agent continually adapts to best use its limited capacity, rather than converging to a fixed solution. However, explicit constraints can be ad hoc, difficult to incorporate, and may limit the effectiveness of scaling up the agent's capacity. In this paper, we characterize a problem setting in which an agent, regardless of its capacity, is constrained by being embedded in the environment.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The key advancement in the model is the concept of subpopulation. For fitting the model, they propose sophisticated initialization procedures and compares methods. In other words, why is the matrix A not block diagonal? Wouldn't it allow any mixture factor model to be represented as well?

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.

While the game Connect-Four has been solved mathematically and the best move can be effectively computed with search based methods, a strong solution in the form of a look-up table was believed to be infeasible. In this paper, we revisit a symbolic search method based on binary decision diagrams to produce strong solutions. With our efficient implementation we were able to produce a 89.6 GB large look-up table in 47 hours on a single CPU core with 128 GB main memory for the standard $7 \times 6$ board size. In addition to this win-draw-loss evaluation, we include an alpha-beta search in our open source artifact to find the move which achieves the fastest win or slowest loss.

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.

This thesis explores advanced approaches to improve explainability in computer vision by analyzing and modeling the features exploited by deep neural networks. Initially, it evaluates attribution methods, notably saliency maps, by introducing a metric based on algorithmic stability and an approach utilizing Sobol indices, which, through quasi-Monte Carlo sequences, allows a significant reduction in computation time. In addition, the EVA method offers a first formulation of attribution with formal guarantees via verified perturbation analysis. Experimental results indicate that in complex scenarios these methods do not provide sufficient understanding, particularly because they identify only "where" the model focuses without clarifying "what" it perceives. Two hypotheses are therefore examined: aligning models with human reasoning -- through the introduction of a training routine that integrates the imitation of human explanations and optimization within the space of 1-Lipschitz functions -- and adopting a conceptual explainability approach. The CRAFT method is proposed to automate the extraction of the concepts used by the model and to assess their importance, complemented by MACO, which enables their visualization. These works converge towards a unified framework, illustrated by an interactive demonstration applied to the 1000 ImageNet classes in a ResNet model.

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.

The outcome of all time series cannot be forecast, e.g. the flipping of a fair coin. Others, like the repeated {01} sequence {010101...} can be forecast exactly. Algorithmic information theory can provide a measure of forecastability that lies between these extremes. The degree of forecastability is a function of only the data. For prediction (or classification) of labeled data, we propose three categories for forecastability: oracle forecastability for predictions that are always exact, precise forecastability for errors up to a bound, and probabilistic forecastability for any other predictions. Examples are given in each case.

We introduce a univariate signal deconvolution method based on the principles of an approach to Artificial General Intelligence in order to build a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We investigate how non-random data may encode information about the physical properties, such as dimensions and length scales of the space in which a signal or message may have been originally encoded, embedded, or generated. Our multidimensional space reconstruction method is based on information theory and algorithmic probability, so that it is proven to be agnostic vis-a-vis the arbitrarily chosen encoding-decoding scheme, computable or semi-computable method of approximation to algorithmic complexity, and computational model. 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 from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. We argue that this method has the potential to be of great value in cryptography, signal processing, causal deconvolution, life and technosignature detection.