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.

The machine stops when it reaches a certain configuration (a combination of what it reads and its internal state). It is said that a Turing machine produces an output if the Turing machine halts, while the locations on the tape the machine has visited represent the output produced. The most remarkable idea advanced by Turing is his demonstration that there is an'a' machine that is able to read other'a' machines and behave as they would for an input s. In other words, Turing proved that it was not necessary to build a new machine for each different task; a single machine that could be reprogrammed sufficed. This erases the distinction between program and data, as well as between software and hardware, as one can always codify data as a program to be executed by another Turing machine and vice versa, just as one can always build a universal machine to execute any program and vice versa.

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method distinguishes between different asymptotic behaviors of a system's average computation time before entering a loop. When applied to elementary cellular automata, we obtain classification results, which correlate very well with Wolfram's manual classification. Further, we use it to classify 2D cellular automata to show that our technique can easily be applied to more complex models of computation. We believe this classification method can help to develop systems, in which complex structures emerge.

To extract and learn representations leading to generative mechanisms from data, especially without making arbitrary decisions and biased assumptions, is a central challenge in most areas of scientific research particularly in connection to current major limitations of influential topics and methods of machine and deep learning as they have often lost sight of the model component. Complex data is usually produced by interacting sources with different mechanisms. Here we introduce a parameter-free model-based approach, based upon the seminal concept of Algorithmic Probability, that decomposes an observation and signal into its most likely algorithmic generative mechanisms. Our methods use a causal calculus to infer model representations. We demonstrate the method ability to distinguish interacting mechanisms and deconvolve them, regardless of whether the objects produce strings, space-time evolution diagrams, images or networks. We numerically test and evaluate our method and find that it can disentangle observations from discrete dynamic systems, random and complex networks. We think that these causal inference techniques can contribute as key pieces of information for estimations of probability distributions complementing other more statistical-oriented techniques that otherwise lack model inference capabilities.

It's surprisingly difficult to come up with a truly random sequence of numbers or items. Doing so requires cognitive skills such as memory and attention, as well as a sense of complexity. "Our brains are wired to find patterns even where there are none – for example, when looking at clouds or stars in the sky," says Hector Zenil at the Karolinska Institute in Stockholm, Sweden, and the LABORES Research Lab in Paris, France. Zenil and his colleagues have now found that our ability to think up random sequences peaks when we reach 25 before declining with age. This mirrors the evolution and decline of our cognitive abilities, suggesting that monitoring this skill could give an insight into these changes over time. They asked more than 3400 people between the ages of 4 and 91 to complete an online assessment that included five tasks designed to measure their ability to generate random sequences.

In the animal kingdom, acting randomly can be the key to avoiding a grisly fate. After all, if you're a field mouse and a hawk can't predict your next move, your chances for survival are much higher. For human beings, the ability to behave randomly isn't a matter of life or death, but it is an important cognitive skill that reflects our capacity for creativity and problem solving. The bad news is that, according to a new study published in PLOS Computational Biology, our aptitude for making random choices peaks at 25, slowly diminishes until we turn 60, and plummets from that point on. That conclusion, which isn't too surprising given what we know about the aging process, was hard to definitively produce before.