In generative training, a model produces an output and is penalised for its difference from an example. With one output per comparison, a model that produces one common answer can outperform a model retaining a broader repertoire. Explorative Modeling (XM) produces $K$ outputs per comparison and updates on the closest, claiming exploration as a "third pretraining axis" associated with generative expressivity. Here I show the third axis is actually freedom, meaning the weakness of the constraint implied by a model's behaviour. Previous work showed freedom is a property of function rather than form. Parameters, architecture, minimum-description-length (MDL), and data can vary while the behavioural constraint remains unchanged. It was formally proved that weakest models are likeliest to generalise, and freedom selection beat MDL by 110-500\% in induction experiments. I prove average XM loss depends on the chance a candidate misses an acceptable region, with exploration raising miss probability to power $K$. For $K>1$, match probability rises with freedom. I then demonstrate empirically that XM optimises for freedom. In a Forward XM experiment, larger $K$ increased or saturated measured freedom, and increased freedom at every tested value under context-dependent targets. I trained XM candidate pools and compared validation selection with a freedom selector that read unlabelled parent contexts. Freedom won in 29 of 30 cases. Generative expressivity is a mode-count proxy for freedom, that discards the extension structure that gives freedom its generalisation significance. XM is a means, freedom an end, and selecting for freedom improved XM under distribution shift.
Pierre Beckmann, Marco Valentino, Andre Freitascs.AI
Three paradigmatic forms of inference recur across scientific reasoning: deduction, induction, and causal abduction. Reliably evaluating LLMs on these in scientific settings is currently out of reach: scientific benchmarks built on human annotations are costly and lack mechanistic ground truth, while synthetic logical-reasoning benchmarks do not resemble real scientific documents. We introduce SciR, a benchmark that combines multi-paradigm reasoning with controllable scientific rendering, anchored on three paradigmatic scientific problems. Tasks are generated from formal objects (deduction tree, inductive rule hypothesis, causal graph) to guarantee verifiable answers, then rendered into multi-document scientific discourse via per-track domain-tuned genres. The construction lets us independently vary two difficulty axes: how hard it is to extract the key information needed for inference, and how hard the principled inference itself is. We test six models. Both axes hurt every model, and their effects compound. The rendering even hurts neurosymbolic pipelines, which hand inference to a verified solver. The two axes yield a per-model extraction-vs-inference profile: for instance, reasoning models like deepseek-r1 mostly surpass non-reasoning instruct models on the inference axis. To our knowledge, SciR is the first multi-paradigm scientific-reasoning benchmark with parametric control on both extraction and inference difficulty.