Bridging Reasoning to Learning: Unmasking Illusions using Complexity Out
  of Distribution Generalization
Authors: name: Mohammad Mahdi Samiei Paqaleh, name: Arash Marioriyad, name: Arman Tahmasebi-Zadeh, name: Mohamadreza Fereydooni, name: Mahdi Ghaznavai, name: Mahdieh Soleymani Baghshah

Recent progress has pushed AI frontiers from pattern recognition tasks toward
problems that require step by step, System2 style reasoning, especially with
large language models. Yet, unlike learning, where generalization and out of
distribution (OoD) evaluation concepts are well formalized, there is no clear,
consistent definition or metric for reasoning ability. We propose Complexity
Out of Distribution (Complexity OoD) generalization as a framework and problem
setting to define and measure reasoning. A model exhibits Complexity OoD
generalization when it maintains performance on test instances whose minimal
required solution complexity, either representational (richer solution
structure) or computational (more reasoning steps/program length), exceeds that
of all training examples. We formalize complexity via solution description
Kolmogorov complexity and operational proxies (e.g., object/relation counts;
reasoning step counts), clarifying how Complexity OoD differs from length and
compositional OoD. This lens unifies learning and reasoning: many cases
solvable with System1 like processing at low complexity become System2 like
under complexity pressure, while System2 can be viewed as generalization over
solution structures. We translate this perspective into practice with
recommendations for operationalizing Complexity OoD across the stack:
incorporating complexity into benchmark and evaluation metric design,
rethinking supervision to target solution traces, seeking and designing
inductive biases for Complexity OoD generalization, addressing learning to
reason spillovers such as spurious shortcuts, semantic robustness, catastrophic
forgetting, and step wise calibration. Because Complexity OoD cannot be solved
by scaling data alone, progress toward robust reasoning will require
architectures and training regimes that explicitly model and allocate
computation with respect to complexity.