Systematic generalization remains a significant challenge in deep learning. In particular, combinatorial generalization - generalizing to new configurations of known factors of variation - is effortless for humans but difficult for standard neural architectures that rely on statistical correlations rather than explicit structural representations. We introduce a new architectural component that embeds structured inductive bias into deep learning: an attention mechanism operating over tensor-product representations (TPRs). Through controlled experiments on compositional tasks, we show that this TPR-attention mechanism outperforms existing architectural components in combinatorial generalization. These results highlight the value of integrating explicit compositional structure into neural attention and point toward a promising path for models capable of systematic generalization.
Akihiro Maeda, Thomas Seiller, Yohei Osekics.CL stat.ML
Compositional generalization is usually evaluated through model accuracy. We instead ask which structural or lexical identifications make held-out COGS examples admissible from the structures observed in training. Sentences are represented as functors from syntactic addresses to lexical tokens, and selective collapses induce Kan extensions that propagate observed associations. Across 21 COGS generalization types, admissibility follows distinct identification profiles, while residual failures separate unsupported structural templates. These data-side diagnoses characterize what the training corpus licenses under specified identifications, without training a predictive model.
Concept-bottleneck controllable generation routes multi-attribute control through a low-dimensional concept code that, at deployment, must be synthesised from a target attribute configuration. We study this problem in concept-bottleneck text generation under multi-axis compositional generalisation, comparing three ways to obtain the inference-time code: classifier inversion against the encoder heads, reference-text encoding, and a post-hoc label-conditioned prior. Since a concept code admits no direct LM-fluency term, regularising inversion must instead constrain the code toward the encoder's training distribution. We therefore test bare inversion and three regularised variants: label-agnostic and label-conditioned Mahalanobis penalties, and a conditional normalising-flow density baseline. Every inversion variant we test underperforms a simple post-hoc prior fitted to per-combination encoder means on the same checkpoints, across three backbone families spanning $124$M to $8$B parameters. The bare form of classifier inversion also silently collapses to chance, traceable to a directly measured off-manifold code. We validate this diagnosis on real-world benchmarks and under external evaluators, enabling fair comparison with published baselines.
Post-training pipelines that combine supervised fine-tuning (SFT) with reinforcement learning (RL) have emerged as the key recipe for transforming large language models (LLMs) into robust reasoners. We argue that this combined success is driven by compositional generalization, which we formalize through a hierarchical latent selection model. In this framework, reasoning traces are generated by a cascade of discrete latent selection variables corresponding to reusable atomic modules, including both skills (local operations) and routing mechanisms (how intermediate information is selected, reused, and composed). Within this model, we theoretically show that SFT and RL play asymmetric, complementary roles: SFT supplies the raw module materials in compositional traces, and RL decomposes those traces to identify the latent atomic modules and enable compositional generalization. We design controlled experiments to validate this theory. Our results demonstrate that RL can extract atomic modules from compound traces supplied by SFT and recombine them to solve new configurations. Moreover, we find that training on compound traces yields stronger generalization than training on isolated atomic modules. Finally, we investigate the relationship between SFT and RL data and identify an effective protocol in which SFT ensures coverage of all atomic modules through compositional traces, while RL focuses on novel compositions outside the SFT support to drive exploration.
Recent work has shown that Transformers' compositional generalization is governed by \emph{complexity control}, initialization scale and weight decay, which steers training toward low-complexity reasoning solutions rather than high-complexity memorization. Existing analyses, however, treat complexity control as a single static hyperparameter choice, leaving open \emph{when} during training this control is actually decisive. We show that the memorization-versus-reasoning fate of a Transformer is determined within a sharp, identifiable window of training. On a controlled compositional task we find that (i)~weight decay applied for a single 25\%-of-training window matches full-training weight decay in out-of-distribution (OOD) accuracy ($0.93$ vs $0.91$); (ii)~holding total regularization budget constant, placing it in the middle of training yields $5{-}9\times$ higher OOD accuracy than placing it early; (iii)~the boundary of the critical window is remarkably sharp, window onset shifted by as little as $100$ optimization steps causes mean OOD to jump from chance ($0.15$) to reasoning-regime ($0.61$); (iv)~the window's position depends systematically on initialization scale, but the basin of attraction for reasoning solutions \emph{shrinks} at small initialization, contradicting the prevailing recommendation that smaller initialization is uniformly better. We further show that the critical-window phenomenon is task-specific: it does not appear on grokking with modular arithmetic, where properly tuned constant weight decay matches scheduled weight decay.