When told that robins have sesamoid bones, people are far more prone to extend the property to sparrows than to whales. This behavior, called category-based property induction, is well documented in humans, but whether and how it develops in language models trained only to predict the next token is unclear. To shed light on this, we construct a hierarchical taxonomy of synthetic entities grouped by the properties they share. We then inject facts from this latent taxonomy into the continued pre-training of Pythia and OLMo 2 models from 70M to 7B parameters, and track the development of inductive behaviors. We find that taxonomically aligned induction emerges from next-token prediction alone: a property learned for one entity transfers more strongly within its taxonomic category than across categories. Internally, entities that share a deeper category become more similar in activation space, and clustering recovers the full taxonomic tree from entity representations. Contrary to the usual expectation that scale helps, we find that induction weakens with model size when the data budget is fixed, suggesting that larger models memorize individual facts rather than compress them into shared structure. Induction also strengthens with more pre-training before the taxonomy injection, transfers to novel in-context properties, and can be overridden by a latent taxonomy implied by the prompt. Together, these results show that a model's inductive generalization reflects the latent organization of its training data, with implications for data curation and for predicting how far a learned fact will spread.
Figures & tables
Figure 1: Overview. (a) Example natural (top) and synthetic (bottom) taxonomies of depth D=2 ; experiments use D=3 . (b) We continue pre-training Pythia and OLMo 2 with synthetic sequences mixed in, and (c) track inductive generalization (Pythia 160M shown; see Figure 2 ).
Figure 2: Logp(property∣entity) over continued pre-training of Pythia 160M and OLMo 2 1B. With shared properties (left), memorization (dashed) > induction within category (green) > induction across categories (red). Without shared properties (right), within- and across-category induction collapse onto each other. Shaded regions: standard error of the mean across three random seeds.
Figure 3: Hierarchical recovery of the taxonomy from entity representations of OLMo 2 1B. Dendrograms before vs. after continued pre-training on entities and properties. Bars below each dendrogram mark the ground-truth L3 and L2 categories (clustering details in Appendix, subsection C.6 ).
Figure 4: More mature checkpoints acquire induction more strongly. Shown is the induction advantage averaged over the last 1,000 steps of synthetic data injection in continued pre-training from various checkpoints (x-axis). Circles show induction advantage for individual evaluation templates, while horizontal lines show the average. All reported values are averages from three random seeds.
Figure 5: At a fixed data budget, scale hurts. Shown is the induction advantage averaged over the last 1,000 data injection steps vs. model size. Circles indicate induction advantage for individual evaluation templates, while horizontal lines show the average induction advantage. All reported values are averages from three random seeds.
Figure 6: Left: induction within vs. across categories during two-phase training (Taxonomy conflict: Yes ), measured against both the old taxonomy T1 (dashed) and the new taxonomy T2 (solid). Right: induction advantage reached under T2 when the model was first trained on a conflicting taxonomy ( Yes ) vs. trained on T2 from the same base checkpoint without the prior phase ( No ).
Figure 7: In-weights taxonomy shapes in-context induction. Left: schematics of the two setups; models are trained only on shared properties, so probe and control properties appear solely in the prompt. Top: inductive generalization of the probe P (green) vs. each control Ci (red) to target E2; one shot lists the probe and all control properties. Bottom: generalization of P to the in-context closest target E3 vs. the in-weights closest target E2; one shot lists all properties in the in-context taxonomy. Shots are capped by each model’s context window; sentences use randomly sampled evaluation templates (Box C.5 ); shaded regions show SEM over five random seeds.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Pythia
OLMo 2
Optimization
Optimizer
AdamW
AdamW
Learning rate
≈3×10−4
≈4×10−4
LR scheduler
constant
constant
Warmup steps
0
0
Adam β1
0.9
0.9
Appendix
Table 1: Hyperparameters used for continued pre-training with injected synthetic taxonomy data. Learning rates are loaded from the optimizer checkpoints and are therefore slightly below the reported values due to their original (global) cosine schedules. A constant learning rate (LR) scheduler was chosen as it approximates the global cosine schedule well on our small training window of 10k training steps.
Figure 9Figure 10
Figure 8: Schematic of the experiment on interference across taxonomies. Models are first trained on taxonomy T1 and then on a conflicting taxonomy T2 that reuses the same entity names but regroups them. Control denotes standard training without taxonomy conflict (Taxonomy conflict: No ).
Figure 9: Mean pairwise cosine similarity between entity representations over continued pre-training, grouped by the deepest level of the ground-truth taxonomy that the two entities share. Similarity increases monotonically with shared depth (L1 < L2 < L3). Shaded regions indicate the standard error of the mean across three random seeds.
Figure 10: Hierarchical recovery of the taxonomy from entity representations of Pythia 160M, before (top) and after (bottom) continued pre-training on entities and properties. Bars below each dendrogram mark the ground-truth L3 and L2 categories.
Figure 11: Logp(property∣entity) over the last 6,000 continued pre-training steps of Pythia 160M (left) and OLMo 2 1B (right), after synthetic data injection stops at step 5,000. Shaded regions indicate the standard error of the mean across three random seeds.
Figure 12: Memorization over training (left) and early induction advantage, averaged over steps 0–1,000 (right), versus model size for the Pythia family. Scale increases the speed of memorization while reducing correct inductive generalization. Circles indicate induction advantage for individual evaluation templates, while horizontal lines show the average. All reported values are averages across three random seeds, and the shaded regions show the standard error of the mean across those seeds.
Figure 13: Comparison for Pythia 160M between the batch size used in all our experiments (32 sequences; 65k tokens) and the batch size of the original Pythia training run ( Biderman et al., 2023 ) (1,024 sequences; 2M tokens). Shaded regions indicate the standard error of the mean across three random seeds.
Language Technologies Institute, Carnegie Mellon University · Department of Computer Science, Data Science and AI Institute, Johns Hopkins University · Khoury College of Computer Science, Northeastern University +1