Practical deployment of large language models (LLMs) requires families of post-trained variants—instruction-tuned, reasoning-tuned, and chat-style models—each at multiple sizes to meet diverse latency and memory budgets. Producing each (variant, size) pair independently is prohibitive, so model families typically span only a handful of coarse-grained sizes per post-trained variant. Boomerang distillation (Kangaslahti et al., 2026) reduces this cost along the size axis for base models. Through model size interpolation, it constructs models of intermediate sizes from a single teacher-student pair without additional training. However, it still treats each post-trained variant as a separate object of optimization. We introduce ADAPT—Amortized Distillation Across Post-Trained LLMs—a framework for amortizing distillation across both axes of a model family: size and post-training variant, producing L × K models for L interpolated sizes across K post-trained variants with a single distillation run. ADAPT combines two components. First, a two-phase distillation procedure constructs post-trained students through pre-training alignment and supervised fine-tuning distillation, enabling smooth size–performance interpolation on generation and reasoning tasks. Second, weight-delta initialization approximates this construction across post-trained variants by transferring the distillation-induced weight change from the base model to students initialized from different post-trained variants. The resulting continuum of interpolated models also enables adaptive model-size selection at inference time, improving the compute–accuracy trade-off for long-form reasoning tasks.

Interpretability research often predicts model responses to targeted mechanistic interventions. But can we predict responses to unseen input data? We propose and demonstrate this alternate objective by using model internals to predict their out-of-distribution (OOD) behavior. We train hundreds of Transformers on simple synthetic tasks, where perfect in-distribution accuracy is compatible with multiple OOD generalization rules. We successfully use attention patterns—observed only on in-distribution data—to predict which rule each model follows on OOD data. Our experiments decouple the mechanistic faithfulness of our interpretation from its predictive value; ablations reveal such internal patterns can suppress rather than support the rule they predict, showing observational analysis can forecast behavior even when causal analysis fails to support a simple cause-effect link. Our findings are a proof-of-concept for a new interpretability objective: understanding model internals to predict behavior and assess reliability under distribution shift.

Children in multilingual communities often code-switch, using multiple languages in a single utterance. Can we induce cross-lingual alignment in language models by training on code-switched text? We pretrain small decoder-only transformers on two 100M-word multilingual corpora: a base corpus formed by mixing the English, Dutch, and Chinese BabyBabelLM datasets, and a corpus generated from it by inserting word- and sentence-level code-switching using an LLM. We find that training on code-switched data aligns the representations of parallel text, particularly across different scripts, and that this alignment persists through training on monolingual documents. Under a learning curriculum that progresses from word-level code-switching, to sentence-level code-switching, to monolingual documents, models trained on code-switched data outperform baselines trained without it on the BabyLM evaluation suite. Our work characterizes code-switching curriculum learning as an effective data augmentation method for multilingual pretraining. We release our code, data, and models at https://github.com/drooryck/multilingual-macaroni.

Early in training, LMs can behave like n-gram models, but eventually, they often learn tree-based syntactic rules and generalize hierarchically out of distribution (OOD). We study this shift using controlled grammar-learning tasks: question formation and tense inflection. We find a model learns to generalize hierarchically if its training data is complex–in particular, if it includes center-embedded clauses, a special syntactic structure. Under this definition, complex data drives hierarchical rules, while less complex data encourages shortcut learning in the form of n-gram-like linear rules. Furthermore, we find that a model uses rules to generalize, whether hierarchical or linear, if its training data is diverse–in particular, if it includes many distinct syntax trees in the training set. Under this definition, diverse data promotes stable rule learning, whereas less diverse data promotes memorization of individual syntactic sequences. Finally, intermediate diversity and intermediate complexity form an unstable regime, which is characterized by oscillatory learning dynamics and inconsistent behaviors across random seeds. These results highlight the central role of training data in shaping generalization and explain why competing strategies can lead to unstable outcomes.

Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving cross-linguistic numeral systems, which humans can learn to solve successfully. We investigate why this task is difficult for LLMs through a series of experiments that untangle the linguistic and mathematical aspects of numbers in language. Our experiments establish that models cannot consistently solve such problems unless the mathematical operations in the problems are explicitly marked using known symbols (+, ×, etc, as in “twenty + three”). In further ablation studies, we probe how individual parameters of numeral construction and combination affect performance. While humans use their linguistic understanding of numbers to make inferences about the implicit compositional structure of numerals, LLMs seem to lack this notion of implicit numeral structure. We conclude that the ability to flexibly infer compositional rules from implicit patterns in human-scale data remains an open challenge for current reasoning models.

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools. Current state-of-the-art methods, however, involve multiple steps, including heuristic post-hoc refinement strategies. In this paper, we cast the correspondence problem directly as an optimal transport (OT) problem, building on the idea that word embeddings arise from metric recovery algorithms. Indeed, we exploit the Gromov-Wasserstein distance that measures how similarities between pairs of words relate across languages. We show that our OT objective can be estimated efficiently, requires little or no tuning, and results in performance comparable with the state-of-the-art in various unsupervised word translation tasks.

We interpret the predictions of any black-box structured input-structured output model around a specific input-output pair. Our method returns an “explanation” consisting of groups of input-output tokens that are causally related. These dependencies are inferred by querying the model with perturbed inputs, generating a graph over tokens from the responses, and solving a partitioning problem to select the most relevant components. We focus the general approach on sequence-to-sequence problems, adopting a variational autoencoder to yield meaningful input perturbations. We test our method across several NLP sequence generation tasks.

Continuous word representations have been remarkably useful across NLP tasks but remain poorly understood. We ground word embeddings in semantic spaces studied in the cognitive-psychometric literature, taking these spaces as the primary objects to recover. To this end, we relate log co-occurrences of words in large corpora to semantic similarity assessments and show that co-occurrences are indeed consistent with an Euclidean semantic space hypothesis. Framing word embedding as metric recovery of a semantic space unifies existing word embedding algorithms, ties them to manifold learning, and demonstrates that existing algorithms are consistent metric recovery methods given co-occurrence counts from random walks. Furthermore, we propose a simple, principled, direct metric recovery algorithm that performs on par with the state-of-the-art word embedding and manifold learning methods. Finally, we complement recent focus on analogies by constructing two new inductive reasoning datasets—series completion and classification—and demonstrate that word embeddings can be used to solve them as well.