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Apple Machine Learning Research

Multilingual Knowledge Transfer under Data Constraints via Lexical Interventions Examining Human-Like Behaviors in LLMs: A Multi-Dimensional Analysis of Model Behaviors, User Factors, and System Prompts The P-Completeness of Inverted Index Traversal: On the Complexity of Evaluating Boolean Query DAGs GRPO Beyond English: A Large-Scale Study of GRPO in Non-English and Multilingual Settings MVICAD2: Multi-View Independent Component Analysis with Delays and Dilations A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport When Unlearning Is Free: Leveraging Low Influence Points to Reduce Computational Costs Scaling Categorical Flow Maps Beyond Next-Token Prediction: A Performance Characterization of Diffusion versus Autoregressive Language Models Arbitrage: Efficient Reasoning via Advantage-Aware Speculation Locking Pretrained Weights via Deep Low-Rank Residual Distillation DeepAmbigQA: Ambiguous Multi-hop Questions for Benchmarking LLM Answer Completeness Taming Outlier Tokens in Diffusion Transformers Understanding Alignment in Multimodal LLMs: A Comprehensive Study Dimensionality Reduction Meets Network Science: Sensemaking on UMAP’s kNN Graph MoMo: Dial Motion Mode in Robot Manipulation with Spatiotemporal Action Tokenization Memory Efficient Audio Synthesis with Decoupled Temporal Depth Diffusion Transformers GH-ESD: Grounded Hypothesis-Driven Error Slice Discovery for Instance-Level Vision Tasks LEAD: Breaking the No-Recovery Bottleneck in Long-Horizon Reasoning Environment-free Synthetic Data Generation for API-Calling Agents Accelerating Text-to-Video Generation with Calibrated Sparse Attention RayRoPE: Projective Ray Positional Encoding for Multi-View Attention LVSum: A Benchmark for Timestamp-Aware Long Video Summarization Length Value Model: Scalable Value Pretraining for Token-Level Length Modeling When Unlearning Is Free: Leveraging Low Influence Points to Reduce Computational Costs Show Me Examples: Inferring Visual Concepts from Image Sets Location-Invariant Properties of Functions Versus Properties of Distributions: United in Testing but Separated in Verification Interactive Proofs for General Distribution Properties Doubly Sub-linear Interactive Proofs of Proximity Personalizing Incremental Video Search with Hybrid Text and ID Embeddings
Scaling Laws for Mixture Pretraining Under Data Constraints
2026-08-20 · via Apple Machine Learning Research

AuthorsAnastasiia Sedova, Skyler Seto, Natalie Schluter, Pierre Ablin

As language models scale, the amount of data they require grows – yet many target data sources, such as low-resource languages or specialized domains, are inherently limited in size. A common strategy is to mix this scarce but valuable target data with abundant generic data, which presents a fundamental trade-off: too little target data in the mixture underexposes the model to the target domain, while too much target data repeats the same examples excessively, yielding diminishing returns and eventual overfitting. We study this trade-off across more than 2,000 language-model training runs spanning multiple model and target dataset sizes, as well as several data types, including multilingual, domain-specific, and quality-filtered mixtures. Across all settings, we find that repetition is a central driver of target-domain performance, and that mixture training tolerates much higher repetition than single-source training: scarce target corpora can be reused 15–20 times, with the optimal number of repetitions depending on the target data size, compute budget, and model scale. Next, we introduce a repetition-aware mixture scaling law that accounts for the decreasing value of repeated target tokens and the regularizing role of generic data. Optimizing the scaling law provides a principled way to compute effective mixture configurations, yielding practical mixture recommendations for pretraining under data constraints.

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Large foundation models are typically trained on data from multiple domains, with the data mixture—the proportion of each domain used—playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes impractical for large-scale pretraining. We propose a systematic method to determine the optimal data mixture for any target domain using scaling laws. Our approach…

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A widespread strategy for obtaining a language model that performs well in a target domain is to fine-tune it by training it to do unsupervised next-token prediction on data from that domain. Fine-tuning presents two challenges: i) if the amount of target data is limited, as is the case in most practical applications, the model will quickly overfit, and ii) the model will drift away from the original model and forget the pre-training…

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