Dataset curation has become a basis for strong large language model (LLM) performance. While various rule-based filtering heuristics exist for English and multilingual datasets, model-based filtering techniques have primarily focused on English. To address the disparity stemming from limited research on non-English languages, we propose a model-based filtering framework for multilingual datasets that aims to identify a diverse set of structured and knowledge-rich samples. Our approach emphasizes transparency, simplicity, and efficiency, leveraging Transformer- and FastText-based classifiers to ensure the broad accessibility of our technique and data. We conduct comprehensive ablation studies on the FineWeb-2 web crawl dataset across diverse language families, scripts, and resource availability to demonstrate the effectiveness of our method. Training a 1B-parameter Llama model for 70B and 119B tokens, our approach can match the baseline MMLU score with as little as 15% of the training tokens, while also improving across other benchmarks. These findings provide strong evidence for the generalizability of our approach to other languages. As a result, we extend our framework to 20 languages for which we release the refined pretraining datasets.

Learning Rate Warmup is a popular heuristic for training neural networks, especially at larger batch sizes, despite limited understanding of its benefits. Warmup decreases the update size $\Delta \mathbf{w}_t = \eta_t \mathbf{u}_t$ early in training by using lower values for the learning rate $\eta_t$. In this work we argue that warmup benefits training by keeping the overall size of $\Delta \mathbf{w}_t$ limited, counteracting large initial values of $\mathbf{u}_t$. Focusing on small-scale GPT training with AdamW/Lion, we explore the following question: Why and by which criteria are early updates $\mathbf{u}_t$ too large? We analyze different metrics for the update size including the $\ell_2$-norm, resulting directional change, and impact on the representations of the network, providing a new perspective on warmup. In particular, we find that warmup helps counteract large angular updates as well as a limited critical batch size early in training. Finally, we show that the need for warmup can be significantly reduced or eliminated by modifying the optimizer to explicitly normalize $\mathbf{u}_t$ based on the aforementioned metrics.

On-device LLMs have gained increasing attention for their ability to enhance privacy and provide a personalized user experience. To facilitate learning with private and scarce local data, federated learning has become a standard approach, though it introduces challenges related to system and data heterogeneity among end users. As a solution, we propose a novel Collaborative learning approach with a Mixture of Generalists and Specialists (CoMiGS), being the first to effectively address both. Our approach distinguishes generalists and specialists by aggregating certain experts across end users while keeping others localized to specialize in user-specific datasets. A key innovation of our method is the bi-level optimization formulation of the Mixture-of-Experts learning objective, where the router is updated using a separate validation set that represents the target distribution. CoMiGS effectively balances collaboration and personalization, as demonstrated by its superior performance in scenarios with high data heterogeneity across multiple datasets. By decoupling resource abundance from data quantity, CoMiGS remains robust against overfitting--due to the generalists' regularizing effect--while adapting to local data through specialist expertise. Large Language Models (LLMs) have been showing great success serving as foundation models, evidenced by their capability to understand a wide range of tasks, such as ChatGPT (OpenAI, 2023), Claude (Anthropic, 2023), Gemini (DeepMind, 2023) and etc. However, cloud-based inference introduces significant delays for end users, and it often fails to meet their personalized needs (Ding et al., 2024; Iyengar & Adusumilli, 2024). Recently, there has been growing interest in deploying LLMs on edge devices, which offer benefits like lower latency, data localization, and more personalized user experiences (Xu et al., 2024). For instance, Apple (2024) recently launched on-device foundation models as part of its personal intelligence system. On-device LLMs present challenges such as limited and variable computational resources, scarce and heterogeneous local data, and privacy concerns related to data sharing (Peng et al., 2024; Wagner et al., 2024).

The Mixture of Experts (MoEs) has been receiving unprecedented attention in the LLM era. While initially it has been proposed by Jacobs et al. (1991) to encourage expert specialization when the model is under-parameterized to fit the whole data domain, the contemporary practices (Fedus et al., 2022; Shazeer et al., 2017) do not specifically seek for expert specialization aspects, instead, they use MoE as a tool to scale up model expressiveness at a reduced inference cost. A study by Zoph et al. (2022a) revealed the existence of expert specialization in encoder blocks, particularly at a lexicon level. Furthermore, the recent Mistral paper by Jiang et al. (2024) provides evidence that the router exhibits structured syntactic behavior rather than topic-level understanding. We posit that the cultivation of fine-grained expert specialization is facilitated by Token-level routing mechanisms.

Weight decay can significantly impact the optimization dynamics of deep neural networks. In certain situations the effects of weight decay and gradient updates on the magnitude of a parameter vector cancel out on average, forming a state known as equilibrium. This causes the expected rotation of the vector in each update to remain constant along with its magnitude. Importantly, equilibrium can arise independently for the weight vectors of different layers and neurons. These equilibria are highly homogeneous for some optimizer and normalization configurations, effectively balancing the average rotation--a proxy for the effective learning rate--across network components. In this work we explore the equilibrium states of multiple optimizers including AdamW and SGD with momentum, providing insights into interactions between the learning rate, weight decay, initialization, normalization and learning rate schedule. We show how rotational equilibrium can be enforced throughout training, eliminating the chaotic transient phase corresponding to the transition towards equilibrium, thus simplifying the training dynamics. Finally, we show that rotational behavior may play a key role in the effectiveness of AdamW compared to Adam with L2-regularization, the performance of different normalization layers, and the need for learning rate warmup.