arXiv subjects

Kairong Luo

Publications and source records attributed to Kairong Luo.

6 recordsLinked to original sources

arXiv2026

SMELT: Scaling Laws for Compute-Matched MoE Looped Transformers

Looped Transformers increase effective depth by iterating a shared block of layers, but most evaluations compare at fixed model size, conflating architectural advantage with extra FLOPs. We study looping on Mixture-of-Experts Transformers while closely matching per-token FLOPs, total non-embedding parameters, and KV cache. Through a series of ablations, we arrive at a recipe we call SMELT (Sparse MoE Transformer, middle layers Loop Twice), which loops the middle half of layers twice while matching the unlooped Baseline on all three budgets. We scale SMELT across four sizes up to 54B non-embedding parameters and fit a separate Chinchilla-style scaling law for each architecture. SMELT's loss drops faster with compute, saving 6.8--18.0\% of training FLOPs on the compute-optimal frontier. The advantage transfers to downstream benchmarks beyond what validation loss predicts, is largest on Code, and grows with sample length and the number of in-context examples. Mechanistic analysis shows that the second visit reduces the attention sink and redirects mass toward content-relevant tokens, an inductive bias that may underlie the observed performance gains. These results show that looping can improve Transformers even under budget matching, offering a practical recipe that turns depth reuse into measurable gains.

cs.LG↗

arXiv2026

Puro-2B: Poor Lab's Qwen2-1.5B Trained on RTX 5090 within $5090

Language model pretraining has become almost synonymous with prohibitive cost, placing it out of reach for much of the academic and open-source communities. Although strong open-source efforts already exist, including open-weight models and open-source training recipes, a cost-efficient, hardware-accessible, and open-source pretraining recipe has long been missing. Even at a small scale, training Llama-3.2-3B costs over \$1.5M, and reproducing SmolLM3-3B needs over \$700K. In this report, we present an open pretraining recipe designed to lower this barrier. Using this recipe, we train a collection of Puro-2B models from scratch on up to 1.4 trillion tokens with FP8 precision on consumer-grade RTX 5090 GPUs. The models in the collection differ in token budgets and selected recipe variants. Our best model is trained at a compute cost of less than \$6.9K and approaches Qwen2.5-1.5B performance under our evaluation protocol. This cost efficiency is enabled by a combination of approaches, including hardware selection, low-precision training, hyperball optimization, curriculum model averaging, and the data recipe. Beyond the recipe itself, we provide two additional results. First, across the Puro-2B collection, we derive a Puro Cost Scaling Law that relates training cost to average model performance; the fitted law suggests that about \$4.4K, less than \$5,090, is sufficient to reach the performance of Qwen2-1.5B. Second, as an end-to-end case study, we examine how pretraining data curricula shape downstream performance after post-training. Such controlled studies are enabled by having access to the full pretraining pipeline rather than model weights alone. We release the full training recipe for Puro-2B, including data, code, and model weights under Apache 2.0 at https://huggingface.co/collections/thu-pacman/puro-2b.

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arXiv2026

How Learning Rate Decay Wastes Your Best Data in Curriculum-Based LLM Pretraining

Due to the scarcity of high-quality data, large language models (LLMs) are often trained on mixtures of data with varying quality levels, even after sophisticated data curation. A natural approach to better leverage high-quality data is curriculum-based pretraining, where the model is trained on data sorted in ascending order of quality as determined by a quality metric. However, prior studies have reported limited improvements from such curriculum-based pretraining strategies. This work identifies a critical factor constraining these methods: the incompatibility between the ascending data quality order and the decaying learning rate (LR) schedule. We find that while curriculum-based training substantially outperforms random shuffling when using a constant LR, its advantage diminishes under standard LR decay schedules. Our experiments show this incompatibility can be mitigated by two simple strategies: (1) employing a more moderate LR decay schedule, where the final LR is only moderately smaller than the peak LR, and (2) replacing LR decay with model averaging, i.e., computing a weighted average of the final few checkpoints. By combining these strategies, we improve the average score on a suite of standard benchmarks by 1.64% over random shuffling, without additional data refinement. Validated on 1.5B-parameter models trained over 30B tokens with various data-quality metrics, our findings call for a re-evaluation of curriculum-based LLM pretraining and underscore the potential of co-designing data curricula with optimization methods.

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arXiv2026

Larger Datasets Can Be Repeated More: A Theoretical Analysis of Multi-Epoch Scaling in Linear Regression

While data scaling laws of large language models (LLMs) have been widely examined in the one-pass regime with massive corpora, their form under limited data and repeated epochs remains largely unexplored. This paper presents a theoretical analysis of how a common workaround, training for multiple epochs on the same dataset, reshapes the data scaling laws in linear regression. Concretely, we ask: to match the performance of training on a dataset of size $N$ for $K$ epochs, how much larger must a dataset be if the model is trained for only one pass? We quantify this using the \textit{effective reuse rate} of the data, $E(K, N)$, which we define as the multiplicative factor by which the dataset must grow under one-pass training to achieve the same test loss as $K$-epoch training. Our analysis precisely characterizes the scaling behavior of $E(K, N)$ for SGD in linear regression under either strong convexity or Zipf-distributed data: (1) When $K$ is small, we prove that $E(K, N) \approx K$, indicating that every new epoch yields a linear gain; (2) As $K$ increases, $E(K, N)$ plateaus at a problem-dependent value that grows with $N$ ($Θ(\log N)$ for the strongly-convex case), implying that larger datasets can be repeated more times before the marginal benefit vanishes. These theoretical findings point out a neglected factor in a recent empirical study (Muennighoff et al. (2023)), which claimed that training LLMs for up to $4$ epochs results in negligible loss differences compared to using fresh data at each step, \textit{i.e.}, $E(K, N) \approx K$ for $K \le 4$ in our notation. Supported by further empirical validation with LLMs, our results reveal that the maximum $K$ value for which $E(K, N) \approx K$ in fact depends on the data size and distribution, and underscore the need to explicitly model both factors in future studies of scaling laws with data reuse.

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arXiv2025

PCMind-2.1-Kaiyuan-2B Technical Report

The rapid advancement of Large Language Models (LLMs) has resulted in a significant knowledge gap between the open-source community and industry, primarily because the latter relies on closed-source, high-quality data and training recipes. To address this, we introduce PCMind-2.1-Kaiyuan-2B, a fully open-source 2-billion-parameter model focused on improving training efficiency and effectiveness under resource constraints. Our methodology includes three key innovations: a Quantile Data Benchmarking method for systematically comparing heterogeneous open-source datasets and providing insights on data mixing strategies; a Strategic Selective Repetition scheme within a multi-phase paradigm to effectively leverage sparse, high-quality data; and a Multi-Domain Curriculum Training policy that orders samples by quality. Supported by a highly optimized data preprocessing pipeline and architectural modifications for FP16 stability, Kaiyuan-2B achieves performance competitive with state-of-the-art fully open-source models, demonstrating practical and scalable solutions for resource-limited pretraining. We release all assets (including model weights, data, and code) under Apache 2.0 license at https://huggingface.co/thu-pacman/PCMind-2.1-Kaiyuan-2B.

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arXiv2025

A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules

Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how the pretraining loss of large language models evolves under different learning rate schedules, such as constant, cosine, and step decay schedules. Our proposed law takes a multi-power form, combining a power law based on the sum of learning rates and additional power laws to account for a loss reduction effect induced by learning rate decay. We extensively validate this law on various model sizes and architectures, and demonstrate that after fitting on a few learning rate schedules, the law accurately predicts the loss curves for unseen schedules of different shapes and horizons. Moreover, by minimizing the predicted final pretraining loss across learning rate schedules, we are able to find a schedule that outperforms the widely used cosine learning rate schedule. Interestingly, this automatically discovered schedule bears some resemblance to the recently proposed Warmup-Stable-Decay (WSD) schedule (Hu et al, 2024) but achieves a slightly lower final loss. We believe these results could offer valuable insights for understanding the dynamics of pretraining and designing learning rate schedules to improve efficiency.

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