Daily Papers

Training a neural network requires choosing a suitable learning rate, which involves a trade-off between speed and effectiveness of convergence. While there has been considerable theoretical and empirical analysis of how large the learning rate can be, most prior work focuses only on late-stage training. In this work, we introduce the maximal initial learning rate eta^{ast} - the largest learning rate at which a randomly initialized neural network can successfully begin training and achieve (at least) a given threshold accuracy. Using a simple approach to estimate eta^{ast}, we observe that in constant-width fully-connected ReLU networks, eta^{ast} behaves differently from the maximum learning rate later in training. Specifically, we find that eta^{ast} is well predicted as a power of depth times width, provided that (i) the width of the network is sufficiently large compared to the depth, and (ii) the input layer is trained at a relatively small learning rate. We further analyze the relationship between eta^{ast} and the sharpness lambda_{1} of the network at initialization, indicating they are closely though not inversely related. We formally prove bounds for lambda_{1} in terms of depth times width that align with our empirical results.

In this paper, we describe a phenomenon, which we named "super-convergence", where neural networks can be trained an order of magnitude faster than with standard training methods. The existence of super-convergence is relevant to understanding why deep networks generalize well. One of the key elements of super-convergence is training with one learning rate cycle and a large maximum learning rate. A primary insight that allows super-convergence training is that large learning rates regularize the training, hence requiring a reduction of all other forms of regularization in order to preserve an optimal regularization balance. We also derive a simplification of the Hessian Free optimization method to compute an estimate of the optimal learning rate. Experiments demonstrate super-convergence for Cifar-10/100, MNIST and Imagenet datasets, and resnet, wide-resnet, densenet, and inception architectures. In addition, we show that super-convergence provides a greater boost in performance relative to standard training when the amount of labeled training data is limited. The architectures and code to replicate the figures in this paper are available at github.com/lnsmith54/super-convergence. See http://www.fast.ai/2018/04/30/dawnbench-fastai/ for an application of super-convergence to win the DAWNBench challenge (see https://dawn.cs.stanford.edu/benchmark/).

As Large Language Models (LLMs) gain widespread practical application, providing the model family of different parameter sizes has become standard practice to address diverse computational requirements. Conventionally, each model in a family is trained independently, resulting in computational costs that scale additively with the number of models. We propose an efficient method for constructing the model family through progressive training, where smaller models are incrementally expanded to larger sizes to create a complete model family. Through extensive experiments with a model family ranging from 1B to 8B parameters, we demonstrate that our method reduces computational costs by approximately 25% while maintaining comparable performance to independently trained models. Furthermore, by strategically adjusting maximum learning rates based on model size, our method outperforms the independent training across various metrics. Beyond performance gains, our approach offers an additional advantage: models in our family tend to yield more consistent behavior across different model sizes.

Large language models (LLMs) are routinely pre-trained on billions of tokens, only to restart the process over again once new data becomes available. A much cheaper and more efficient solution would be to enable the continual pre-training of these models, i.e. updating pre-trained models with new data instead of re-training them from scratch. However, the distribution shift induced by novel data typically results in degraded performance on past data. Taking a step towards efficient continual pre-training, in this work, we examine the effect of different warm-up strategies. Our hypothesis is that the learning rate must be re-increased to improve compute efficiency when training on a new dataset. We study the warmup phase of models pre-trained on the Pile (upstream data, 300B tokens) as we continue to pre-train on SlimPajama (downstream data, 297B tokens), following a linear warmup and cosine decay schedule. We conduct all experiments on the Pythia 410M language model architecture and evaluate performance through validation perplexity. We experiment with different pre-training checkpoints, various maximum learning rates, and various warmup lengths. Our results show that while rewarming models first increases the loss on upstream and downstream data, in the longer run it improves the downstream performance, outperforming models trained from scratchx2013even for a large downstream dataset.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

We present the Large Language Model from Power Law Decoder Representations (PLDR-LLM), a language model that leverages non-linear and linear transformations through Power Law Graph Attention mechanism to generate well-defined deductive and inductive outputs. We pretrain the PLDR-LLMs of varying layer sizes with a small batch size of 32 and sim8B tokens from the RefinedWeb dataset, and show that they achieve competitive performance in zero-shot and few-shot settings compared to scaled dot-product LLMs of similar model size reported in the literature. We show that deductive outputs of PLDR-LLMs can be used to compare model characteristics or improve the performance by introducing the Directed Acyclic Graph (DAG) loss as a metric and regularizer. Our results indicate that the initial maximum learning rate and warm-up steps have a lasting impact on deductive outputs throughout the pretraining. We provide a detailed description of PLDR-LLM architecture, its implementation and the pretraining procedure.

Finding the optimal learning rate for language model pretraining is a challenging task. This is not only because there is a complicated correlation between learning rate, batch size, number of training tokens, model size, and other hyperparameters but also because it is prohibitively expensive to perform a hyperparameter search for large language models with Billions or Trillions of parameters. Recent studies propose using small proxy models and small corpus to perform hyperparameter searches and transposing the optimal parameters to large models and large corpus. While the zero-shot transferability is theoretically and empirically proven for model size related hyperparameters, like depth and width, the zero-shot transfer from small corpus to large corpus is underexplored. In this paper, we study the correlation between optimal learning rate, batch size, and number of training tokens for the recently proposed WSD scheduler. After thousands of small experiments, we found a power-law relationship between variables and demonstrated its transferability across model sizes. Based on the observation, we propose a new learning rate scheduler, Power scheduler, that is agnostic about the number of training tokens and batch size. The experiment shows that combining the Power scheduler with Maximum Update Parameterization (muP) can consistently achieve impressive performance with one set of hyperparameters regardless of the number of training tokens, batch size, model size, and even model architecture. Our 3B dense and MoE models trained with the Power scheduler achieve comparable performance as state-of-the-art small language models. We open-source these pretrained models at https://ibm.biz/BdKhLa.

LLMs are commonly trained with a learning rate (LR) warmup, followed by cosine decay to 10% of the maximum (10x decay). In a large-scale empirical study, we show that under an optimal peak LR, a simple linear decay-to-zero (D2Z) schedule consistently outperforms other schedules when training at compute-optimal dataset sizes. D2Z is superior across a range of model sizes, batch sizes, datasets, and vocabularies. Benefits increase as dataset size increases. Leveraging a novel interpretation of AdamW as an exponential moving average of weight updates, we show how linear D2Z optimally balances the demands of early training (moving away from initial conditions) and late training (averaging over more updates in order to mitigate gradient noise). In experiments, a 610M-parameter model trained for 80 tokens-per-parameter (TPP) using D2Z achieves lower loss than when trained for 200 TPP using 10x decay, corresponding to an astonishing 60% compute savings. Models such as Llama2-7B, trained for 286 TPP with 10x decay, could likely have saved a majority of compute by training with D2Z.

When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the usual tool applied to experimental cognition. Our objective in this work is to show that the estimation of the learning rate cannot be efficient if the learning rate is constant in the classical Exp3 (Exponential weights for Exploration and Exploitation) algorithm. Secondly, we show that if the learning rate decreases polynomially with the sample size, then the prediction error and in some cases the estimation error of the MLE satisfy bounds in probability that decrease at a polynomial rate.

Accurate classification of computed tomography (CT) images is essential for diagnosis and treatment planning, but existing methods often struggle with the subtle and spatially diverse nature of pathological features. Current approaches typically process images uniformly, limiting their ability to detect localized abnormalities that require focused analysis. We introduce UGPL, an uncertainty-guided progressive learning framework that performs a global-to-local analysis by first identifying regions of diagnostic ambiguity and then conducting detailed examination of these critical areas. Our approach employs evidential deep learning to quantify predictive uncertainty, guiding the extraction of informative patches through a non-maximum suppression mechanism that maintains spatial diversity. This progressive refinement strategy, combined with an adaptive fusion mechanism, enables UGPL to integrate both contextual information and fine-grained details. Experiments across three CT datasets demonstrate that UGPL consistently outperforms state-of-the-art methods, achieving improvements of 3.29%, 2.46%, and 8.08% in accuracy for kidney abnormality, lung cancer, and COVID-19 detection, respectively. Our analysis shows that the uncertainty-guided component provides substantial benefits, with performance dramatically increasing when the full progressive learning pipeline is implemented. Our code is available at: https://github.com/shravan-18/UGPL

Energy-efficient ventilation control plays a vital role in reducing building energy consumption while ensuring occupant health and comfort. While Computational Fluid Dynamics (CFD) simulations offer high-fidelity modeling of airflow for building HVAC design, their high computational cost makes them impractical for practical adoption in real-time building management system. In this work, we present a data-driven framework that combines the physical accuracy of CFD with the computational efficiency of machine learning to enable energy-efficient building ventilation control. Our method jointly optimizes airflow supply rates and vent angles to reduce energy use and adhere to air quality constraints. We train a neural operator transformer to learn the mapping from building control actions to airflow field distributions using high-resolution CFD data. This learned operator enables a gradient-based control framework capable of optimal decision-making. Experimental results demonstrate that our approach achieves substantial energy savings compared to maximum airflow rate control, rule-based control, and data-driven control based on regional average CO2 predictions, while consistently maintaining safe indoor air quality. These results highlight the practicality and scalability of our method for enabling safe and energy-efficient building management.

We present automatic speech recognition (ASR) systems for Tamil and Kannada based on subword modeling to effectively handle unlimited vocabulary due to the highly agglutinative nature of the languages. We explore byte pair encoding (BPE), and proposed a variant of this algorithm named extended-BPE, and Morfessor tool to segment each word as subwords. We have effectively incorporated maximum likelihood (ML) and Viterbi estimation techniques with weighted finite state transducers (WFST) framework in these algorithms to learn the subword dictionary from a large text corpus. Using the learnt subword dictionary, the words in training data transcriptions are segmented to subwords and we train deep neural network ASR systems which recognize subword sequence for any given test speech utterance. The output subword sequence is then post-processed using deterministic rules to get the final word sequence such that the actual number of words that can be recognized is much larger. For Tamil ASR, We use 152 hours of data for training and 65 hours for testing, whereas for Kannada ASR, we use 275 hours for training and 72 hours for testing. Upon experimenting with different combination of segmentation and estimation techniques, we find that the word error rate (WER) reduces drastically when compared to the baseline word-level ASR, achieving a maximum absolute WER reduction of 6.24% and 6.63% for Tamil and Kannada respectively.

In the realm of image quantization exemplified by VQGAN, the process encodes images into discrete tokens drawn from a codebook with a predefined size. Recent advancements, particularly with LLAMA 3, reveal that enlarging the codebook significantly enhances model performance. However, VQGAN and its derivatives, such as VQGAN-FC (Factorized Codes) and VQGAN-EMA, continue to grapple with challenges related to expanding the codebook size and enhancing codebook utilization. For instance, VQGAN-FC is restricted to learning a codebook with a maximum size of 16,384, maintaining a typically low utilization rate of less than 12% on ImageNet. In this work, we propose a novel image quantization model named VQGAN-LC (Large Codebook), which extends the codebook size to 100,000, achieving an utilization rate exceeding 99%. Unlike previous methods that optimize each codebook entry, our approach begins with a codebook initialized with 100,000 features extracted by a pre-trained vision encoder. Optimization then focuses on training a projector that aligns the entire codebook with the feature distributions of the encoder in VQGAN-LC. We demonstrate the superior performance of our model over its counterparts across a variety of tasks, including image reconstruction, image classification, auto-regressive image generation using GPT, and image creation with diffusion- and flow-based generative models. Code and models are available at https://github.com/zh460045050/VQGAN-LC.

In this paper, we propose a unified pre-training approach called UniSpeech to learn speech representations with both unlabeled and labeled data, in which supervised phonetic CTC learning and phonetically-aware contrastive self-supervised learning are conducted in a multi-task learning manner. The resultant representations can capture information more correlated with phonetic structures and improve the generalization across languages and domains. We evaluate the effectiveness of UniSpeech for cross-lingual representation learning on public CommonVoice corpus. The results show that UniSpeech outperforms self-supervised pretraining and supervised transfer learning for speech recognition by a maximum of 13.4% and 17.8% relative phone error rate reductions respectively (averaged over all testing languages). The transferability of UniSpeech is also demonstrated on a domain-shift speech recognition task, i.e., a relative word error rate reduction of 6% against the previous approach.

Traditional Long Short-Term Memory (LSTM) networks are effective for handling sequential data but have limitations such as gradient vanishing and difficulty in capturing long-term dependencies, which can impact their performance in dynamic and risky environments like stock trading. To address these limitations, this study explores the usage of the newly introduced Extended Long Short Term Memory (xLSTM) network in combination with a deep reinforcement learning (DRL) approach for automated stock trading. Our proposed method utilizes xLSTM networks in both actor and critic components, enabling effective handling of time series data and dynamic market environments. Proximal Policy Optimization (PPO), with its ability to balance exploration and exploitation, is employed to optimize the trading strategy. Experiments were conducted using financial data from major tech companies over a comprehensive timeline, demonstrating that the xLSTM-based model outperforms LSTM-based methods in key trading evaluation metrics, including cumulative return, average profitability per trade, maximum earning rate, maximum pullback, and Sharpe ratio. These findings mark the potential of xLSTM for enhancing DRL-based stock trading systems.