Daily Papers

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

Large-scale transformer models have become the de-facto architectures for various machine learning applications, e.g., CV and NLP. However, those large models also introduce prohibitive training costs. To mitigate this issue, we propose a novel random and layerwise token dropping method (random-LTD), which skips the computation of a subset of the input tokens at all middle layers. Particularly, random-LTD achieves considerable speedups and comparable accuracy as the standard training baseline. Compared to other token dropping methods, random-LTD does not require (1) any importance score-based metrics, (2) any special token treatment (e.g., [CLS]), and (3) many layers in full sequence length training except the first and the last layers. Besides, a new LayerToken learning rate schedule is proposed for pretraining problems that resolve the heavy tuning requirement for our proposed training mechanism. Finally, we demonstrate that random-LTD can be applied to broader applications, including GPT and BERT pretraining as well as ViT and GPT finetuning tasks. Our results show that random-LTD can save about 33.3% theoretical compute cost and 25.6% wall-clock training time while achieving similar zero-shot evaluations on GPT-31.3B as compared to baseline.

Multi-turn reinforcement learning (RL) for multi-modal agents built upon vision-language models (VLMs) is hampered by sparse rewards and long-horizon credit assignment. Recent methods densify the reward by querying a teacher that provides step-level feedback, e.g., Guided Thought Reinforcement (GTR) and On-Policy Distillation, but rely on costly, often privileged models as the teacher, limiting practicality and reproducibility. We introduce GTR-Turbo, a highly efficient upgrade to GTR, which matches the performance without training or querying an expensive teacher model. Specifically, GTR-Turbo merges the weights of checkpoints produced during the ongoing RL training, and then uses this merged model as a "free" teacher to guide the subsequent RL via supervised fine-tuning or soft logit distillation. This design removes dependence on privileged VLMs (e.g., GPT or Gemini), mitigates the "entropy collapse" observed in prior work, and keeps training stable. Across diverse visual agentic tasks, GTR-Turbo improves the accuracy of the baseline model by 10-30% while reducing wall-clock training time by 50% and compute cost by 60% relative to GTR.

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they often suffer from poor meta-generalization, especially when training networks larger than those seen during meta-training. To address this, we use the recently proposed Maximal Update Parametrization (muP), which allows zero-shot generalization of optimizer hyperparameters from smaller to larger models. We extend muP theory to learned optimizers, treating the meta-training problem as finding the learned optimizer under muP. Our evaluation shows that LOs meta-trained with muP substantially improve meta-generalization as compared to LOs trained under standard parametrization (SP). Notably, when applied to large-width models, our best muLO, trained for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest publicly available learned optimizer, meta-trained with 4000 TPU-months of compute. Moreover, muLOs demonstrate better generalization than their SP counterparts to deeper networks and to much longer training horizons (25 times longer) than those seen during meta-training.

We present Galactic, a large-scale simulation and reinforcement-learning (RL) framework for robotic mobile manipulation in indoor environments. Specifically, a Fetch robot (equipped with a mobile base, 7DoF arm, RGBD camera, egomotion, and onboard sensing) is spawned in a home environment and asked to rearrange objects - by navigating to an object, picking it up, navigating to a target location, and then placing the object at the target location. Galactic is fast. In terms of simulation speed (rendering + physics), Galactic achieves over 421,000 steps-per-second (SPS) on an 8-GPU node, which is 54x faster than Habitat 2.0 (7699 SPS). More importantly, Galactic was designed to optimize the entire rendering + physics + RL interplay since any bottleneck in the interplay slows down training. In terms of simulation+RL speed (rendering + physics + inference + learning), Galactic achieves over 108,000 SPS, which 88x faster than Habitat 2.0 (1243 SPS). These massive speed-ups not only drastically cut the wall-clock training time of existing experiments, but also unlock an unprecedented scale of new experiments. First, Galactic can train a mobile pick skill to >80% accuracy in under 16 minutes, a 100x speedup compared to the over 24 hours it takes to train the same skill in Habitat 2.0. Second, we use Galactic to perform the largest-scale experiment to date for rearrangement using 5B steps of experience in 46 hours, which is equivalent to 20 years of robot experience. This scaling results in a single neural network composed of task-agnostic components achieving 85% success in GeometricGoal rearrangement, compared to 0% success reported in Habitat 2.0 for the same approach. The code is available at github.com/facebookresearch/galactic.

Reinforcement learning with verifiable rewards (RLVR) generates hundreds of thousands of tokens per training step, with rollout generation dominating the computational cost. The overall token budget can be controlled along two main dimensions: (i) deciding which prompts to allocate rollouts to, and (ii) deciding how long each rollout should be. Prior work has generally controlled only one of these dimensions at a time. We show that jointly tuning both decisions under a shared compute budget improves both reasoning quality and wall-clock training time. We instantiate this view as DUal-controlled tokEn allocaTion (DUET), a computationally efficient layer over GRPO that uses a lightweight pre-rollout surrogate of prompt informativeness to set how many rollouts each prompt receives, and a marker-gated abort rule with importance reweighting to set when to stop them. On Qwen3-1.7B trained on MATH, DUET outperforms full-budget GRPO and the other three budget-aware baseline methods. DUET's advantage further generalizes to other benchmarks across math and coding, and is on par with the best baseline on the scientific Q\&A domain, while also achieving a 1.62times wall-clock speedup. More notably, using only 50\% of the token budget, DUET still outperforms all baseline methods at their full budget, achieving an even higher 2.51times speedup over full-budget GRPO. We verify the high performance of DUET on other backbone LLMs, including Qwen3-4B and Llama-3.2-3B-Instruct. Notably, the gap between DUET and the strongest baseline widens as the budget tightens, contrary to the usual pattern in which efficient methods trade off quality as compute decreases. More broadly, these results suggest that DUET budget-aware control strategies are valuable not only for accelerating training, but also for improving the quality of the learning signal.

Data selection for finetuning Large Language Models (LLMs) can be framed as a budget-constrained optimization problem: maximizing a model's downstream performance under a strict training data budget. Solving this problem is generally intractable, and existing approximate approaches are pretraining-oriented and transfer poorly to the fine-tuning setting. We reformulate this problem as a tractable Markov Decision Process (MDP) and train agents using various Reinforcement Learning (RL) methods to learn optimal data selection policies, guided by an efficient, proxy-model-based reward signal. Across four datasets, training on a 5% subset selected by our approach matches or outperforms fine-tuning on the full dataset by up to 10.8 accuracy points, while cutting wall-clock training time by up to 2 times, highlighting the promise of RL-guided data selection.

Reinforcement learning is time-consuming for complex tasks due to the need for large amounts of training data. Recent advances in GPU-based simulation, such as Isaac Gym, have sped up data collection thousands of times on a commodity GPU. Most prior works used on-policy methods like PPO due to their simplicity and ease of scaling. Off-policy methods are more data efficient but challenging to scale, resulting in a longer wall-clock training time. This paper presents a Parallel Q-Learning (PQL) scheme that outperforms PPO in wall-clock time while maintaining superior sample efficiency of off-policy learning. PQL achieves this by parallelizing data collection, policy learning, and value learning. Different from prior works on distributed off-policy learning, such as Apex, our scheme is designed specifically for massively parallel GPU-based simulation and optimized to work on a single workstation. In experiments, we demonstrate that Q-learning can be scaled to tens of thousands of parallel environments and investigate important factors affecting learning speed. The code is available at https://github.com/Improbable-AI/pql.

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce a surrogate model that not only sheds new light on the design of Muon, but more importantly leads to a new optimizer. In the same spirit as the derivation of Newton's method, the surrogate approximates the loss as a quadratic function of the perturbation to a weight matrix W using only three matrices: the gradient G, an output-space curvature matrix H, and the data matrix Z that stacks the layer inputs. By minimizing this surrogate in one step and adopting a certain isotropic assumption on the weights, we obtain the closed-form update rule (up to momentum and weight decay) W leftarrow W - ηcdot msgn(G(ZZ^top)^{-1}), where η is the learning rate and msgn(X)=UV^top if X=USV^top is a compact singular value decomposition. This new optimization method, which we refer to as Newton-Muon, shows that standard Muon can be interpreted as an implicit Newton-type method that neglects the right preconditioning induced by the input second moment. Empirically, on a reproduction of the earliest publicly released Modded-NanoGPT speedrun configuration using Muon for GPT-2 pretraining, Newton-Muon reaches the target validation loss in 6\% fewer iteration steps and reduces wall-clock training time by about 4\%.

Existing LLM training and inference frameworks struggle in boosting efficiency with sparsity while maintaining the integrity of context and model architecture. Inspired by the sharding concept in database and the fact that attention parallelizes over heads on accelerators, we propose Sparsely-Sharded (S2) Attention, an attention algorithm that allocates heterogeneous context partitions for different attention heads to divide and conquer. S2-Attention enforces each attention head to only attend to a partition of contexts following a strided sparsity pattern, while the full context is preserved as the union of all the shards. As attention heads are processed in separate thread blocks, the context reduction for each head can thus produce end-to-end speed-up and memory reduction. At inference, LLMs trained with S2-Attention can then take the KV cache reduction as free meals with guaranteed model quality preserve. In experiments, we show S2-Attentioncan provide as much as (1) 25.3X wall-clock attention speed-up over FlashAttention-2, resulting in 6X reduction in end-to-end training time and 10X inference latency, (2) on-par model training quality compared to default attention, (3)perfect needle retrieval accuracy over 32K context window. On top of the algorithm, we build DKernel, an LLM training and inference kernel library that allows users to customize sparsity patterns for their own models. We open-sourced DKerneland make it compatible with Megatron, Pytorch, and vLLM.

Reinforcement learning, such as PPO and GRPO, has powered recent breakthroughs in LLM reasoning. Scaling rollout to sample more prompts enables models to selectively use higher-quality data for training, which can stabilize RL training and improve model performance. However, this comes at the cost of significant computational overhead. In this paper, we show that a substantial portion of this overhead can be avoided by skipping uninformative prompts before rollout. Our analysis of reward dynamics reveals a strong temporal consistency in prompt value: prompts that are uninformative in one epoch of training are likely to remain uninformative in future epochs. Based on these insights, we propose GRESO (GRPO with Efficient Selective Rollout), an online, lightweight pre-rollout filtering algorithm that predicts and skips uninformative prompts using reward training dynamics. By evaluating GRESO on a broad range of math reasoning benchmarks and models, such as Qwen2.5-Math-1.5B, DeepSeek-R1-Distill-Qwen-1.5B, and Qwen2.5-Math-7B, we show that GRESO achieves up to 2.4x wall-clock time speedup in rollout and up to 2.0x speedup in total training time without accuracy degradation.

Reinforcement learning (RL) is a critical component of large language model (LLM) post-training. However, existing on-policy algorithms used for post-training are inherently incompatible with the use of experience replay buffers, which can be populated scalably by distributed off-policy actors to enhance exploration as compute increases. We propose efficiently obtaining this benefit of replay buffers via Trajectory Balance with Asynchrony (TBA), a massively scalable LLM RL system. In contrast to existing approaches, TBA uses a larger fraction of compute on search, constantly generating off-policy data for a central replay buffer. A training node simultaneously samples data from this buffer based on reward or recency to update the policy using Trajectory Balance (TB), a diversity-seeking RL objective introduced for GFlowNets. TBA offers three key advantages: (1) decoupled training and search, speeding up training wall-clock time by 4x or more; (2) improved diversity through large-scale off-policy sampling; and (3) scalable search for sparse reward settings. On mathematical reasoning, preference-tuning, and automated red-teaming (diverse and representative post-training tasks), TBA produces speed and performance improvements over strong baselines.

Fast and high-quality language generation is the holy grail that people pursue in the age of AI. In this work, we introduce Discrete Diffusion Divergence Instruct (DiDi-Instruct), a training-based method that initializes from a pre-trained (masked) discrete diffusion language model (dLLM) and distills a few-step student for fast generation. The resulting DiDi-Instruct model achieves comparable or superior performance to its dLLM teacher and the GPT-2 baseline while enabling up to 64times acceleration. The theoretical foundation of DiDi-Instruct is a novel framework based on integral KL-divergence minimization, which yields a practical training algorithm. We further introduce grouped reward normalization, intermediate-state matching, and the reward-guided ancestral sampler that significantly improve training stability, model coverage, and inference quality. On OpenWebText, DiDi-Instruct achieves perplexity from 62.2 (8 NFEs) to 18.4 (128 NFEs), which outperforms prior accelerated dLLMs and GPT-2 baseline. These gains come with a negligible entropy loss (around 1%) and reduce additional training wall-clock time by more than 20times compared to competing dLLM distillation methods. We further validate the robustness and effectiveness of DiDi-Instruct through extensive ablation studies, model scaling, and the generation of discrete protein sequences. In conclusion, DiDi-Instruct is an efficient yet effective distillation method, enabling language generation in the blink of an eye. We will release both code and models at github.com/haoyangzheng-ai/didi-instruct.

Over the past several years, the synchronization between audio and visual signals has been leveraged to learn richer audio-visual representations. Aided by the large availability of unlabeled videos, many unsupervised training frameworks have demonstrated impressive results in various downstream audio and video tasks. Recently, Masked Audio-Video Learners (MAViL) has emerged as a state-of-the-art audio-video pre-training framework. MAViL couples contrastive learning with masked autoencoding to jointly reconstruct audio spectrograms and video frames by fusing information from both modalities. In this paper, we study the potential synergy between diffusion models and MAViL, seeking to derive mutual benefits from these two frameworks. The incorporation of diffusion into MAViL, combined with various training efficiency methodologies that include the utilization of a masking ratio curriculum and adaptive batch sizing, results in a notable 32% reduction in pre-training Floating-Point Operations (FLOPS) and an 18% decrease in pre-training wall clock time. Crucially, this enhanced efficiency does not compromise the model's performance in downstream audio-classification tasks when compared to MAViL's performance.

Networks in the current 5G and beyond systems increasingly carry heterogeneous traffic with diverse quality-of-service constraints, making real-time routing decisions both complex and time-critical. A common approach, such as a heuristic with human intervention or training a single centralized RL policy or synchronizing updates across multiple learners, struggles with scalability and straggler effects. We address this by proposing an asynchronous multi-agent reinforcement learning (AMARL) framework in which independent PPO agents, one per service, plan routes in parallel and commit resource deltas to a shared global resource environment. This coordination by state preserves feasibility across services and enables specialization for service-specific objectives. We evaluate the method on an O-RAN like network simulation using nearly real-time traffic data from the city of Montreal. We compared against a single-agent PPO baseline. AMARL achieves a similar Grade of Service (acceptance rate) (GoS) and end-to-end latency, with reduced training wall-clock time and improved robustness to demand shifts. These results suggest that asynchronous, service-specialized agents provide a scalable and practical approach to distributed routing, with applicability extending beyond the O-RAN domain.

Activation sparsity can enable practical inference speedups in large language models (LLMs) by reducing the compute and memory-movement required for matrix multiplications during the forward pass. However, existing methods face limitations that inhibit widespread adoption. Some approaches are tailored towards older models with ReLU-based sparsity, while others require extensive continued pre-training on up to hundreds of billions of tokens. This paper describes TEAL, a simple training-free method that applies magnitude-based activation sparsity to hidden states throughout the entire model. TEAL achieves 40-50% model-wide sparsity with minimal performance degradation across Llama-2, Llama-3, and Mistral families, with sizes varying from 7B to 70B. We improve existing sparse kernels and demonstrate wall-clock decoding speed-ups of up to 1.53times and 1.8times at 40% and 50% model-wide sparsity. TEAL is compatible with weight quantization, enabling further efficiency gains.

Training and serving long-context large language models (LLMs) incurs substantial overhead. To address this, two critical steps are often required: a pretrained LLM typically undergoes a separate stage for context length extension by training on long-context data, followed by architectural modifications to reduce the overhead of KV cache during serving. This paper argues that integrating length extension with a GPU-friendly KV cache reduction architecture not only reduces training overhead during length extension, but also achieves better long-context performance. This leads to our proposed LongGen, which finetunes a pretrained LLM into an efficient architecture during length extension. LongGen builds on three key insights: (1) Sparse attention patterns, such as window attention (attending to recent tokens), attention sink (initial ones), and blockwise sparse attention (strided token blocks) are well-suited for building efficient long-context models, primarily due to their GPU-friendly memory access patterns, enabling efficiency gains not just theoretically but in practice as well. (2) It is essential for the model to have direct access to all tokens. A hybrid architecture with 1/3 full attention layers and 2/3 efficient ones achieves a balanced trade-off between efficiency and long-context performance. (3) Lightweight training on 5B long-context data is sufficient to extend the hybrid model's context length from 4K to 128K. We evaluate LongGen on both Llama-2 7B and Llama-2 70B, demonstrating its effectiveness across different scales. During training with 128K-long contexts, LongGen achieves 1.55x training speedup and reduces wall-clock time by 36%, compared to a full-attention baseline. During inference, LongGen reduces KV cache memory by 62%, achieving 1.67x prefilling speedup and 1.41x decoding speedup.

We present Fast Language-Image Pre-training (FLIP), a simple and more efficient method for training CLIP. Our method randomly masks out and removes a large portion of image patches during training. Masking allows us to learn from more image-text pairs given the same wall-clock time and contrast more samples per iteration with similar memory footprint. It leads to a favorable trade-off between accuracy and training time. In our experiments on 400 million image-text pairs, FLIP improves both accuracy and speed over the no-masking baseline. On a large diversity of downstream tasks, FLIP dominantly outperforms the CLIP counterparts trained on the same data. Facilitated by the speedup, we explore the scaling behavior of increasing the model size, data size, or training length, and report encouraging results and comparisons. We hope that our work will foster future research on scaling vision-language learning.

Training large models with distributed data parallelism (DDP) requires frequent communication of gradients across workers, which can saturate bandwidth. Infrequent communication strategies (e.g., Local SGD) reduce this overhead but, when applied to adaptive optimizers, often suffer a performance gap relative to fully synchronous DDP. We trace this gap to a time-scale mismatch: the optimizer's fast-moving momentum, tuned for frequent updates, decays too quickly to smooth gradients over long intervals, leading to noise-dominated optimization. To address this, we propose MT-DAO, a family of optimizers that employs multiple slow- and fast-moving first momenta or the gradient to track update dynamics across different time scales, for which we provide the first convergence guarantees. Empirically, for language-model pre-training, this eliminates the performance gap with DDP, outperforming infrequent-communication baselines in perplexity and reducing iso-token wall-clock time by 6-27% on Ethernet interconnects. At the 720M scale, MT-DAO reaches a target perplexity in 24% fewer steps and 35% less time than the single-momentum DDP baseline. MT-DAO enables effective cross-datacenter training and training over wide geographic areas.

Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance optimizations that our implementation leverages to train deep networks at-scale in PyTorch. Our implementation enables fast multi-GPU distributed data-parallel training by distributing the memory and computation associated with blocks of each parameter via PyTorch's DTensor data structure and performing an AllGather primitive on the computed search directions at each iteration. This major performance enhancement enables us to achieve at most a 10% performance reduction in per-step wall-clock time compared against standard diagonal-scaling-based adaptive gradient methods. We validate our implementation by performing an ablation study on training ImageNet ResNet50, demonstrating Shampoo's superiority over standard training recipes with minimal hyperparameter tuning.

Training competitive deep video models is an order of magnitude slower than training their counterpart image models. Slow training causes long research cycles, which hinders progress in video understanding research. Following standard practice for training image models, video model training assumes a fixed mini-batch shape: a specific number of clips, frames, and spatial size. However, what is the optimal shape? High resolution models perform well, but train slowly. Low resolution models train faster, but they are inaccurate. Inspired by multigrid methods in numerical optimization, we propose to use variable mini-batch shapes with different spatial-temporal resolutions that are varied according to a schedule. The different shapes arise from resampling the training data on multiple sampling grids. Training is accelerated by scaling up the mini-batch size and learning rate when shrinking the other dimensions. We empirically demonstrate a general and robust grid schedule that yields a significant out-of-the-box training speedup without a loss in accuracy for different models (I3D, non-local, SlowFast), datasets (Kinetics, Something-Something, Charades), and training settings (with and without pre-training, 128 GPUs or 1 GPU). As an illustrative example, the proposed multigrid method trains a ResNet-50 SlowFast network 4.5x faster (wall-clock time, same hardware) while also improving accuracy (+0.8% absolute) on Kinetics-400 compared to the baseline training method. Code is available online.

Local stochastic gradient descent (Local-SGD), also referred to as federated averaging, is an approach to distributed optimization where each device performs more than one SGD update per communication. This work presents an empirical study of {\it asynchronous} Local-SGD for training language models; that is, each worker updates the global parameters as soon as it has finished its SGD steps. We conduct a comprehensive investigation by examining how worker hardware heterogeneity, model size, number of workers, and optimizer could impact the learning performance. We find that with naive implementations, asynchronous Local-SGD takes more iterations to converge than its synchronous counterpart despite updating the (global) model parameters more frequently. We identify momentum acceleration on the global parameters when worker gradients are stale as a key challenge. We propose a novel method that utilizes a delayed Nesterov momentum update and adjusts the workers' local training steps based on their computation speed. This approach, evaluated with models up to 150M parameters on the C4 dataset, matches the performance of synchronous Local-SGD in terms of perplexity per update step, and significantly surpasses it in terms of wall clock time.

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active, where samples are selected according to a measure of their quality (e.g., experimental design). In both of these cases, we are building a sequence of models that incorporate an increasing amount of data. We would like each of these models in the sequence to be performant and take advantage of all the data that are available to that point. Conventional intuition suggests that when solving a sequence of related optimization problems of this form, it should be possible to initialize using the solution of the previous iterate -- to "warm start" the optimization rather than initialize from scratch -- and see reductions in wall-clock time. However, in practice this warm-starting seems to yield poorer generalization performance than models that have fresh random initializations, even though the final training losses are similar. While it appears that some hyperparameter settings allow a practitioner to close this generalization gap, they seem to only do so in regimes that damage the wall-clock gains of the warm start. Nevertheless, it is highly desirable to be able to warm-start neural network training, as it would dramatically reduce the resource usage associated with the construction of performant deep learning systems. In this work, we take a closer look at this empirical phenomenon and try to understand when and how it occurs. We also provide a surprisingly simple trick that overcomes this pathology in several important situations, and present experiments that elucidate some of its properties.

The data used to pretrain large language models has a decisive impact on a model's downstream performance, which has led to a large body of work on data selection methods that aim to automatically determine the most suitable data to use for pretraining. Existing data selection methods suffer from slow and computationally expensive processes, a problem amplified by the increasing size of models and of pretraining datasets. Data mixing, on the other hand, reduces the complexity of data selection by grouping data points together and determining sampling probabilities across entire groups. However, data mixing proportions are typically fixed before training and therefore cannot adapt to changing training dynamics. To address these limitations, we develop an efficient algorithm for Online Data Mixing (ODM) that combines elements from both data selection and data mixing. Based on multi-armed bandit algorithms, our online approach optimizes the data mixing proportions during training. Remarkably, our method trains a model that reaches the final perplexity of the next best method with 19\% fewer training iterations, and improves performance on the 5-shot MMLU benchmark by 1.9% relative accuracy, while adding negligible wall-clock time during pretraining.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Training large language models requires jointly configuring two interdependent aspects of the system: the global batch size, which governs statistical efficiency, and the 3D parallelism strategy, which governs hardware throughput. Existing approaches make these decisions independently: optimization work adapts the batch size to track the evolving critical batch size while keeping parallelism fixed, and systems work selects the fastest parallelism for a given fixed batch size without anticipating that the optimal batch size could change. We show that these decisions are tightly coupled: the throughput-optimal parallelism strategy may shift as the global batch size changes, so any method that fixes one while adapting the other operates with a suboptimal configuration for part of the training run. We present COPUS, a system that adaptively tunes the global batch size, parallelism strategy, and micro-batch size as training evolves. COPUS is guided by Goodput, the product of throughput and statistical efficiency, which models both hardware and statistical effects jointly and directly measures useful convergence per unit of wall-clock time. The system combines online gradient noise scale estimation under 3D parallelism with throughput-aware evaluation of candidate configurations, and supports efficient reconfiguration of both batch size and parallelism during training. We evaluate COPUS on LLM pre-training workloads across 1-4 nodes of 8xH100 and 8xMI210 GPUs and model sizes from 3B to 32B parameters, demonstrating average time-to-convergence speedups of 3.9-8.0% over the fastest baseline across four configurations, with peak gains up to 11.1%, including system overheads.

Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years, and more sophisticated second-order (Hessian-based) optimizers often incur too much per-step overhead. In this paper, we propose Sophia, Second-order Clipped Stochastic Optimization, a simple scalable second-order optimizer that uses a light-weight estimate of the diagonal Hessian as the pre-conditioner. The update is the moving average of the gradients divided by the moving average of the estimated Hessian, followed by element-wise clipping. The clipping controls the worst-case update size and tames the negative impact of non-convexity and rapid change of Hessian along the trajectory. Sophia only estimates the diagonal Hessian every handful of iterations, which has negligible average per-step time and memory overhead. On language modeling with GPT-2 models of sizes ranging from 125M to 770M, Sophia achieves a 2x speed-up compared with Adam in the number of steps, total compute, and wall-clock time. Theoretically, we show that Sophia adapts to the curvature in different components of the parameters, which can be highly heterogeneous for language modeling tasks. Our run-time bound does not depend on the condition number of the loss.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

In unsupervised learning, collecting more data is not always a costly process unlike the training. For example, it is not hard to enlarge the 40GB WebText used for training GPT-2 by modifying its sampling methodology considering how many webpages there are in the Internet. On the other hand, given that training on this dataset already costs tens of thousands of dollars, training on a larger dataset naively is not cost-wise feasible. In this paper, we suggest to train on a larger dataset for only one epoch unlike the current practice, in which the unsupervised models are trained for from tens to hundreds of epochs. Furthermore, we suggest to adjust the model size and the number of iterations to be performed appropriately. We show that the performance of Transformer language model becomes dramatically improved in this way, especially if the original number of epochs is greater. For example, by replacing the training for 10 epochs with the one epoch training, this translates to 1.9-3.3x speedup in wall-clock time in our settings and more if the original number of epochs is greater. Under one epoch training, no overfitting occurs, and regularization method does nothing but slows down the training. Also, the curve of test loss over iterations follows power-law extensively. We compare the wall-clock time of the training of models with different parameter budget under one epoch training, and we show that size/iteration adjustment based on our proposed heuristics leads to 1-2.7x speedup in our cases. With the two methods combined, we achieve 3.3-5.1x speedup. Finally, we speculate various implications of one epoch training and size/iteration adjustment. In particular, based on our analysis we believe that we can reduce the cost to train the state-of-the-art models as BERT and GPT-2 dramatically, maybe even by the factor of 10.

Benchmarks play an important role in the development of machine learning algorithms. For example, research in reinforcement learning (RL) has been heavily influenced by available environments and benchmarks. However, RL environments are traditionally run on the CPU, limiting their scalability with typical academic compute. Recent advancements in JAX have enabled the wider use of hardware acceleration to overcome these computational hurdles, enabling massively parallel RL training pipelines and environments. This is particularly useful for multi-agent reinforcement learning (MARL) research. First of all, multiple agents must be considered at each environment step, adding computational burden, and secondly, the sample complexity is increased due to non-stationarity, decentralised partial observability, or other MARL challenges. In this paper, we present JaxMARL, the first open-source code base that combines ease-of-use with GPU enabled efficiency, and supports a large number of commonly used MARL environments as well as popular baseline algorithms. When considering wall clock time, our experiments show that per-run our JAX-based training pipeline is up to 12500x faster than existing approaches. This enables efficient and thorough evaluations, with the potential to alleviate the evaluation crisis of the field. We also introduce and benchmark SMAX, a vectorised, simplified version of the popular StarCraft Multi-Agent Challenge, which removes the need to run the StarCraft II game engine. This not only enables GPU acceleration, but also provides a more flexible MARL environment, unlocking the potential for self-play, meta-learning, and other future applications in MARL. We provide code at https://github.com/flairox/jaxmarl.

Transformer-based language models spread FLOPs uniformly across input sequences. In this work we demonstrate that transformers can instead learn to dynamically allocate FLOPs (or compute) to specific positions in a sequence, optimising the allocation along the sequence for different layers across the model depth. Our method enforces a total compute budget by capping the number of tokens (k) that can participate in the self-attention and MLP computations at a given layer. The tokens to be processed are determined by the network using a top-k routing mechanism. Since k is defined a priori, this simple procedure uses a static computation graph with known tensor sizes, unlike other conditional computation techniques. Nevertheless, since the identities of the k tokens are fluid, this method can expend FLOPs non-uniformly across the time and model depth dimensions. Thus, compute expenditure is entirely predictable in sum total, but dynamic and context-sensitive at the token-level. Not only do models trained in this way learn to dynamically allocate compute, they do so efficiently. These models match baseline performance for equivalent FLOPS and wall-clock times to train, but require a fraction of the FLOPs per forward pass, and can be upwards of 50\% faster to step during post-training sampling.

Transformers are slow to train on videos due to extremely large numbers of input tokens, even though many video tokens are repeated over time. Existing methods to remove such uninformative tokens either have significant overhead, negating any speedup, or require tuning for different datasets and examples. We present Run-Length Tokenization (RLT), a simple approach to speed up video transformers inspired by run-length encoding for data compression. RLT efficiently finds and removes runs of patches that are repeated over time prior to model inference, then replaces them with a single patch and a positional encoding to represent the resulting token's new length. Our method is content-aware, requiring no tuning for different datasets, and fast, incurring negligible overhead. RLT yields a large speedup in training, reducing the wall-clock time to fine-tune a video transformer by 30% while matching baseline model performance. RLT also works without any training, increasing model throughput by 35% with only 0.1% drop in accuracy. RLT speeds up training at 30 FPS by more than 100%, and on longer video datasets, can reduce the token count by up to 80%. Our project page is at https://rccchoudhury.github.io/projects/rlt/.

Large language models (LLMs) excel at complex reasoning when they include intermediate steps, known as "chains of thought" (CoTs). However, these rationales are often overly verbose, even for simple problems, leading to wasted context, increased latency, and higher energy consumption. We observe that verbose, English-heavy CoTs and concise, math-centric CoTs occupy distinct regions in the model's residual-stream activation space. By extracting and injecting a "steering vector" to transition between these modes, we can reliably shift generation toward more concise reasoning, effectively compressing CoTs without retraining. We formalize this approach as Activation-Steered Compression (ASC), an inference-time technique that shortens reasoning traces by directly modifying hidden representations. In addition, we provide a theoretical analysis of the impact of ASC on the output distribution, derived from a closed-form KL-divergence-bounded constraint to regulate steering strength. Using only 100 paired verbose and concise examples, ASC achieves up to 67.43% reduction in CoT length on MATH500 and GSM8K datasets, while maintaining accuracy across 7B, 8B, and 32B parameter models. As a training-free method, ASC introduces negligible runtime overhead and, on MATH500, delivers an average 2.73x speedup in end-to-end reasoning wall-clock time on an 8B model. This makes ASC a practical and efficient tool for streamlining the deployment of reasoning-capable LLMs in latency- or cost-sensitive settings. The code is available at: https://github.com/ArminAzizi98/ASC

Training of large language models (LLMs) is typically distributed across a large number of accelerators to reduce training time. Since internal states and parameter gradients need to be exchanged at each and every single gradient step, all devices need to be co-located using low-latency high-bandwidth communication links to support the required high volume of exchanged bits. Recently, distributed algorithms like DiLoCo have relaxed such co-location constraint: accelerators can be grouped into ``workers'', where synchronizations between workers only occur infrequently. This in turn means that workers can afford being connected by lower bandwidth communication links without affecting learning quality. However, in these methods, communication across workers still requires the same peak bandwidth as before, as the synchronizations require all parameters to be exchanged across all workers. In this paper, we improve DiLoCo in three ways. First, we synchronize only subsets of parameters in sequence, rather than all at once, which greatly reduces peak bandwidth. Second, we allow workers to continue training while synchronizing, which decreases wall clock time. Third, we quantize the data exchanged by workers, which further reduces bandwidth across workers. By properly combining these modifications, we show experimentally that we can distribute training of billion-scale parameters and reach similar quality as before, but reducing required bandwidth by two orders of magnitude.

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important tool for practical machine learning is the model Exponential Moving Average (EMA), which is a model copy that does not receive gradient information, but instead follows its target model with some momentum. This model EMA can improve the robustness and generalization properties of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have treated the model EMA separately from optimization, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of model EMAs and demonstrate its validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, optimally a 6times wall-clock time reduction.

Training modern neural networks on large datasets is computationally and environmentally costly. We introduce GRAFT, a scalable in-training subset selection method that (i) extracts a low-rank feature representation for each batch, (ii) applies a Fast MaxVol sampler to select a small, diverse subset that spans the batch's dominant subspace, and (iii) dynamically adjusts the subset size using a gradient-approximation criterion. By operating in low-rank subspaces and training on carefully chosen examples instead of full batches, GRAFT preserves the training trajectory while reducing wall-clock time, energy consumption, and CO_2 emissions. Across multiple benchmarks, GRAFT matches or exceeds recent selection baselines in both accuracy and efficiency, providing a favorable trade-off between accuracy, efficiency, and emissions.

Recent advances in large language models highlighted the excessive quadratic cost of self-attention. Despite the significant research efforts, subquadratic attention methods still suffer from inferior performance in practice. We hypothesize that dynamic, learned content-based sparsity can lead to more efficient attention mechanisms. We present Mixture of Sparse Attention (MoSA), a novel approach inspired by Mixture of Experts (MoE) with expert choice routing. MoSA dynamically selects tokens for each attention head, allowing arbitrary sparse attention patterns. By selecting k tokens from a sequence of length T, MoSA reduces the computational complexity of each attention head from O(T^2) to O(k^2 + T). This enables using more heads within the same computational budget, allowing higher specialization. We show that among the tested sparse attention variants, MoSA is the only one that can outperform the dense baseline, sometimes with up to 27% better perplexity for an identical compute budget. MoSA can also reduce the resource usage compared to dense self-attention. Despite using torch implementation without an optimized kernel, perplexity-matched MoSA models are simultaneously faster in wall-clock time, require less memory for training, and drastically reduce the size of the KV-cache compared to the dense transformer baselines.

We present AutoResearch-RL, a framework in which a reinforcement learning agent conducts open-ended neural architecture and hyperparameter research without human supervision, running perpetually until a termination oracle signals convergence or resource exhaustion. At each step the agent proposes a code modification to a target training script, executes it under a fixed wall clock time budget, observes a scalar reward derived from validation bits-per-byte (val-bpb), and updates its policy via Proximal Policy Optimisation (PPO). The key design insight is the separation of three concerns: (i) a frozen environment (data pipeline, evaluation protocol, and constants) that guarantees fair cross-experiment comparison; (ii) a mutable target file (train.py) that represents the agent's editable state; and (iii) a meta-learner (the RL agent itself) that accumulates a growing trajectory of experiment outcomes and uses them to inform subsequent proposals. We formalise this as a Markov Decision Process, derive convergence guarantees under mild assumptions, and demonstrate empirically on a single GPU nanochat pretraining benchmark that AutoResearch-RL discovers configurations that match or exceed hand-tuned baselines after approximately 300 overnight iterations, with no human in the loop.

Reinforcement learning (RL) plays a central role in large language model (LLM) post-training. Among existing approaches, Group Relative Policy Optimization (GRPO) is widely used, especially for RL with verifiable rewards (RLVR) fine-tuning. In GRPO, each query prompts the LLM to generate a group of rollouts with a fixed group size N. When all rollouts in a group share the same outcome, either all correct or all incorrect, the group-normalized advantages become zero, yielding no gradient signal and wasting fine-tuning compute. We introduce Adaptive Efficient Rollout Optimization (AERO), an enhancement of GRPO. AERO uses an adaptive rollout strategy, applies selective rejection to strategically prune rollouts, and maintains a Bayesian posterior to prevent zero-advantage dead zones. Across three model configurations (Qwen2.5-Math-1.5B, Qwen2.5-7B, and Qwen2.5-7B-Instruct), AERO improves compute efficiency without sacrificing performance. Under the same total rollout budget, AERO reduces total training compute by about 48% while shortening wall-clock time per step by about 45% on average. Despite the substantial reduction in compute, AERO matches or improves Pass@8 and Avg@8 over GRPO, demonstrating a practical, scalable, and compute-efficient strategy for RL-based LLM alignment.

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

We propose Adam-mini, an optimizer that achieves on-par or better performance than AdamW with 45% to 50% less memory footprint. Adam-mini reduces memory by cutting down the learning rate resources in Adam (i.e., 1/v). We find that geq 90% of these learning rates in v could be harmlessly removed if we (1) carefully partition the parameters into blocks following our proposed principle on Hessian structure; (2) assign a single but good learning rate to each parameter block. We further find that, for each of these parameter blocks, there exists a single high-quality learning rate that can outperform Adam, provided that sufficient resources are available to search it out. We then provide one cost-effective way to find good learning rates and propose Adam-mini. Empirically, we verify that Adam-mini performs on par or better than AdamW on various language models sized from 125M to 7B for pre-training, supervised fine-tuning, and RLHF. The reduced memory footprint of Adam-mini also alleviates communication overheads among GPUs and CPUs, thereby increasing throughput. For instance, Adam-mini achieves 49.6% higher throughput than AdamW when pre-training Llama2-7B on 2times A800-80GB GPUs, which saves 33% wall-clock time for pre-training.

Progress in machine learning (ML) has been fueled by scaling neural network models. This scaling has been enabled by ever more heroic feats of engineering, necessary for accommodating ML approaches that require high bandwidth communication between devices working in parallel. In this work, we propose a co-designed modular architecture and training approach for ML models, dubbed DIstributed PAth COmposition (DiPaCo). During training, DiPaCo distributes computation by paths through a set of shared modules. Together with a Local-SGD inspired optimization (DiLoCo) that keeps modules in sync with drastically reduced communication, Our approach facilitates training across poorly connected and heterogeneous workers, with a design that ensures robustness to worker failures and preemptions. At inference time, only a single path needs to be executed for each input, without the need for any model compression. We consider this approach as a first prototype towards a new paradigm of large-scale learning, one that is less synchronous and more modular. Our experiments on the widely used C4 benchmark show that, for the same amount of training steps but less wall-clock time, DiPaCo exceeds the performance of a 1 billion-parameter dense transformer language model by choosing one of 256 possible paths, each with a size of 150 million parameters.

Direct Preference Optimization (DPO) is widely used after supervised fine-tuning (SFT) to align language models, yet empirical behavior under small backbones and modest data is under-specified. We systematically compare SFT-only, DPO-only, and staged SFT-to-DPO training alongside full fine-tuning (FFT) versus LoRA on a GPT-2-scale decoder, evaluating paraphrase detection and Shakespearean sonnet continuation. DPO yields small, task-dependent gains over strong SFT and can match competitive SFT accuracy without a warm start when the preference construction closely parallels the supervised objective. In contrast, parameterization dominates: FFT consistently outperforms LoRA at matched training depth, and LoRA does not reduce wall-clock time on our hardware. These findings indicate that, in this small-scale regime, supervised full-parameter adaptation remains the primary performance lever, while preference optimization and low-rank adaptation provide limited marginal returns.

Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges on a handful of carefully handpicked components; namely, neighbour proposal distribution and temperature annealing schedule. In this work, we view SA from a reinforcement learning perspective and frame the proposal distribution as a policy, which can be optimised for higher solution quality given a fixed computational budget. We demonstrate that this Neural SA with such a learnt proposal distribution, parametrised by small equivariant neural networks, outperforms SA baselines on a number of problems: Rosenbrock's function, the Knapsack problem, the Bin Packing problem, and the Travelling Salesperson problem. We also show that Neural SA scales well to large problems - generalising to significantly larger problems than the ones seen during training - while achieving comparable performance to popular off-the-shelf solvers and other machine learning methods in terms of solution quality and wall-clock time.

Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.

Sparse mixture of expert architectures (MoEs) scale model capacity without large increases in training or inference costs. Despite their success, MoEs suffer from a number of issues: training instability, token dropping, inability to scale the number of experts, or ineffective finetuning. In this work, we proposeSoft MoE, a fully-differentiable sparse Transformer that addresses these challenges, while maintaining the benefits of MoEs. Soft MoE performs an implicit soft assignment by passing different weighted combinations of all input tokens to each expert. As in other MoE works, experts in Soft MoE only process a subset of the (combined) tokens, enabling larger model capacity at lower inference cost. In the context of visual recognition, Soft MoE greatly outperforms standard Transformers (ViTs) and popular MoE variants (Tokens Choice and Experts Choice). For example, Soft MoE-Base/16 requires 10.5x lower inference cost (5.7x lower wall-clock time) than ViT-Huge/14 while matching its performance after similar training. Soft MoE also scales well: Soft MoE Huge/14 with 128 experts in 16 MoE layers has over 40x more parameters than ViT Huge/14, while inference time cost grows by only 2%, and it performs substantially better.

We introduce NOBLE (Nonlinear lOw-rank Branch for Linear Enhancement), an architectural augmentation that adds nonlinear low-rank branches to transformer linear layers. Unlike LoRA and other parameter-efficient fine-tuning (PEFT) methods, NOBLE is designed for pretraining from scratch. The branch is a permanent part of the architecture as opposed to an adapter for finetuning on top of frozen weights. The branch computes σ(xWdown)Wup where σ is a learnable nonlinearity. We evaluate several activation functions and find that CosNet, a two-layer cosine nonlinearity with learnable frequency and phase with a linear projection in between them in the bottleneck space, performs best. NOBLE achieves substantial improvements with minimal overhead: up to 1.47x step speedup to reach baseline eval loss (up to 32% fewer training steps), with as low as 4% additional parameters and 7% step time overhead, resulting in up to 1.22x net wallclock speedup. Experiments on LLMs (250M and 1.5B parameters), BERT, VQGAN, and ViT consistently show improved training efficiency. We identify one caveat: Mixup/CutMix augmentation interferes with NOBLE's benefits in Imagenet classification along with other stochastic augmentations, but when disabled, ViT also improves. This discrepancy is possibly explained by regularization techniques that encourage smoother fits to the target function while NOBLE may specialize more in sharper aspects of the target function.

Recognizing the flow of time in a story is a crucial aspect of understanding it. Prior work related to time has primarily focused on identifying temporal expressions or relative sequencing of events, but here we propose computationally annotating each line of a book with wall clock times, even in the absence of explicit time-descriptive phrases. To do so, we construct a data set of hourly time phrases from 52,183 fictional books. We then construct a time-of-day classification model that achieves an average error of 2.27 hours. Furthermore, we show that by analyzing a book in whole using dynamic programming of breakpoints, we can roughly partition a book into segments that each correspond to a particular time-of-day. This approach improves upon baselines by over two hours. Finally, we apply our model to a corpus of literature categorized by different periods in history, to show interesting trends of hourly activity throughout the past. Among several observations we find that the fraction of events taking place past 10 P.M jumps past 1880 - coincident with the advent of the electric light bulb and city lights.