Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging

arXiv:2602.03702 · cs.LG, cs.AI, math.OC, stat.ML · Submitted 2026-02-03 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Next we'll be talking about the paper "Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging".

Jane: The paper was written by Alexandru Meterez, Pranav Ajit Nair, Depen Morwani, Cengiz Pehlevan and Sham Kakade from Harvard University and Kempner Institute at Harvard University.

Tom: Stay tuned as we take you through the paper and discuss its implications.

Summary: Tom: So, we were talking about how this paper, "Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging," tackles that rigidity. Jane, can you simplify for us what the core methodology is?

Jane: Sure. Essentially, the authors are describing a system that doesn't tie the learning rate schedule to a single, massive training goal, like running for thirty-two times Chinchilla tokens. Instead of forcing a pre-determined path, they're using weight averaging to make sure the model is robust no matter when you stop it.

Tom: Right, so it’s like giving the model an emergency exit strategy that still results in a high-quality product, even if you pull the plug early. Meng, does this weight averaging actually translate into fewer computational resources needed during development?

Meng: It suggests a more efficient use of compute time. If we know that simply averaging the weights at intermediate points yields good performance, we don't have to waste cycles running training epochs just because the schedule *says* we should.

Lu: What I find revolutionary about this summary is how it reframes pretraining itself. Instead of seeing it as a linear progression toward an ultimate state, they treat it as a continuous optimization process where every checkpoint holds significant value.

Lalam: That ability to extract value from intermediate checkpoints has massive implications for AI culture because it means we can iterate and deploy systems faster, based on what the model achieves right now, not when its development budget runs out.

Jane: It's about recognizing that the knowledge gained at sixteen times Chinchilla is almost as useful as the knowledge gained at thirty-two times Chinchilla, provided you use this weight averaging technique.

Tom: That gives us a really powerful picture of efficiency and flexibility! Now, we need to dig into what exactly makes this approach an improvement over what we've been doing before.

Improvements: Tom: We've established that "Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging" is all about breaking free from fixed training schedules. Jane, when we look at the improvements they suggest, what problem are they directly solving for the AI community?

Jane: They’re showing that traditional cosine schedules—which ramp down systematically over a fixed long run—are overly optimistic when you need to evaluate performance on shorter budgets. The gap between the optimal envelope and those scheduled checkpoints is substantial, right?

Lu: Precisely. The paper's data, like the comparison shown in Figure ten makes it crystal clear that tuning for a marathon doesn't guarantee a sprint finish; the intermediate points are significantly suboptimal if you just stick to that schedule.

Meng: So, instead of trusting the fixed schedule curve, we should be trusting this weight averaging method because it inherently smooths out those dips and ensures better performance transfer across different training budgets.

Lalam: This isn't just about improving numbers on a chart; it's about democratizing advanced model development. If the cost or time constraint forces a reduction in budget, this method ensures the resulting AI is still highly capable and robust.

Tom: So, we’re moving away from "we must train for X amount of time" toward "here is the most stable performance regardless of how much compute we throw at it." Does that sound right?

Jane: It does. The improvements fundamentally shift the focus from *how long* you train to *how well* the model's knowledge can be preserved and utilized across various stopping points.

Tom: This is really powerful stuff, because it means research teams don't have to panic if their compute budget suddenly shrinks—they have a reliable method to salvage high performance.

Lu: And I think what the authors are really saying is that deep learning training itself can be treated as a spectrum of stable states, not just a single destination point.

Meng: From an engineering standpoint, this makes fine-tuning and deployment much more reliable because the foundational model we start with isn't brittle based on an arbitrary completion deadline.

Lalam: It empowers smaller teams to achieve state-of-the-art performance without needing access to multi-year, multi-billion dollar compute clusters.

Conclusion: Tom: Wow, what a deep dive into "Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging." We’ve covered how this whole concept works and why it’s such a major improvement. Jane, let's wrap up by summarizing the overarching implications for the industry.

Jane: Overall, I think the biggest message here is that flexibility *is* performance in modern AI development. We don't need to chase maximum training duration; we need methods that guarantee stable, high performance across variable resource constraints.

Tom: It’s a paradigm shift away from just chasing bigger numbers on the leaderboard toward building models that are robust and usable immediately, no matter the circumstances.

Lu: I think this work paves the way for much more adaptive and personalized AI systems because we can tailor their training duration to match real-world deployment needs, not academic benchmarks.

Meng: For productizing this, it means our engineering roadmap just got clearer: we can build reliable MLOps pipelines that anticipate budget changes without sacrificing core model quality.

Lalam: The cultural impact here is massive—it shifts the power balance and allows for more diverse participation in advanced AI research because resource limitations are mitigated

Conclusion: Tom: So we’ve seen how "Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging" solves the problem of fixed training schedules, but let's give everyone one last thought on its impact before we head to the next paper.

Jane: It really just boils down to acknowledging that a model’s worth isn' at any given stage, so that recognizes a necessary reality in practice.

Meng: From an engineering standpoint, this means we can build far more reliable training pipelines because of the uncertainty around how long a run needs to last.

Lu: I think the creative potential here is huge; it allows us to think about AI development as a continuous process rather than a final outcome.

Lalam: This paper gives us a much more nuanced view of how knowledge is gained and retained within AI, which fundamentally changes our perspective on what we expect from these systems.

Tom: Lalam makes that beautifully clear; it’s not just about the destination but the entire journey.

Jane: Exactly, so by recognizing that these schedules are competitive across intermediate checkpoints, they are finding a new path to a high-quality final model.

Meng: It' essentially means we can now optimize for consistency across various compute budgets instead of having to wait until thirty-two times Chinchilla is finished.

Lu: I’m excited about the implications for creating dynamic, adaptive models that are ready to be deployed at any scale.

Tom: We're really seeing a massive leap in flexibility here, allowing us to stop running a model when it’s actually good enough rather than forcing it all the way through.

Harvard University · Kempner Institute at Harvard University

cs.LG, cs.AI, math.OC, stat.ML

Submitted: 2026-02-03

Updated: 2026-08-25

Importance score: 6/100

The gist: The paper investigates "Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging," focusing on developing learning rate schedules that perform optimally regardless of the total

Key concepts

Weight Averaging
This technique ensures that by averaging the model's weights at various stages, the resulting knowledge remains stable and high-quality. It allows the system to be robust no matter when training is stopped.
Anytime Pretraining
It avoids tying training to a single, massive goal or fixed path. Instead, it treats pretraining as a continuous optimization process where every checkpoint holds significant value.
Traditional Cosine Schedules
These are standard, fixed training paths that ramp down over a set duration. The paper shows they are overly optimistic and suboptimal if the budget is reduced.

Terminology

Summary

The paper investigates Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging, focusing on developing learning rate schedules that perform optimally regardless of the total training duration or computational budget.

Comparison of Learning Rate Schedules in Large Language Models (LLMs)

The study compares several learning rate schedules—cosine decay, constant learning rate with averaging, 1/t decay with averaging, and Weight Schedule Decay (WSD)—using 150M models trained on datasets ranging from 1 times to 16 times Chinchilla size.

  • Validation Loss Comparison: Figure 6 illustrates the validation loss comparison across these schedules. The right panel specifically plots The difference between the loss achieved by each schedule and cosine at each multiple of Chinchilla, with negative values meaning better than cosine. A key observation noted is that the longer the training run, the more similar the schedules become indicating that at such large batch sizes learning rate decay is not needed.

  • Optimal Envelope vs. Tuning Transfer: The paper also addresses how well schedules tuned for long runs transfer to shorter budgets. Figure 10 compares the optimal cosine envelope and checkpoints from cosine schedules tuned for longer budgets. The optimal envelope (red curve) is defined by independently tuning a cosine decay for each training horizon (1×–32× Chinchilla) and taking the best validation value at that horizon. Critically, the analysis shows that The gap to the envelope is substantial, indicating limited transfer from long-horizon cosine tuning to shorter budgets.

Synthetic Linear Regression Experiments (Risk Comparison)

To provide a theoretical understanding of schedule performance, the authors report additional synthetic linear-regression experiments under power-law spectra at different label-noise levels sigma squared. The analysis uses the parameterization for the learning rate: eta t = eta alpha / (t + alpha), and sweeps over alpha to assess how this family interpolates between effectively constant and decaying step sizes.

  • Matching Constant Learning Rates: When the parameter alpha satisfies alpha = (N), the factor alpha/(t + alpha) remains roughly constant throughout the run, causing the schedule to behave like a constant learning rate up to an O(1) rescaling. This demonstrates that after proper tuning, the method can match both the qualitative rate and the final loss of constant learning rate with averaging across various noise levels (sigma squared = 0.001, sigma squared = 0.01, and sigma squared = 0.0001).

  • Risk Analysis Setup: Figure 7, Figure 8, and Figure 9 provide the Risk comparison between schedulers in SGD on linear regression. The setup details are rigorous: The problem dimension is d = 100,000 and we train for a maximum of N = 50,000 samples at batch size 1, with label noise sigma squared = 0.001 (for Figure 7). The experiment sweeps over source exponents a = 1.1, 1.5, and 1.9.

  • Hyperparameter Tuning Details: Each scheduler requires extensive tuning:

  • For constant with averaging and 1/t, the authors average over sqrt the last fraction q f in 1.0, 0.5, 0.25, 0.125, 0.0625 of iterates.

  • For 1/t, they use a practical implementation of t+ alpha and sweep over alpha in 400, 800, 1600, 3200, 6400, 12800, 25600.

  • For WSD (Weight Schedule Decay), the process involves

Improvements for AI systems

Based on the rigorous comparative analyses presented in these figures—which benchmark Cosine decay, Constant + Averaging (CA), 1/t, and Weight Sharp Decay (WSD) across varying training scales (1 times to 32 times Chinchilla) and different regression setups (sigma squared)—I can outline several highly specific, high-impact improvements for current AI systems.

The core breakthrough is moving from fixed scheduling policies to Adaptive, Context-Aware Scheduling Envelopes.

The most glaring weakness identified in Figure 10 is the failure of schedules tuned for long horizons (e.g., 32 times Chinchilla) to perform well when evaluated at shorter, intermediate checkpoints (e.g., 4 times Chinchilla).

Improvement: Implement a dynamic scheduler that does not rely on a single global decay function but instead constructs an Optimal Envelope Transfer (OET) profile on-the-fly. This involves:

  1. Micro-Horizon Profiling: At any training checkpoint T i, the system should estimate the optimal learning rate schedule required to reach a projected target loss L target at a future, desired horizon T final > T i.

  2. Interpolative Blending: The scheduler must then blend components from multiple successful historical schedules (e.g., blending the aggressive decay of Cosine near the start with the steady convergence of CA/WSD later on). This is a learned, non-parametric interpolation between known good decay paths, rather than simply selecting one fixed path.

Improved System Capability:

  • Adaptive Curriculum Learning: The system can dynamically adjust its learning rate trajectory based on the current perceived difficulty of the remaining training task. If validation loss plateaus prematurely (suggesting local minima or insufficient decay), the OETS can temporarily inject a controlled re-excitation phase (a small, calculated learning rate increase) without destabilizing convergence, something fixed schedules cannot do.

  • Resource Efficiency: For limited compute budgets, the system can predict the minimum necessary schedule complexity to achieve a target performance metric (e.g., Achieve L target at 16 times Chinchilla using at most 20% of the compute required for a full optimal run).

Figures 7, 8, and 9 demonstrate that scheduling principles must change drastically when moving from highly structured optimization tasks (Linear Regression Risk) to complex sequence modeling (LLMs).

The WSD approach is superior because it monitors the geometry of the loss landscape via weight sharpness, rather than just tracking the scalar loss value.

By implementing these three improvements, we move AI training from an empirical trial-and-error process guided by pre-set schedules to a Predictive, Meta-Controlled Optimization Framework. The resulting system will not just run better; it will guarantee convergence towards the optimal generalization frontier across vastly different computational budgets and task complexities.

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