Anytime Pretraining Strategies

• Anytime pretraining is a method that produces robust, adaptable model checkpoints at any training stage using horizon-free and continual self-supervised methodologies.
• It leverages dynamic learning rate schedules, weight averaging, and curriculum learning to minimize forgetting and boost generalization.
• Practical implementations include prompt-based hypernetworks and non-i.i.d. data handling, ensuring reliable fine-tuning without a fixed training endpoint.

Anytime pretraining refers to a family of algorithmic and systems principles for language and vision models that guarantee robust, transferable, and stable representations at every intermediate checkpoint during pretraining, regardless of whether the training horizon or future domain/task structure is known in advance. This property enables models to be reliably fine-tuned or evaluated "at any time"—after any number of training steps, domain shifts, or data arrivals—without suffering from catastrophic forgetting, impaired generalization, or brittle schedule dependencies. Anytime pretraining encompasses: (1) learning-rate schedules and optimization rules that do not require a fixed endpoint (horizon-free training), (2) continual/self-supervised pretraining scenarios with non-i.i.d. data streams and evolving domains, (3) explicit handling of the stability-plasticity dilemma such that adaptability to new domains does not degrade performance on prior or unseen distributions, and (4) practical interventions, such as prompt-based hypernetwork modules or curriculum-enhanced sampling, to ensure desirable anytime properties. These advancements aim to bridge the gap between static, one-shot model pretraining and real-world, incremental, or open-ended learning deployments.

1. Formal Definitions and Problem Scenarios

Anytime pretraining strictly requires that for any intermediate model $B^i$ resulting from continual exposure to domains $D_1,\ldots,D_i$, performance after fine-tuning on any downstream task—regardless of whether that task resides in $\{D_1,\ldots,D_i\}$ (seen), $D_{i+1},\ldots$ (future), or is entirely out-of-domain—remains non-decreasing relative to any prior model $B^{i-k}$ ($k>0$). This is operationalized via the \emph{anytime-fine-tuning accuracy table} with entries $a^i_j$ (accuracy of $B^i$ fine-tuned on domain-$j$ task), and three core metrics:

• Adaptability: average of $a^i_i$ (diagonal; fine-tune on latest domain).
• Generalization: average of $a^i_j$ for $j>i$ (future or OOD domains).
• Forgetting: extent to which $a^i_j$ for $j<i$ drops relative to previous checkpoints.

Failure modes arise when mechanisms focus on current domain adaptation and backward forgetting (e.g., via parameter isolation, masking, or vanilla regularization), but neglect explicit preservation of upper-triangle (future-domain) accuracy. This results in decreased transfer and poor robustness if training is halted arbitrarily or novel tasks arise (Jiang et al., 2023, Cossu et al., 2022).

2. Horizon-Free Optimization and Weight Averaging

In the context of LLMs, most traditional learning-rate schedules (e.g., cosine decay) are "horizon-aware," requiring the total number of optimization steps $N$ to be known and tuned in advance. This is incompatible with open-ended or variable-horizon training, leading to suboptimal performance at most checkpoints except the intended terminal point.

Anytime (horizon-free) optimization instead utilizes step-size schedules independent of $N$, such as polynomially-decayed learning rates ($\eta_t = \eta / t^\gamma$, $0 < \gamma < 1$) or parameterizations like $\eta_t = \eta \sqrt{\alpha/(t+\alpha)}$. Crucially, these schedules are paired with \emph{weight averaging} (e.g., tail averaging, exponential moving average) to recover the minimax convergence guarantees and eliminate variance/bias accumulation at intermediate points. Empirical results in 150M/300M parameter LMs show that constant or $1/\sqrt{t}$ schedules with weight averaging closely track the optimal performance envelope of per-horizon-tuned cosine schedules across all scales, with negligible loss increases (maximum $\lesssim$0.01 bits/word) and full "anytime" compatibility (Meterez et al., 3 Feb 2026).

Theoretical analyses establish that, in overparameterized linear models, the optimal decay exponent $\gamma^* = \max(1-a/b,\,0)$, where $a$ and $b$ quantify spectral (capacity/source) properties, resulting in risk scaling that matches minimax lower bounds (Meterez et al., 3 Feb 2026).

3. Continual and Self-Supervised Pretraining Protocols

Continual pretraining ("anytime" or lifelong) generalizes beyond horizon-free SGD to accommodate non-stationary and non-i.i.d. data streams arranged as experiences $e_1, ..., e_T$, each supplying new unlabeled/self-supervised data and, optionally, downstream tasks. The goal is to update model parameters $\theta_{i-1} \rightarrow \theta_i$ while maintaining stable performance on both held-out control (Forgetting Control, FC) sets and all prior/future domains (Cossu et al., 2022).

Key empirical findings:

• Self-supervised objectives (e.g., MLM, MIM) yield near-zero catastrophic forgetting on FC datasets ($< 1\%$ drop across 5 experiences for BERT, RoBERTa, BEiT).
• Forward and backward transfer both remain robust: new experiences improve adaptation, while past task performance is recovered within one fine-tuning epoch.
• In contrast, supervised protocols or naïve fine-tuning require explicit memory or regularization (replay buffers, EWC) for stability, but still exhibit significant forgetting.
• No explicit regularizer is needed with self-supervised continuation; knowledge is retained implicitly (Cossu et al., 2022).

4. Prompt-Based and Hypernetwork Methods for Anytime Generalization

Recent advances explicitly target the inability of standard continual pretraining methods to preserve transfer to unseen domains at arbitrary interruption points. The Hypernetwork Prompt module (Jiang et al., 2023) introduces the following architecture:

1. For input $x$ from domain $D^i$, compute contextual embedding $\hat{h}=E(x)$ via a frozen encoder.
2. Pass $\hat{h}$ through a hypernetwork $F_\Theta$ to generate a sample/domain-specific prompt $P^i$ as a weighted combination of $M$ learned basis prompt components.
3. Prefix $P^i$ to the token embeddings of $x$; process $[P^i; x]$ in the LM backbone $B$.
4. Jointly optimize backbone and hypernetwork via masked-LM loss, \emph{agreement loss} (maintaining similar hidden states under random prompting to maximize generalization), and \emph{disagreement loss} (orthogonality penalties to ensure domain-exclusive features).

This approach decouples prompt inference from external domain-IDs, encourages parameter sharing and efficient plasticity, and reduces domain interference during training and fine-tuning. Empirical results on DAPset and TWEET (temporal shift) benchmarks show improvement in adaptability ($+3.57\%$, $+3.4\%$), final accuracy and future-domain generalization versus all prior continual pretraining baselines (Jiang et al., 2023).

5. Curriculum Learning for Anytime Performance

Curriculum learning (CL) strategies, when applied to pretraining, reorder or pace data to improve early and mid-training dynamics. Empirical analysis demonstrates the compatibility of various CL regimes with anytime pretraining objectives (Zhang et al., 12 Jun 2025):

• Vanilla CL: Data ordered from easy to hard by difficulty metric (e.g., compression ratio, lexical diversity, Flesch readability), yielding up to $1.8\%$ peak accuracy gain using $17.9\%$ fewer tokens.
• Pacing-based sampling: Tokens are sampled across difficulty buckets with linear/quadratic/inverse-quadratic pacing, allowing robust annealing toward difficult examples.
• Interleaved CL: Multiple curriculum phases ensure all difficulty levels are seen repeatedly for sustained improvement.
• Warmup: CL used only in initial phase followed by standard random sampling leads to lasting gains ($+3.5\%$ final accuracy with MTLD warmup).

Compression ratio, lexical diversity (MTLD), and readability are consistently most effective as difficulty signals. These curriculum methods, by maximizing early information gain and structuring exposure, accelerate convergence and improve anytime evaluation checkpoints.

6. Implementation Practices and Limitations

Practical recommendations drawn from these studies include:

• Preference for horizon-free learning-rate schedules ($1/\sqrt{t}$ decay with weight averaging) for robust, horizon-agnostic optimization.
• Continual self-supervised pretraining (e.g., MLM/MIM) is the dominant default as it minimizes forgetting without replay/regularization overheads.
• Prompt-based approaches with agreement/disagreement losses substantially improve adaptation/generation trade-offs, especially in multi-domain scenarios.
• Curriculum ordering by compression ratio, lexical diversity, or readability is effective for early and sustained gains in anytime performance.
• Caution: Warmup-stable-decay and other hybrid schedules may involve minor implicit horizon dependencies. Theoretical analysis is mature for convex/quadratic settings; for nonconvex deep models, empirical validation is the main evidence (Meterez et al., 3 Feb 2026).
• For scalable deployment, maintain one or more weight-averaged checkpoints (e.g., multiple EMA half-lives) for optimal validation selection, and continually update via a single-epoch/few-epoch protocol per new pretraining experience.

These principles form the foundation of robust, flexible, and transferable anytime pretraining pipelines suitable for dynamic, open-ended, or uncertain operational environments.