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arxiv: 2605.12484 · v2 · submitted 2026-05-12 · 💻 cs.LG · cs.AI

Recognition: no theorem link

Learning, Fast and Slow: Towards LLMs That Adapt Continually

Rishabh Tiwari , Kusha Sareen , Lakshya A Agrawal , Joseph E. Gonzalez , Matei Zaharia , Kurt Keutzer , Inderjit S Dhillon , Rishabh Agarwal
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Devvrit Khatri
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Pith reviewed 2026-05-15 05:14 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords continual learningfast-slow learninglarge language modelsin-context learningcatastrophic forgettingsample efficiencyplasticityreinforcement learning
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The pith

Treating optimized context as fast weights alongside slow parameter updates allows LLMs to learn continually with less forgetting and higher efficiency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors introduce a fast-slow learning framework for large language models. Model parameters serve as slow weights that change gradually to preserve general reasoning, while optimized context acts as fast weights that quickly absorb task-specific information from textual feedback. This separation lets the model adapt to new tasks up to three times more sample-efficiently than updating parameters alone through reinforcement learning. The approach keeps the model closer to its base version, cutting KL divergence by up to 70 percent and reducing catastrophic forgetting. In sequences of changing tasks, the fast-slow method continues improving where pure parameter training plateaus.

Core claim

Fast-Slow Training (FST) combines parameter updates as slow weights with context optimization as fast weights. The fast weights learn task-specific details from feedback, allowing slow weights to remain near the base LLM. This yields up to 3x sample efficiency over RL, higher performance ceilings, up to 70% less KL divergence from the base model, and better adaptation to new tasks after initial training.

What carries the argument

The fast-slow framework, with LLM parameters as slow weights for general knowledge and optimized context as fast weights for task-specific adaptation.

If this is right

  • FST achieves up to 3 times higher sample efficiency than reinforcement learning on reasoning tasks.
  • FST models reach higher performance levels than slow-only training.
  • Trained models show up to 70% less KL divergence from the base LLM.
  • FST reduces catastrophic forgetting compared to parameter-only updates.
  • FST preserves plasticity, enabling better adaptation to subsequent tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Separating learning into fast and slow components could apply to other machine learning domains where forgetting is an issue.
  • Context optimization might function as a lightweight form of memory that avoids overwriting core model capabilities.
  • Deployed systems could use this to handle evolving user requirements without full retraining cycles.

Load-bearing premise

Optimizing context through textual feedback can capture task-specific information effectively enough to reduce the need for large parameter changes that would otherwise cause forgetting.

What would settle it

Compare adaptation performance on a second task after FST versus RL training on the first task, checking whether FST models show faster learning and less degradation on the original task.

Figures

Figures reproduced from arXiv: 2605.12484 by Devvrit Khatri, Inderjit S Dhillon, Joseph E. Gonzalez, Kurt Keutzer, Kusha Sareen, Lakshya A Agrawal, Matei Zaharia, Rishabh Agarwal, Rishabh Tiwari.

Figure 1
Figure 1. Figure 1: FST jointly optimizes slow parameters θ and a fast textual-context pool Φ via interleaved fast and slow update loops. The slow loop (top) updates θ from the scalar reward alone (θc → θc+1). The fast loop (bottom) updates Φ via reflective optimization, additionally consuming the rollout’s full text including thoughts, tool calls, errors, and rich feedback (Φc → Φc+1). Maintaining Φ as a Pareto-frontier popu… view at source ↗
Figure 2
Figure 2. Figure 2: Data efficiency across three training families. Top row: matched-step validation reward (running max, mean@4) — FST reaches RL’s running peak in substantially fewer training steps (3.0× on CodeIO, 1.4× on Math (Polaris), 3.0× on HoVer-hard). Bottom row: 6/8-axis coverage radars for Base→GEPA, RL→GEPA, and FST→GEPA on Mean@8 and Best@8, with axes grouped by in-distribution (sage), cross-domain (coral), and … view at source ↗
Figure 2
Figure 2. Figure 2: Slow weights and fast weights co-evolve through interleaved updates. The slow loop (top) updates θ from the scalar reward alone (θc → θc+1). The fast loop (bottom) updates Φ via reflective optimization, additionally consuming the rollout’s full text including thoughts, tool calls, errors, and rich feedback (Φc → Φc+1). Maintaining Φ as a Pareto-frontier population (rather than a single best prompt) preserv… view at source ↗
Figure 3
Figure 3. Figure 3: Performance asymptote on CodeIO, Math (Polaris), and HoVer-hard. For each run we fit a 4- parameter sigmoid R − R0 = A−R0 1+(Cmid/C)B to the validation-accuracy trajectory and annotate the upper asymptote A. FST’s asymptote (green) is higher than RL’s (blue) on all three tasks. Solid curves cover the fit window; dotted curves are extrapolation past the last training step. we compute token-level KL from the… view at source ↗
Figure 3
Figure 3. Figure 3: Data efficiency across three training families. Top row: matched-step validation accuracy (running max, mean@4); dash-dot GEPA-only reference rises from the step-0 base accuracy to the prompt-only ceiling within GEPA’s inference budget. FST reaches RL’s running peak in substantially fewer training steps (3.0× on CodeIO, 1.4× on Math (Polaris), 3.0× on HoVer-hard). Bottom row: out-of-distribution accuracy a… view at source ↗
Figure 4
Figure 4. Figure 4: Validation reward versus KL(πtrain ∥ πbase)trajectories on CodeIO, HoVer, and Physics. Translucent markers are per-checkpoint measurements; the line is a rolling-mean smoothing along training step. At matched reward, FST (green) sits to the left of RL (blue) on every task, reaching the same reward at a significantly lower KL from the base policy. methods. FST reaches near-peak in every stage while learning… view at source ↗
Figure 4
Figure 4. Figure 4: Performance asymptote on CodeIO, Math (Polaris), and HoVer-hard. For each run we fit a 4- parameter sigmoid R − R0 = A−R0 1+(Cmid/C)B to the validation-accuracy trajectory and annotate the upper asymptote A. FST’s asymptote (green) is higher than RL’s (blue) on all three tasks. Solid curves cover the fit window; dotted curves are extrapolation past the last training step. Across all three training families… view at source ↗
Figure 5
Figure 5. Figure 5: Plasticity probe: starting from a Math (left) or Physics (right) checkpoint trained with either RL or FST, we run a fresh RL pass on HoVer-hard and plot HoVer validation accuracy over 400 steps. Base init (dotted) is the no-prior-training reference. FST-init (green) preserves more capacity for the new task than RL-init (blue) on both arms; on the Math arm, prior RL collapses HoVer-hard learnability to near… view at source ↗
Figure 5
Figure 5. Figure 5: Validation reward versus KL(πtrain ∥ πbase)trajectories on CodeIO, HoVer, and Physics. Translucent markers are per-checkpoint measurements; the line is a rolling-mean smoothing along training step. At matched reward, FST (green) sits to the left of RL (blue) on every task, reaching the same reward at a significantly lower KL from the base policy. Full figure in Appendix G. Advantage 4: Fast-Slow Training P… view at source ↗
Figure 6
Figure 6. Figure 6: Continual learning across HoVer → CodeIO → Physics: a single uninterrupted training run that switches task every 200 steps. The y-axis is per-task validation accuracy normalized with respect to the peak accuracy reached across methods within each stage. FST (solid) reaches near-peak on every stage; RL (dashed) acquires HoVer but completely stalls on CodeIO and only partially recovers on Physics. represents… view at source ↗
Figure 6
Figure 6. Figure 6: Plasticity probe: starting from a Math (left) or Physics (right) checkpoint trained with either RL or FST, we run a fresh RL pass on HoVer-hard and plot HoVer validation accuracy over 400 steps. Base init (dotted) is the no-prior-training reference. FST-init (green) preserves more capacity for the new task than RL-init (blue) on both arms; on the Math arm, prior RL collapses HoVer-hard learnability to near… view at source ↗
Figure 7
Figure 7. Figure 7: Star Graph Search Task. FST escapes the zero-reward regime by step ∼50, an order of magnitude before RL begins to move signal at ∼300. 0 200 400 600 Step 15 20 25 30 35 40 45 50 Validation reward (%) 0 200 400 600 Step 0.1 0.2 0.3 0.4 0.5 Actor entropy (nats) RL FST FST-distill GEPA [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 7
Figure 7. Figure 7: Continual learning across HoVer → CodeIO → Physics: a single uninterrupted training run that switches task every 200 steps. The y-axis is per-task validation accuracy normalized with respect to the peak accuracy reached across methods within each stage. FST (solid) reaches near-peak on every stage; RL (dashed) acquires HoVer but completely stalls on CodeIO and only partially recovers on Physics. 0 50 100 1… view at source ↗
Figure 8
Figure 8. Figure 8: HoVer training: FST (green) lifts validation accuracy above the prompt-only ceiling (GEPA only, dashed), RL (blue) plateaus, and FST-distill, fast-weight self-distillation that relies on GEPA to drive reward gains. Fast and slow weights: complementary learning systems. The fast/slow decomposition predates deep learning, with roots in the neuroscience of complementary learning systems [25, 34] and a long li… view at source ↗
Figure 8
Figure 8. Figure 8: Star Graph Search Task. FST escapes the zero-reward regime by step ∼50, an order of magnitude before RL begins to move signal at ∼250. fast-to-slow distillation algorithm can substitute for direct RL on the slow weights. Our initial results using naive distillation suggest that it cannot. Distillation alone plateaus well below FST, confirming that both channels need to optimize against reward jointly to li… view at source ↗
Figure 9
Figure 9. Figure 9: CodeIO design ablations (val mean@4 at training step 500). Sage bars mark the headline config￾uration in each panel; gray bars are the alternatives swept; the dashed line indicates RL-only at the same matched step. (a) Population size K. (b) Advantage baseline at K=2: per-prompt (Prompt baseline) vs. per-problem (Problem baseline). (c) Cycle length T at K=8, Problem baseline. (d) Light vs. full GEPA recipe… view at source ↗
Figure 9
Figure 9. Figure 9: In-distribution gain decomposed into slow- and fast-weight contributions (pass@1, %). For each task, we evaluate four combinations: base or FST-trained weights, with the original prompt or the FST-evolved prompt. On HoVer-hard and CodeIO, both channels contribute and the joint cell (FST weights + FST prompt) dominates. On Math (Polaris), almost all of the gain is carried by the slow weights . represents a … view at source ↗
Figure 10
Figure 10. Figure 10: Rollout reuse on HoVer-hard, training step [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 10
Figure 10. Figure 10: CodeIO design ablations (val mean@4 at training step 500). Sage bars mark the headline config￾uration in each panel; gray bars are the alternatives swept; the dashed line indicates RL-only at the same matched step. (a) Population size K. (b) Advantage baseline at K=2: per-prompt (Prompt baseline) vs. per-problem (Problem baseline). (c) Cycle length T at K=8, Problem baseline. (d) Light vs. full GEPA recip… view at source ↗
Figure 11
Figure 11. Figure 11: Validation reward versus KL(πtrain ∥ πbase) on all four training tasks: CodeIO, Math (Polaris), HoVer, and Physics. Same axes, smoothing, and conventions as [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 11
Figure 11. Figure 11: Rollout reuse on HoVer-hard, training step [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Validation reward versus KL(πtrain ∥ πbase) on all four training tasks: CodeIO, Math (Polaris), HoVer, and Physics. Same axes, smoothing, and conventions as [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Explicit fast-to-slow distillation on HoVer. FST (green) is compared to FST-distill (orange), which updates θ only via the on-policy reverse-KL loss in Eq. 9 using a FST-evolved prompt ϕ as the teacher. Left: Validation reward. FST-distill rises above the prompt-only level by transferring fast-weight signal into the parameters across multiple updates, but plateaus well below FST, which has both channels o… view at source ↗
Figure 14
Figure 14. Figure 14: Decomposing the Fast vs. Slow gain on CodeIO. Step-matched (training step 650) validation accuracy (pass@1, computed from n=8 rollouts) on the held-out CodeIO set. Slow only isolates the parametric channel (RL- or FST-trained weights, evaluated without any GEPA prompt). Fast only isolates the textual channel (base weights with a GEPA-evolved prompt). Slow + Fast combines them. Both channels contribute, an… view at source ↗
read the original abstract

Large language models (LLMs) are trained for downstream tasks by updating their parameters (e.g., via RL). However, updating parameters forces them to absorb task-specific information, which can result in catastrophic forgetting and loss of plasticity. In contrast, in-context learning with fixed LLM parameters can cheaply and rapidly adapt to task-specific requirements (e.g., prompt optimization), but cannot by itself typically match the performance gains available through updating LLM parameters. There is no good reason for restricting learning to being in-context or in-weights. Moreover, humans also likely learn at different time scales (e.g., System 1 vs 2). To this end, we introduce a fast-slow learning framework for LLMs, with model parameters as "slow" weights and optimized context as "fast" weights. These fast "weights" can learn from textual feedback to absorb the task-specific information, while allowing slow weights to stay closer to the base model and persist general reasoning behaviors. Fast-Slow Training (FST) is up to 3x more sample-efficient than only slow learning (RL) across reasoning tasks, while consistently reaching a higher performance asymptote. Moreover, FST-trained models remain closer to the base LLM (up to 70% less KL divergence), resulting in less catastrophic forgetting than RL-training. This reduced drift also preserves plasticity: after training on one task, FST trained models adapt more effectively to a subsequent task than parameter-only trained models. In continual learning scenarios, where task domains change on the fly, FST continues to acquire each new task while parameter-only RL stalls.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a Fast-Slow Training (FST) framework for LLMs that treats model parameters as slow weights and optimized context as fast weights. It claims that jointly optimizing both yields up to 3x higher sample efficiency than pure RL parameter updates on reasoning tasks, higher asymptotic performance, up to 70% less KL divergence from the base model (reducing catastrophic forgetting), and better preservation of plasticity for subsequent tasks in continual learning scenarios.

Significance. If the empirical results hold under rigorous controls, the work provides a practical bridge between in-context adaptation and parameter-based learning, offering a concrete mechanism to mitigate forgetting while retaining general capabilities. This dual-timescale approach could influence continual learning methods for LLMs by demonstrating that context optimization can absorb task-specific information without forcing large parameter drift.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Experiments): the central quantitative claims (3x sample efficiency, 70% less KL divergence, higher asymptote) are stated without reference to the specific reasoning tasks, number of independent runs, variance, or statistical tests; this leaves the load-bearing performance comparison unverified and requires explicit tables or figures with controls against standard RL baselines.
  2. [§3.2] §3.2 (Fast weight optimization): the assumption that textual feedback can be absorbed into context (fast weights) while keeping slow weights close to the base model is load-bearing for the forgetting and plasticity claims, yet no ablation is described that isolates whether context updates alone suffice or whether interference occurs when tasks share reasoning structure.
minor comments (2)
  1. [Introduction] The citation to dual-process theories (System 1 vs. 2) in the introduction would benefit from one or two additional references to recent cognitive science literature on multi-timescale learning.
  2. [§3] Notation for fast vs. slow weights should be introduced with a clear equation or diagram early in §3 to avoid ambiguity when discussing KL divergence and plasticity metrics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will make revisions to improve the clarity and rigor of the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experiments): the central quantitative claims (3x sample efficiency, 70% less KL divergence, higher asymptote) are stated without reference to the specific reasoning tasks, number of independent runs, variance, or statistical tests; this leaves the load-bearing performance comparison unverified and requires explicit tables or figures with controls against standard RL baselines.

    Authors: We agree that the quantitative claims require more precise reporting for verifiability. The results are aggregated over multiple reasoning tasks (including GSM8K-style arithmetic and multi-step logical deduction benchmarks). In the revised manuscript we will add a dedicated table in §4 listing each task, the number of independent runs (5 per condition), mean performance with standard deviations, and p-values from paired t-tests against the RL baseline. Learning curves in the relevant figures will include error bars, and we will explicitly reference these details in the abstract. revision: yes

  2. Referee: [§3.2] §3.2 (Fast weight optimization): the assumption that textual feedback can be absorbed into context (fast weights) while keeping slow weights close to the base model is load-bearing for the forgetting and plasticity claims, yet no ablation is described that isolates whether context updates alone suffice or whether interference occurs when tasks share reasoning structure.

    Authors: We acknowledge the value of an explicit ablation isolating context-only optimization, especially for tasks with shared reasoning structure. Our current comparisons (FST vs. parameter-only RL) already demonstrate reduced KL divergence and preserved plasticity, but we did not report a dedicated context-only condition on overlapping tasks. In the revision we will add this ablation to §3.2 and §4, including experiments that optimize only context on sequential tasks with shared structure to quantify interference and confirm that joint optimization is necessary for the reported gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents FST as an empirical training framework separating slow parameter updates from fast context optimization, with performance claims (3x sample efficiency, 70% lower KL divergence, preserved plasticity) supported by direct experimental comparisons to RL baselines on reasoning tasks. No equations, uniqueness theorems, or self-citations are invoked to derive results by construction; the separation of timescales is introduced as a modeling choice motivated by human learning analogies rather than proven from prior self-work. All reported outcomes are measured outcomes on held-out tasks and continual scenarios, not reductions of fitted parameters renamed as predictions. The central claims remain falsifiable via external benchmarks and do not collapse to input definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claim rests on the separation of learning speeds and the ability of context optimization to act as fast weights without disrupting slow weights, with no free parameters or invented entities detailed beyond the framework itself.

axioms (2)
  • domain assumption In-context learning with fixed parameters can adapt to tasks but cannot by itself match performance gains from updating parameters
    Used to motivate the need for combining both approaches.
  • domain assumption Humans learn at different time scales such as System 1 vs System 2
    Analogy invoked to justify the fast-slow framework.
invented entities (2)
  • fast weights as optimized context no independent evidence
    purpose: To absorb task-specific information rapidly from textual feedback
    Core component of the proposed framework.
  • slow weights as model parameters no independent evidence
    purpose: To persist general reasoning behaviors close to the base model
    Core component of the proposed framework.

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discussion (0)

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