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Meta-Experience Replay (MER)

Updated 7 July 2026
  • Meta-Experience Replay (MER) is a continual learning approach that combines memory replay with first-order meta-learning to promote positive gradient alignment and mitigate interference.
  • It employs reservoir sampling and Reptile-style meta-updates to approximate gradient alignment, reducing catastrophic forgetting on non-stationary data streams.
  • MER has shown improved retention across domains, from lifelong language learning to large-scale continual pre-training, demonstrating its practical advantage over replay-only methods.

Searching arXiv for the cited MER papers to ground the article in recent sources. Meta-Experience Replay (MER) is a continual-learning method that combines experience replay with optimization-based meta-learning so that updates on new data become less likely to interfere with past knowledge and more likely to transfer positively. In the original formulation, MER addresses online learning over non-stationary streams by using replay to approximate training on past experience and Reptile-style first-order meta-learning to encourage positive gradient alignment across examples. Subsequent work adapted the same core idea to lifelong language learning with sparse experience replay and, later, to continual pre-training of LLMs under severe distribution shift, where MER is implemented as replay plus periodic Reptile-style parameter interpolation (Riemer et al., 2018, Abbes et al., 3 Aug 2025).

1. Conceptual foundation

MER is grounded in the continual-learning problem in which data arrives as a stream and the learner updates after every experience rather than training offline on a fixed i.i.d. dataset. The original paper characterizes this as the “locally i.i.d.” setting: within a task, data is sampled from one distribution, but across time the distribution shifts. Catastrophic forgetting arises because SGD on a changing stream can improve loss on the current distribution while increasing loss on earlier examples, since shared parameters make new learning capable of overwriting old learning (Riemer et al., 2018).

The central conceptual move is to frame continual learning as a temporally symmetric trade-off between transfer and interference. For two examples, transfer is defined by a positive gradient dot product,

L(xi,yi)θL(xj,yj)θ>0,\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} > 0,

and interference by a negative one,

L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.

This makes forgetting an optimization-geometric phenomenon: if gradients align, an update that helps one example tends also to help the other; if they oppose, the update tends to damage earlier knowledge. The same interpretation is adopted in the later continual pre-training study, which states that if the dot product is positive, updates transfer, and if negative, they interfere (Riemer et al., 2018).

A common misconception is that MER is only a replay strategy. The papers instead treat replay as necessary but not sufficient. Replay reintroduces old data into optimization, but MER adds a meta-learning mechanism intended to shift the distribution of gradient dot products over time so that future updates are more compatible across past and present data. This suggests that MER is best understood as a method for altering both data exposure and update geometry.

2. Formal objective and mechanism

The original MER paper starts from the standard stationary-learning objective

θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],

and augments it with a preference for aligned gradients across examples: θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}]. Because the gradient dot product appears with a minus sign, minimizing the objective favors larger, more positive dot products and therefore more transfer and less interference (Riemer et al., 2018).

MER addresses two practical obstacles identified in that paper. First, the stream is non-stationary, so current examples are not a stationary sample of all data seen so far. Second, differentiating the dot-product regularizer introduces second derivatives. MER addresses the first problem with experience replay and the second with a first-order meta-learning approximation based on Reptile. The Reptile connection is made explicit through the objective

θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],

which already contains the desired gradient-alignment term (Riemer et al., 2018).

The 2025 continual pre-training paper uses the same bridge from Reptile to gradient alignment and reproduces the batch-sequence objective

arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],

interpreting it as ordinary loss minimization plus a regularizer that favors positive pairwise gradient dot products across batches. In both formulations, the key claim is not that MER exactly computes this objective, but that first-order meta-learning approximately optimizes it. This suggests that MER’s distinctive feature is not merely rehearsal, but meta-optimization toward parameter regions in which future updates are better behaved.

3. Algorithmic structure and variants

In its original form, MER maintains a finite memory MM of past examples using reservoir sampling, so that after NN total examples, each seen example has equal probability Msize/NM_{size}/N of being in memory. At each incoming example (x,y)(x,y), MER samples L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.0 batches; each batch contains the current example plus L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.1 random examples from the replay buffer. The current example is always included to preserve plasticity (Riemer et al., 2018).

The algorithm then applies both within-batch and across-batch Reptile meta-updates. For each batch, it processes examples one at a time with SGD,

L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.2

then performs a within-batch meta-update,

L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.3

and after all L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.4 batches performs an across-batch meta-update,

L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.5

The main hyperparameters are L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.6. The paper notes that when L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.7, Algorithm 1 closely approximates the intended objective (Riemer et al., 2018).

The same paper also proposes two variants. “One Big Batch (OBB)” uses one long sequence of L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.8 examples and one Reptile update. “Current Example Learning Rate (CEL)” uses one memory batch and gives the current example an amplified learning rate L(xi,yi)θL(xj,yj)θ<0.\frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta} < 0.9. The paper argues that these variants approximate similar objectives, and reports that CEL often gives a strong accuracy/efficiency tradeoff (Riemer et al., 2018).

A second misconception is that MER is equivalent to full MAML-style second-order meta-learning. The cited works are explicit that MER relies on first-order approximations. Later language-learning and LLM pre-training papers retain this first-order character even when the implementation changes substantially.

4. Language-task and LLM-scale adaptations

A language-learning instantiation appears in “Meta-Learning with Sparse Experience Replay for Lifelong Language Learning,” which does not reintroduce MER under that exact name but builds on the same principle through OML-ER and ANML-ER. The training procedure is episodic: a support set consists of θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],0 consecutive minibatches from the stream, and the query set is either the next minibatch from the stream or a random sample from memory. Replay is sparse in both time and size, controlled by the replay interval θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],1, replay rate θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],2, and write probability θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],3. Because replay is episodic, the replay frequency is

θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],4

OML-ER splits the model into a representation learning network θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],5 and a prediction learning network θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],6, with inner-loop adaptation on the support set and an outer-loop update on query loss. ANML-ER adds a neuromodulatory gating network but follows the same meta-training structure (Holla et al., 2020).

The 2025 continual pre-training paper adapts MER to large-scale LLM training under severe distribution shift. The setting is sequential pre-training on massive corpora: in the main multilingual setup, a Llama-family model is trained on English, then French, then German; in an extended setting it continues through Arabic and Japanese as well, with 100 billion tokens per stage and no resetting of model state or optimizer state between tasks. Replay uses a mixed batch in which a fraction θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],7 is sampled from memory and the remaining θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],8 comes from the incoming stream, with θ=argminθE(x,y)D[L(x,y)],\theta = arg \min_\theta \mathbb{E}_{(x,y) \sim D}[L(x,y)],9 (Abbes et al., 3 Aug 2025).

The LLM-scale implementation is deliberately simplified. MER keeps exactly the same replay batches as ordinary replay and adds a periodic Reptile meta-update: θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].0 with θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].1 and θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].2 in the reported experiments. In appendix pseudocode this appears as

θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].3

Algorithmically, the paper characterizes this as “replay + occasional lookback interpolation.” It emphasizes that this requires no extra forward passes or backward passes over replay or current data, and later quantifies the overhead as “three times the model size in FLOPs every 500 batches,” which it describes as negligible relative to the cost of gradient updates. Replay itself is engineered for scale through disk-backed storage, asynchronous prefetching and caching, offset-based raw-byte storage, and metadata for persistence (Abbes et al., 3 Aug 2025).

5. Empirical behavior across domains

Across the cited literature, MER and MER-style methods are reported to improve retained performance relative to replay-only baselines, with the gap often increasing as non-stationarity increases or memory becomes sparse (Riemer et al., 2018, Holla et al., 2020, Abbes et al., 3 Aug 2025).

Setting Comparison Reported result
MNIST Rotations, memory 5120 GEM vs MER RA θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].4 vs θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].5
MNIST Permutations, buffer 200 GEM vs MER RA θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].6 vs θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].7
Lifelong text classification REPLAY vs OML-ER θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].8 vs θ=argminθE[(xi,yi),(xj,yj)]D[L(xi,yi)+L(xj,yj)αL(xi,yi)θL(xj,yj)θ].\theta = arg \min_\theta \mathbb{E}_{[ (x_i,y_i) , (x_j,y_j) ] \sim D}[L(x_i,y_i)+L(x_j,y_j) - \alpha \frac{\partial L(x_i,y_i)}{\partial \theta} \cdot \frac{\partial L(x_j,y_j)}{\partial \theta}].9
Lifelong relation extraction REPLAY vs OML-ER θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],0 vs θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],1
6B continual pre-training 25% replay vs 25% replay + Reptile retained loss θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],2 vs θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],3
6B continual pre-training 50% replay vs 50% replay + Reptile retained loss θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],4 vs θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],5

The original MER paper provides direct mechanism evidence through gradient-dot-product analysis. Mean dot product between gradients of incoming examples and sampled past examples shifts from negative under ER to slightly positive under MER: for MNIST Permutations, ER θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],6 versus MER θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],7; for MNIST Rotations, ER θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],8 versus MER θ=argminθEB1,...,BsD[2i=1s[L(Bi)j=1i1αL(Bi)θL(Bj)θ]],\theta = arg \min_\theta \mathbb{E}_{B_1, ..., B_s \sim D}[2 \sum_{i=1}^s [L(B_i) - \sum_{j=1}^{i-1} \alpha \frac{\partial L(B_i)}{\partial \theta} \cdot \frac{\partial L(B_j)}{\partial \theta}]],9; for Many Permutations, ER arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],0 versus MER arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],1. This is presented as support for the claim that MER changes the gradient distribution from net interference to slight positive transfer (Riemer et al., 2018).

The NLP paper reports similar patterns under a single-pass, no-task-ID setting. On lifelong text classification, SEQ gives arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],2, REPLAY arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],3, and both OML-ER and ANML-ER arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],4. On lifelong relation extraction, SEQ gives arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],5, REPLAY arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],6, OML-ER arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],7, and ANML-ER arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],8. The ablations show that removing replay produces large drops, indicating that meta-learning alone does not replace rehearsal (Holla et al., 2020).

The LLM continual pre-training study reports that “50% replay with Reptile consistently achieves the lowest average forgetting score” across all model sizes, and that in a five-task setup “replay-based strategies, particularly 50% replay with Reptile, maintain strong performance, even achieving negative forgetting.” Retained-loss and learned-loss tables show systematic gains from adding Reptile on top of replay. The downstream results are described as noisier, but at 6B the average benchmark score rises from arg minθtEB1,...,Bk[2i=1k[L(Bi)j=1i1βL(Bi)θtL(Bj)θt]],\argmin_{\theta_t} \mathbb{E}_{B_1, ..., B_k}[2 \sum_{i=1}^k [L(B_i) - \sum_{j=1}^{i-1} \beta \frac{\partial L(B_i)}{\partial \theta_t} \cdot \frac{\partial L(B_j)}{\partial \theta_t}]],9 with 25% replay to MM0 with 25% replay + Reptile, and from MM1 with 50% replay alone to MM2 with 50% replay + Reptile (Abbes et al., 3 Aug 2025).

6. Tradeoffs, limitations, and adjacent concepts

MER is not a no-memory method. The original formulation depends on an episodic buffer, and its derivation is approximate, relying on first-order Taylor expansions, replay approximating a stationary sample of past data, and randomization assumptions. It also introduces additional hyperparameters—MM3 in the original formulation, and replay rate MM4, Reptile interval MM5, and interpolation coefficient MM6 in the LLM adaptation—which the cited papers do not exhaustively characterize (Riemer et al., 2018, Abbes et al., 3 Aug 2025).

Relative to replay-only methods, MER adds computation, although the size of that addition depends on the implementation. The original paper states that MER is more expensive than vanilla SGD and plain replay because each incoming example triggers multiple sequential updates and meta-updates. By contrast, the LLM pre-training paper argues that its Reptile-based approximation adds “negligible overhead, both in terms of compute and memory requirements,” because it requires only a parameter snapshot and periodic interpolation, while the main compute cost still comes from replay itself. That paper is explicit that 50% replay means about MM7 more FLOPs per gradient step than 0% replay for fixed model size, and its scaling conclusion is that “small rates of replaying old examples are definitely a more valuable use of compute than investing in model size, but that it is more compute efficient to scale the size of the model than invest in high rates of replaying old examples” (Abbes et al., 3 Aug 2025).

MER is also distinct from several neighboring families of methods. Relative to EWC, the original paper presents MER as more forward-looking: instead of protecting parameters deemed important for past tasks, it tries to learn parameters that make future updates more likely to transfer positively. Relative to GEM, A-GEM, or PCGrad, the 2025 paper emphasizes that its approach avoids explicit constrained optimization or gradient surgery per step; the preference is for a meta-learning mechanism through which “the network can learn to shift its distribution of gradient dot products over the course of learning rather than performing adhoc gradient projections only associated with a single batch” (Riemer et al., 2018, Abbes et al., 3 Aug 2025).

A further distinction concerns the use of “meta-experience” in later work. “Internalizing Meta-Experience into Memory for Guided Reinforcement Learning in LLMs” is described as highly relevant in spirit but not literally a replay-buffer method. Its main contribution is characterized as extract–validate–distill: it derives reusable knowledge from correct and incorrect reasoning trajectories, validates that knowledge by replaying it in context, and internalizes it into parametric memory. The paper’s own summary is that MEL “should be viewed as a meta-experience extraction-and-consolidation framework with a replay-based validation stage, rather than a pure Meta-Experience Replay method.” This clarifies that MER, in the narrow algorithmic sense, remains the replay-plus-meta-learning family defined by the continual-learning literature rather than any broader system that reuses “meta-experience” (Huang et al., 10 Feb 2026).

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