Batch Size

Stochastic gradient descent (SGD) is the primary workhorse for large-scale optimization. While the average behavior of its iterates, typically characterized by mean-squared error bounds, is well-understood, obtaining high-probability guarantees for the last iterate remains challenging. Prior approaches to this problem have either imposed restrictive assumptions (such as bounded domains or gradients) or relied on complex proofs involving auxiliary sequences. In this work, we propose Batched SGD, a simple variant that partitions online samples into epochs and performs a single update per epoch using a refined, low-variance gradient estimate. Our main contribution demonstrates that this batching mechanism enables a surprisingly simple high-probability analysis that avoids both restrictive assumptions and auxiliary sequences. Under standard smoothness and norm-sub-Gaussian noise assumptions, we establish near-optimal rates for both strongly convex and non-convex objectives. Furthermore, we show that our batching idea extends naturally to federated learning (FL). We provide the first high-probability guarantees for FL, achieving logarithmic communication complexity, linear speedup in the number of agents, and resilience to data heterogeneity.

The rise of privacy-preserving artificial intelligence (AI) has shifted the focus of model adaptation and personalization towards on-device learning, where deep learning models are finetuned directly on edge hardware using local user data. However, this shift requires optimization of deep learning training on resource-constrained hardware to maximize throughput while maintaining predictive accuracy. This paper introduces a novel technique for on-device model training that incorporates an efficient Bayesian optimization-based batch size tuning approach to maximize hardware throughput. To evaluate the impact of this hyperparameter on the learning dynamics, we investigated two distinct paradigms: standard supervised learning (SL) and online continual learning (CL). Experimental results across various edge devices demonstrate a throughput ceiling, beyond which increasing the batch size yields no additional throughput gains. The proposed tuning approach identifies the optimal batch size, which, when combined with gradient accumulation and linear learning rate scaling, achieves up to a 2X increase in training throughput on platforms such as Raspberry Pi 4 compared to maximum batch sizes, without compromising model accuracy. Furthermore, in the CL paradigm, we demonstrate that optimal batch sizes maintain the stability-plasticity balance required for incremental learning, effectively mitigating catastrophic forgetting while maximizing computational efficiency on edge-hardware.

Every supervised fine-tuning run forces the same chain of decisions, such as learning rate, batch size, LoRA or full fine-tuning, how many epochs, which optimiser, and what data to feed the model. Each of these is typically rediscovered from scratch for every new model and dataset. Here we measure them under one instrument: a sweep that varies one lever at a time, and spans dense and mixture-of-experts models in two families (Qwen3 and Llama), on four real-world customer SFT datasets, for both LoRA and full fine-tuning. These datasets give a controlled testbed: each task carries an evaluation built with the customer, and its training data is produced by iterative supervised fine-tuning that refines model outputs until they pass that evaluation, so the supervised target is internally consistent and the task judge we report against is the criterion the data was built to satisfy. We ask how the optimal learning rate and batch size move with model scale, family, and data, and whether one selection rule transfers across them; what LoRA trades against full fine-tuning, and how its rank and alpha set what the adapter can learn; whether validation loss (or other metrics, such as loss landscape flatness) faithfully ranks downstream quality; whether post-training gains scale with model size and data volume, on a model ladder extended through mixtures-of-experts to 235B parameters; how many epochs to train before general instruction-following erodes; and whether a geometry-aware optimiser improves on AdamW. Each recommendation is paired with a measure of its uncertainty.

We study the scaling behavior of learning rate and batch size in pretraining dense large language models on English-prevalent corpora. Beyond scaling jointly optimal learning rates and batch sizes, we investigate their marginal evolution with model capacity and data scale and develop a model that captures these relationships. As we employ a Warmup-Stable-Decay learning rate schedule, we further investigate the gains from learning rate annealing over a broad range of hyperparameters settings, models and data budgets, and whether the optimal learning rate and batch size transfer between the stable and decay phases. Finally, we characterize the dependence of loss on model capacity and dataset size, evaluating recently proposed scaling forms that explicitly model their interaction. We find these approaches particularly effective at capturing both undertraining and overtraining regimes across our experiments. This study establishes a first baseline and scaling procedure for the development of future OpenEuroLLM models. We open-source the complete collection of pretraining runs used in this study.

Acceleration for deterministic root-finding problems has been extensively studied in recent years; specifically, the anchor-based, or Halpern-type methods achieve optimal convergence rates with respect to the operator norm. However, acceleration via these methods does not directly carry over to stochastic setting due to accumulation of errors, unless one enforces diminishing variance via increasing batch sizes or variance reduction techniques. In this work, we show that another class of acceleration, namely the dual-anchor mechanism, extends to the stochastic setting without such error accumulation, in contrast to anchor-based algorithms. Consequently, we cleanly achieve $O(ε^{-3})$ complexity with iteration-independent batch size, without any variance reduction or double-loop recursive regularization, for stochastic root-finding (resp. fixed-point) problems with cocoercivity (resp. square-nonexpansivity) in expectation. For strongly monotone operators, the same algorithm attains a sharper $\widetilde{O} (ε^{-2})$ complexity, nearly matching the lower bound in terms of $ε$-dependence.

Tokenizer vocabulary size is a foundational design choice in large language model (LLM) infrastructure, yet it is typically fixed at training time based on convention rather than deployment analysis. We show that the cost-optimal vocabulary is not a constant but a function of the serving regime. We formalize total deployment cost as $C_{lifecycle}(V) = C_{train}(V) + λ\cdot C_{infer}(V, B)$, where $λ$ is inference volume and $B$ is the serving batch size. Through controlled experiments on two GPU families spanning the memory-bound to compute-bound regimes (A10G, ridge $\approx$ 117 FLOP/byte; A100, ridge $\approx$ 183 FLOP/byte), we demonstrate: (1) the inference-optimal vocabulary shifts 16x with serving batch, from 32k at $B=1$ to 524k at $B=64+$, driven by amortization of the $V \times d$ unembedding matrix read; (2) at 1.3-2.3B model scale, quality (bits per byte, BPB) is optimized at $V=65$k, confirming scale-dependent vocabulary preference; (3) the lifecycle-optimal vocabulary diverges from training-optimal by up to 16x for production deployments. Quality is approximately invariant across the optimal range ($<$2% BPB spread), making vocabulary a pure systems optimization with no quality penalty in the measured range. Our results provide actionable capacity planning guidance: on-device deployments ($B=1$) should use $V \approx 32$k; datacenter serving ($B \geq 64$, $λ\geq 10$) should use $V \approx 131$-262k.

Large-scale neural recommender systems are typically trained with a softmax cross-entropy objective over the full item vocabulary. For a typical large number of possible items $K$, the final classification layer dominates memory, requiring $O(nK)$ logits and gradients to materialize for a batch of $n$ examples. Sampled softmax reduces this cost by restricting the objective to only $k \ll K$ candidate negative items, resulting in an $O(nk)$ memory. However, for a fixed budget $B = n k$, it remains unclear whether one should prioritize larger batches or the inclusion of more negative items. We address this question by analyzing sampled-softmax training under a fixed memory constraint. Under standard smoothness and variance assumptions, our theoretical evidence suggests that the fastest convergence arises from an $n \sim B, k \sim 1$ allocation. So, an actionable rule is to include as many objects as possible given computational constraints. Our theory is supported by controlled synthetic and synthetic and four real sequential recommendation benchmarks, including MovieLens-20M. The suggested configuration achieve faster convergence and better final recommendation quality than imbalanced alternatives within the same memory constraint. These findings provide a theoretical and empirical foundation for configuring memory during the training of recommender systems. Code, reproducibility materials, and all scripts for generating figures are available at https://anonymous.4open.science/r/LimitedMemoryRule-BBFB

Modern deep learning typically keeps the batch size static throughout training, thus overlooking the joint effect of learning rate and batch size on the training dynamics. In this paper, we study the deep learning dynamics through the lens of convex optimization and derive a joint characterization of loss in terms of both schedules, applicable to general optimizers and model architectures. This characterization yields a closed-form optimal batch size schedule for any prescribed learning rate schedule, and further leads to joint scaling laws that consistently outperform static batch size baselines, highlighting the significance of dynamic batch size schedule in large language model training.

State-space sequence models are attractive for streaming speech because they maintain compact recurrent state, but scan-style training kernels can have unfavorable constants for short audio tasks. We study cumsum-composable phase transport, a streaming-native temporal layer for keyword spotting. Each layer projects acoustic frames to complex channels, transports them by learned unitary rotations, accumulates a finite window using prefix differences, and applies a gated residual update. The same prefix representation gives exact batched training with ordinary cumulative sums and exact online inference with one prefix update per frame. Unitary transport is the key constraint: inverse rotations have norm one, keeping prefix terms well conditioned while memory is supplied by windows or block readouts. On Google Speech Commands v2 with 12 labels, mel+cumsum models retain competitive accuracy with compact baselines. The strongest single-seed run reaches 97.3% test accuracy; a 51.6K-parameter tied model also reaches 97.3%, and a 24.8K tied model reaches 96.8% versus 97.1% for a 25.6K MelCNNMaxPool baseline. In a matched cumsum-versus-scan benchmark, cumsum+window gives comparable accuracy, 94.82% versus 94.33%, while training 1.07x faster and reducing single-example latency from 7.09 ms to 5.01 ms on a Tesla T4. These results support cumsum phase transport as a simple low-cost temporal primitive for streaming keyword spotting.

Common practice when training Convolutional Neural Networks (CNNs) is to use randomly shuffled mini-batches. This creates two limitations: slower convergence, and a diminishing learning signal, since many samples are quickly classified as easy during training. We address these inefficiencies with A*-Inspired Batch Selection (A*-BS), a lightweight, model-agnostic strategy that formulates mini-batch scheduling as a heuristic search problem. Each batch is treated as a node in a search space and ranked using an A*-like score combining a loss-based difficulty measure with a reuse penalty. This encourages informative gradient updates and batch diversity throughout training, without modifying network architectures or optimization algorithms, so it integrates seamlessly into existing pipelines. We evaluate A*-BS on the twelve 2D classification tasks of the MedMNIST-v2 benchmark, using a deliberately simple architecture of approximately 2.25x10^5 parameters, compared against the ResNet-18 and ResNet-50 baselines reported by the benchmark. On half of these tasks, the lightweight model with A*-BS reaches higher accuracy and AUC than both ResNet baselines, with relative gains of up to 15%. An ablation under identical architecture and hyperparameters shows A*-BS outperforms random batch shuffling on all twelve tasks. Wall-clock measurements further show the lightweight CNN with A*-BS trains substantially faster than ResNet-18 and ResNet-50 on identical hardware. These results indicate that intelligent batch ordering can partially compensate for reduced architectural complexity, offering a computationally efficient alternative to deeper models, with reliability reinforced by strong performance even against deeper, more sophisticated architectures.

We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law). Fitting the proposed law on a large set of training runs, we find that it correctly recovers the scaling of the optimal batch size. Moreover, because it makes use of training runs with suboptimal batch size, our proposed law can be robustly fit with a significantly smaller amount of training runs. We further show that the three-term law can be used to derive scaling laws for suboptimal batch sizes, and that it matches previous empirical findings related to the critical batch size.

Test-Time Adaptation (TTA) enables models trained on a source domain to adapt online to unlabeled test data under distribution shifts. While recent TTA methods have moved beyond static settings and begun to consider continual domain shifts, they primarily address distribution drift and fail to account for class imbalance in dynamic scenarios. In real-world test-time streams, class imbalance and continual domain shifts often occur at the same time and interact with each other. In this paper, we propose a novel Balanced and Prototype-Guided Test-Time Adaptation (BP-TTA) method, which combines batch-balanced sampling with prototype-guided adaptation to handle the class imbalance and continual domain shift problems. BP-TTA constructs balanced adaptation batches by integrating current samples with high-confidence historical instances, effectively mitigating bias toward dominant classes and stabilizing online updates. Meanwhile, BP-TTA maintains evolving class prototypes during inference and leverages prototype similarity as a constraint for model adaptation, thereby improving the reliability of pseudo-labels and enhancing the stability of online updates under persistent domain shifts. Extensive experiments demonstrate that BP-TTA consistently outperforms state-of-the-art TTA methods in dynamic test-time streaming settings.

Stochastic momentum methods such as heavy ball (HB), Nesterov momentum, and variants of Accelerated SGD (ASGD) [Kidambi et al., 2018] are widely used in modern training, but their stochastic benefits depend on two distinct quantities: serial runtime, the number of iterations needed to reach a target accuracy, and compute efficiency (CE), the inverse total gradient-query or FLOP cost. Larger batches reduce serial runtime without hurting CE only when the contraction gap grows linearly with batch size. We study stochastic HB and ASGD for consistent linear regression with Gaussian covariates and prove finite-dimensional, discrete-time lower bounds on their batch-size tradeoffs. Our first result shows that HB does not improve the CE frontier over SGD for arbitrary spectra; rather, it preserves SGD-level CE over a larger batch-size window, allowing larger batches to reduce serial runtime until HB reaches its deterministic accelerated scale. This window can be a factor $\sqrtκ$ larger than the SGD critical batch size. For ASGD, the picture is more spectrum-dependent: for rapidly decaying power-law spectra, ASGD improves small-batch CE over HB/SGD, but as batch size grows it trades this CE advantage for improved serial runtime. Synthetic linear-regression experiments verify these qualitative regimes, including near-overlap of ASGD and HB for slowly decaying spectra and the predicted CE--serial tradeoff for rapidly decaying spectra.

Conventional wisdom holds that large-batch training is fundamentally incompatible with Reinforcement Learning (RL) - beyond a modest threshold, increasing batch sizes typically yields diminishing returns or performance degradation due to the inherent non-stationarity of the data distribution. We challenge this view by observing that non-stationarity is not a fixed property of RL, but evolves throughout training: early stages exhibit rapid behavioral shifts that demand small batches for plasticity, whereas late stages approach a quasi-stationary regime where large batches enable precise convergence. Motivated by this observation, we propose Adaptive Batch Scaling (ABS), that dynamically adjusts the effective batch size according to the stability of the learning policy. Central to ABS is Behavioral Divergence, a novel metric that quantifies policy non-stationarity by measuring action-level shifts between consecutive updates, which we use to scale batch size inversely to policy volatility. Integrated with the Parallelised Q-Network (PQN) algorithm and evaluated on the ALE benchmark, ABS seamlessly reconciles early-stage plasticity with late-stage stable convergence. Strikingly, contrary to conventional wisdom, our results reveal that the combination of larger networks and larger batch sizes achieves the best performance - a scaling behavior previously thought to be unattainable in RL, now unlocked through adaptive batch control.

Accelerating stochastic gradient methods with classical momentum schemes, such as Polyak's heavy ball, has proven highly successful in training large-scale machine learning models, particularly when combined with the hardware acceleration of large mini-batch computations. Yet, the effect of classical momentum on stochastic mini-batch optimization has been poorly understood theoretically, with prior works requiring strong noise assumptions and extremely large mini-batches. In this work, we develop a general theory of stochastic momentum acceleration for optimizing over quadratics in the interpolation regime, a popular abstraction for studying deep learning dynamics which also includes classical methods such as randomized Kaczmarz and coordinate descent. Our framework encompasses both heavy ball and Nesterov-style momentum, allows for arbitrary mini-batch sizes, and makes minimal assumptions on the stochastic noise. In particular, we show that acceleration from classical momentum is directly proportional to the gradient mini-batch size (up to a natural saturation point), thereby enabling perfect parallelization of mini-batch computations. Our theory also provides a simple choice for the momentum parameter, which is shown to be effective empirically.

Reinforcement learning is structurally harder than supervised learning because the policy changes the data distribution it learns from. The resulting fragility is especially visible in large-model training, where the training and rollout systems differ in numerical precision, sampling, and other implementation details. Existing methods manage this fragility by adding hyper-parameters to the training objective, which makes the algorithm more sensitive to its configuration and requires retuning whenever the task, model scale, or distribution mismatch changes. This fragility traces to two concerns that current objectives entangle through hyper-parameters set before training begins: a trust-region concern, that updates should not move the policy too far from its current value, and an off-policy concern, that data from older or different behavior policies should influence the update only to the extent that it remains reliable. Neither concern is a constant to set in advance, and their severity is reflected in the policy-ratio distribution of the current batch. We present a simple yet effective batch-adaptive objective that replaces fixed clipping with the normalized effective sample size of the policy ratios. The same statistic caps the score-function weight and sets the strength of an off-policy regularizer, so the update stays close to the usual on-policy score-function update when ratios are nearly uniform, and tightens automatically when stale or mismatched data cause ratio concentration, while retaining a nonzero learning signal on high-ratio tokens. Experiments across a wide range of settings show that our method matches or exceeds tuned baselines, introducing no new objective hyper-parameters and removing several existing ones. The code is available at https://github.com/FeynRL-project/FeynRL.

Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce numerical integration cost. Yet, the population-level coupling induced by repeated minibatch OT remains only partially understood. We formalize this coupling as the expected batch OT plan $\overlineπ_{k}$, obtained by averaging empirical OT plans over independent minibatches of size $k$. We then establish its large-batch consistency and, in the semidiscrete case relevant to generative modeling, derive rates for both the transport-cost bias and the convergence of $\overlineπ_{k}$ to the OT plan. For FM, this yields a population coupling whose induced velocity field is regular enough to define a unique flow from the source to the discrete target. We finally quantify how OT batch size interacts with numerical integration in a tractable two-atom model and in synthetic and image experiments.

We introduce a predictive model that estimates the pre-training loss of large models from model size (N), batch size (B) and number of weight updates (K). This is the first loss prediction model that can handle changing batch size. The model outperforms Chinchilla's loss model, a model of the test loss using the batch size and number of tokens, in terms of projecting the loss at extrapolated compute budgets (up to 1000 folds). A natural use of the model is to find optimal N, B, K configurations under explicit and compound resource constraints like time, memory and compute. In our experiments, the model-selected configurations are close to ground-truth optimal. Our work advocates for loss prediction as a better alternative to heuristic-based laws, which are growing in complexity. The implementation is available on https://github.com/chuningxdy/Noisy-Quadratic-System.

Auto-regressive token generation in large language models is memory-bound because it requires "attending to" key and value tensors (KV cache) of all previous tokens. Prior work aims to improve the efficiency of this decode process by batching multiple requests together, and maximizing batch size subject to GPU memory constraints. The key observation of our work is that with prefix-sharing workloads, smaller, prefix-homogeneous batches -- where all requests share a common prefix -- can achieve higher decode throughput than larger, heterogeneous batches, due to better spatial and temporal locality during KV cache accesses. However, prefix-aware schedulers in state-of-the-art inference engines maximize prefix reuse within a batch only to reduce KV cache memory footprint, but do not stop batch formation at smaller homogeneous batches that could have performed better. Further, we show that shared prefix detection in existing schedulers relies on radix-tree traversals, incurring substantial CPU overhead that is often comparable to GPU execution time. This paper presents Feather, a prefix-aware scheduler that uses reinforcement learning (RL) to learn the optimal tradeoff between batch size and prefix homogeneity. We also introduce Chunked Hash Tree (CHT), a lightweight data structure that enables fast prefix detection and efficient request selection for the RL scheduler, avoiding expensive tree traversals. We integrate Feather into vLLM and SGLang, and our evaluation shows that Feather achieves 2--10$\times$ higher end-to-end throughput as compared to existing schedulers, while doing no worse than the status quo when the workload does not have enough prefix sharing. Feather achieves these gains by reducing the total number of KV cache accesses, surpassing the performance of prefix-aware attention kernels that have the same goal.

Systematic reviews and meta-analyses frequently require numerical data that authors report only as figures, yet manual digitisation is slow and does not scale. We present PlotPick, an open-source tool that uses vision-language models (VLMs) to batch-extract structured tabular data from scientific figures. We evaluate six VLMs from three providers on two established chart-to-table benchmarks (ChartX and PlotQA) and compare against the dedicated chart-to-table model DePlot. All six VLMs outperform DePlot on both benchmarks. On ChartX (restricted to bar charts, line charts, box plots, and histograms; n=300), VLMs achieve 88-96% recall versus 71% for DePlot. On PlotQA (n=529), VLMs achieve 86-99% RMSF1 versus 94% for DePlot. The gap is largest on chart types absent from the dedicated models' training data: on box plots, DePlot achieves 24% RMSF1 while VLMs achieve 83-97%. PlotPick is available at https://plotpick.streamlit.app.

Dynamic quantization emerged as a practical approach to increase the utilization and efficiency of the machine learning serving flow. Unlike static quantization, which applies quantization offline, dynamic quantization operates on tensors at run-time, adapting its parameters to the actual input data. Today's mainstream machine learning frameworks, including ML compilers and inference engines, frequently recommend dynamic quantization as an initial step for optimizing model serving. This is because dynamic quantization can significantly reduce memory usage and computational load, leading to faster token generation and improved model serving efficiency without substantial loss in model accuracy. In this paper, we reveal a critical vulnerability in dynamic quantization: an adversary can exploit such quantization strategy to steal sensitive user data placed in the same batch as the adversary's input. Our analysis demonstrates that dynamic quantization, when improperly implemented or configured, can create side channels that expose information about other inputs within the same batch. We call this phenomenon Quantamination, describing contamination from quantization. Specifically, we show that at least 4 of the most popular ML frameworks in use today either default to or can use configurations that leak data across the batch boundary. This data leakage, in theory, allows attackers to partially or even fully recover other users' batched input data, representing a serious privacy risk for existing ML serving frameworks.

Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to propose draft tokens that are subsequently verified by a larger target model. However, the performance of standard SD is often limited by the strictly sequential execution of these drafting and verification stages. To address this, this paper proposes MineDraft, a batch parallel speculative decoding (PSD) framework designed to effectively hide drafting latency by overlapping it with verification. Our theoretical analysis shows that PSD is substantially more efficient than standard SD. MineDraft realizes the PSD through a novel batch-parallel design that maintains two batches of requests, overlapping drafting for one batch with verification for the other. Our experimental results show significant improvements of \alg{} in both throughput (up to 75%) and end-to-end latency (up to 39%) over standard SD. Furthermore, we have implemented MineDraft as a plugin for vLLM, demonstrating its practicality for production-ready inference systems.

To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune. Existing adaptive strategies based on gradient noise scale (GNS) offer a principled alternative. However, their assumption of SGD's Euclidean geometry creates a fundamental mismatch with popular optimizers based on generalized norms, such as signSGD / Signum ($\ell_\infty$) and stochastic spectral descent (specSGD) / Muon ($\mathcal{S}_\infty$). In this work, we derive gradient noise scales for signSGD and specSGD that naturally emerge from the geometry of their respective dual norms. To practically estimate these non-Euclidean metrics, we propose an efficient variance estimation procedure that leverages the local mini-batch gradients on different ranks in distributed data-parallel systems. Our experiments demonstrate that adaptive batch size strategies using non-Euclidean GNS enable us to match the validation loss of constant-batch baselines while reducing training steps by up to 66% for Signum and Muon on a 160 million parameter Llama model.

Inference optimizations are routinely evaluated by throughput alone, without verifying output correctness. We conduct a forensic analysis of batch speculative decoding and find that several widely-used implementations silently produce corrupted outputs (repetitive tokens, <unk> symbols) while reporting competitive speed; failures invisible to metrics like ROUGE. We trace the root cause to the ragged tensor problem: variable token acceptance desynchronizes position IDs, attention masks, and KV-cache across a batch. We formalize the synchronization invariants (rectangular alignment and position-ID contiguity) that valid batched inference must preserve and show that maintaining them incurs superlinear alignment overhead under contiguous layouts. EQSPEC enforces the invariants without custom kernels; EXSPEC schedules same-length sequences to bypass realignment. On SpecBench across three model families, EXSPEC reaches 3 x throughput at batch size 8 with 95% exact match to standard decoding; residual divergence traces to floating-point non-determinism, not synchronization error. Code:https://github.com/eBay/spec_dec

Temporal graph networks suffer from irregular supervision in realworld dynamic graphs, as most minibatches contain few labeled events. The lack of labels leads to high-variance gradient updates and, consequently, slow wall-clock convergence. To constructively reduce sparsity, our Moving-Averaged Labels (MAL) assigns soft pseudo-targets based on past supervised signals using a running label distribution while leaving the loss and the model architecture unchanged. Thus, supervision gaps are replaced with informative signals independent of a temporal graph model and the message passing or memory components used. Theoretical analysis supports our insight that aggregating historical supervision into moving average targets reduces stochastic gradient variance, yielding faster convergence under mild assumptions. Experimentally, for TGNv2 and DyRepv2 (our modification of DyRep) models, MAL boosts predictive performance, establishing a new SOTA, and improves time-to-accuracy (on average 6x faster to reach the top score) for a common suite of Temporal Graph Benchmark datasets.