In real-world applications, event data is typically received in a streaming manner, where the distribution of patterns may shift over time. Additionally, privacy and memory constraints are commonly observed in practical scenarios, further compounding the challenges.

For example, transactions infinancial systems, serverlogs, and user activity traces can allnaturally be represented as discrete events in continuous time.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate $η$ and weight decay $λ$. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, $τ= B/(ηλD)$, should remain constant across training settings, and we verify the implication that optimal $λ$ scales linearly with B, for a fixed N and D. However, as N and D scale, we show optimal $τ$ obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict $λ$opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast to prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives. All experiments were run on Cerebras CS-3 systems.

Continual pre-training (CPT) for domain adaptation must balance target-domain gains with stability on the base domain. Existing CPT scaling laws typically assume a fixed pre-training budget, which limits their ability to forecast adaptation outcomes for models trained at different tokens-per-parameter (PTPP). We present \emph{PTPP-aware} adaptation scaling laws that make the pre-training budget an explicit variable, enabling accurate \emph{prediction} of adaptation loss at unseen \ptpp. On a multilingual setup (English/Arabic $\rightarrow$ French), PTPP-aware formulations trained on early stages (\ptpp{}=\{15,31\}) predict target loss at \ptpp{}=279 and outperform a PTPP-agnostic \dcpt{} transfer baseline on metrics (Huber-on-log, MAE$_\mathrm{rel}$, calibration slope); full diagnostics (RMSE, MAPE) are in the appendix. Beyond forecasting, we show a practical use case: planning replay ratios and adaptation token budgets that satisfy target and forgetting constraints under compute limits.

Temporal point processes are powerful generative models for event sequences that capture complex dependencies in time-series data. They are commonly specified using autoregressive models that learn the distribution of the next event from the previous events. This makes sampling inherently sequential, limiting efficiency. In this paper, we propose a novel algorithm based on rejection sampling that enables exact sampling of multiple future values from existing TPP models, in parallel, and without requiring any architectural changes or retraining. Besides theoretical guarantees, our method demonstrates empirical speedups on real-world datasets, bridging the gap between expressive modeling and efficient parallel generation for large-scale TPP applications.

Event data is abundant in the real world and is encountered in various important applications.