# Target-Constrained Pooling for Trajectory Extrapolation

arXiv: https://arxiv.org/abs/2610.13034 · HTML: https://mlsanity.com/paper/2610.13034/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [A Survey on Negative Transfer](https://mlsanity.com/paper/2009.00909/) (2020)
- [On the Value of Target Data in Transfer Learning](https://mlsanity.com/paper/2002.04747/) (2020)
- [A Hitchhiker's Guide to Scaling Law Estimation](https://mlsanity.com/paper/2410.11840/) (2024)
- [How Much More Data Do I Need? Estimating Requirements for Downstream Tasks](https://mlsanity.com/paper/2207.01725/) (2022)
- [Scaling Gaussian Processes for Learning Curve Prediction via Latent Kronecker Structure](https://mlsanity.com/paper/2410.09239/) (2024)
- [Scalable Gaussian Processes with Latent Kronecker Structure](https://mlsanity.com/paper/2506.06895/) (2025)
- [Bayesian Neural Scaling Law Extrapolation with Prior-Data Fitted Networks](https://mlsanity.com/paper/2505.23032/) (2025)

## Abstract (arXiv)

Trajectory extrapolation from a partial target trajectory is underdetermined, but completed related trajectories provide information about the unresolved continuation. We propose target-constrained pooling (TCP), which separates the finite-horizon endpoint from continuation shape and estimates that endpoint from two complementary source signals. Uniform pooling captures final response levels, while matched-increment pooling captures the remaining change after aligning source and target states. TCP selects representative sources, projects both endpoint estimates onto a target-consistent region, converts them into corrections of the free forecast, and controls their influence through strength calibration and degradation-aware weighting. Across 25,245 targets from five domains and both forecasting directions, TCP reduces mean RMSE by 35.8% to 42.1% for all ten target-only forecasters and improves all 100 forecaster, dataset, and direction comparisons. The two endpoint signals consistently outperform either alone, while representative selection remains within 0.64% to 1.02% of the full donor pool using 12.7x fewer donor inputs and 138.8x fewer matching distance computations.