We propose a soft gradient boosting framework for sequential regression that embeds a learnable linear feature transform within the boosting procedure. At each boosting iteration, we train a soft decision tree and learn a linear input feature transform Q together. This approach is particularly advantageous in high-dimensional, data-scarce scenarios, as it discovers the most relevant input representations while boosting. We demonstrate, using both synthetic and real-world datasets, that our method effectively and efficiently increases the performance by an end-to-end optimization of feature selection/transform and boosting while avoiding overfitting. We also extend our algorithm to differentiable non-linear transforms if overfitting is not a problem. To support reproducibility and future work, we share our code publicly.