Gradient Surgery: Resolving Conflicting Task Gradients (PCGrad)

In multi-task learning, a single shared parameter vector must satisfy every task's loss at once, and when two tasks' gradients point in opposing directions the naive sum of their gradients can partially cancel — or even move backward on one task. This simulator renders each task's quadratic loss as a bowl on a shared 3D landscape, lets you dial a conflict angle between task optima, and compares plain gradient summation against PCGrad's "gradient surgery": projecting out the conflicting component of one task's gradient onto the other's normal plane before summing. Run the optimizer, watch the instanced trail of past positions, and read live cosine-similarity and combined-loss telemetry to see exactly when and why gradient surgery helps.