On “too global”: guides often warn that high perplexity destroys structure. On this dataset it does not — separation and KL both keep improving up to 50, and the captions report that. The failure mode needs conditions absent here: perplexity approaching the sample count (300), or hierarchical data where high perplexity swallows fine sub-clusters. Perplexity is a dataset-dependent knob, not a dial with a universally correct setting.
Running t-SNE at four perplexity settings…
Calibrating per-point bandwidths by binary search, then minimising KL(P‖Q) by gradient descent over 300 points in 32 dimensions. These positions are computed, not pre-drawn.
What is perplexity?
Perplexity controls the effective number of neighbours each point considers. Low values (5–10) focus on very local structure — the same digit may appear in multiple disconnected mini-clusters. High values (40–50) consider too many neighbours, making clusters lose their shape. The sweet spot (25–35) balances local and global structure, revealing the natural digit classes in MNIST.