The Strong Lottery Ticket Hypothesis for Multi-Head Attention Mechanisms

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Hey,

Your paper on SLTH for attention mechanisms is brilliant. Seriously. I've been following lottery ticket research for a while, but applying it specifically to multi-head attention with that level of theoretical depth? That's fresh.

What I love most is that this isn't just theoretical elegance — it's actionable. But I'm trying to wrap my head around the full training procedure, and I'd love your insight.

From my understanding, the training flow would look something like:

Phase 1: Overparameterized Pre-training

• Start with 4x key dimensions, 4x value dimensions
• Use your n^(1/4) initialization scaling
• Train on standard language modeling objective (next token prediction)

Question:
Do you use any special attention dropout or regularization here?
I'm wondering if the overparameterization needs stabilization techniques.

Phase 2: Lottery Ticket Identification

• Apply iterative magnitude pruning (IMP) to attention weight matrices
• Calculate pruning thresholds based on weight magnitudes

Question:
Do you prune Q, K, V, and O projections at the same rate, or does each need different sparsity?
I imagine K/V with 4x dimensions can tolerate more aggressive pruning.

Phase 3: Sparse Retraining

• Rewind to initial (scaled) weights
• Apply discovered masks
• Retrain with masks frozen

Question:
Do you find the sparse network needs the same number of training steps, or can it converge faster?

The part I'm most curious about is how this interacts with multi-head attention specifically.
Does each head discover its own lottery ticket independently?
Or do you need to maintain some kind of head-wise balance?

Also wondering about the computational trade-offs during training — obviously the overparameterized phase is more expensive, but if the lottery ticket is strong enough, does the sparse retraining compensate?
What's the total training cost compared to just training a standard dense model?

And one more practical question:
For the 4x overparameterization, is that dimension increase applied before or after the head split?

Like, if you have 12 heads with 64-dim each (768 total), do you go to 768×4 = 3072 before splitting into heads, or 64×4 = 256 per head?

The reason I'm digging into this is that I think your approach could be a game-changer for how we think about training large models:

Train big, compress smart, deploy efficiently — but the devil's in the details of making it actually work.

Looking forward to your thoughts, and seriously, keep pushing this work forward!

Cheers,
Ujjwal Tyagi
AI Researcher & Scientist, Shirova AI