@Cernovich I have a close high school in college buddy who spent his life in military intelligence. He told me being over there he thought we could end the war by just providing a little boys.
The British army once sentenced Daniel Morgan to 500 lashes, a punishment that usually killed a man, for the crime of knocking out an officer who struck him. He survived every stroke. And he spent the rest of his life joking that the drummer had miscounted and only given him 499, so the British still owed him one. He collected that debt at a place called Cowpens.
Morgan was not born to anything. He was a rough, barely educated frontiersman who made his living hauling freight by wagon on the Virginia frontier, a big, powerful, hot-tempered young man. During the French and Indian War, serving as a civilian teamster with the British army, a British lieutenant struck him with the flat of a sword. Morgan answered with his fist and dropped the officer cold. For a colonial to strike a British officer was close to a capital offense, and the court-martial sentenced him to five hundred lashes with the cat-o'-nine-tails, a flogging meant to flay a man and very often to kill him.
They tied him up and laid it on, and Daniel Morgan did not die. He carried the ridged scars on his back for the rest of his life. But instead of breaking him, that brutal punishment forged something. It left him with a cold, permanent hatred of the British army and its contempt for colonial men like him, a hatred he would one day repay with interest. And it gave him his lifelong joke: the drummer lost count and stopped at 499, so the British, he liked to say, were still one lash short of paying him in full.
When the Revolution came, that uneducated wagoner turned out to be a natural soldier of rare gifts. He raised a company of frontier riflemen, crack shots who could kill at distances that terrified British regulars, and he led them north to Saratoga, where his marksmen helped shatter Burgoyne's army and win the turning-point victory of the war. Morgan had a feel for battle that trained European officers lacked, an instinct for ground, for timing, and above all for the men he led. He understood that his militia were not professional soldiers and could not be asked to do what professionals did, so instead of cursing them for it, he built his tactics around what they could do.
That genius reached its peak at the Battle of Cowpens in January 1781, one of the most perfectly fought battles in American history. Facing the dreaded Banastre Tarleton, Morgan set a trap built entirely on human nature. He put his unreliable militia in the front line and asked them only for two volleys, then permission to fall back, which they gladly did. Tarleton's British, seeing the Americans retreat, charged forward in a confident rush straight into Morgan's real line of hardened Continentals, and then Morgan sprang the jaws, hitting the British on both flanks at once in a double envelopment while his cavalry rode down their rear. In minutes Tarleton's command was destroyed, hundreds killed and captured, one of the most crushing and complete victories of the war, and Tarleton himself barely escaped. It was the frontier wagoner out-generaling the darlings of the British army.
So the debt was paid. The boy they tried to flog to death grew up to be the man who methodically dismantled the British in the field, who understood soldiers because he had been treated like dirt as one, and who turned the hard lessons of his own back into some of the finest tactics the Revolution ever saw. Remember Daniel Morgan. The British gave him 499 lashes and made an enemy who never forgot, and he collected the last one at Cowpens, with interest.
๐๐ป๐ผ๐๐ต๐ฒ๐ฟ ๐๐ง๐ฆ๐ฅ ๐ฒ๐ ๐ฎ๐บ๐ฝ๐น๐ฒ ๐๐ฝ๐ผ๐๐๐ฒ๐ฑ. ๐จ๐๐ถ๐ป๐ด ฮฑ ๐๐ผ ๐ฎ๐ฑ๐ท๐๐๐ ๐น๐ฎ๐๐ฒ๐ฟ ๐น๐ฒ๐ฎ๐ฟ๐ป๐ถ๐ป๐ด ๐ฟ๐ฎ๐๐ฒ๐. Iโve been talking about this for years with Heavy-Tailed Self-Regularization (HTSR): use the weightwatcher layer ฮฑโs to help decide how that much each layer should learn.
โ๐ข๐ป๐ฒ ๐๐ฅ ๐๐ผ๐ฒ๐๐ปโ๐ ๐๐ถ๐ ๐๐น๐น: ๐๐ฒ๐ฎ๐๐-๐ง๐ฎ๐ถ๐น ๐๐๐ถ๐ฑ๐ฒ๐ฑ ๐๐ฎ๐๐ฒ๐ฟ๐๐ถ๐๐ฒ ๐๐ฒ๐ฎ๐ฟ๐ป๐ถ๐ป๐ด ๐ฅ๐ฎ๐๐ฒ๐ ๐ณ๐ผ๐ฟ ๐๐๐ ๐,โ by Di He and colleagues presents another approach
Hereโs how their 1รโ5ร setting works:
โข Estimate the power-law exponent ฮฑ for each weight matrix. They rolled their own estimator; you can use WeightWatcher for this or vibe up your own.
โข Compute each matrixโs target learning rate
ฮทโ = ฮทโ ร [1 + 4(ฮฑโ โ ฮฑโแตขโ)/(ฮฑโโโ โ ฮฑโแตขโ)]
where ฮทโ is the scheduled base rate. ฮฑโแตขโ and ฮฑโโโ are the smallest and largest exponents among the matrices being scaled.
Lowest ฮฑ โ 1ร. Midpoint ฮฑ โ 3ร. Highest ฮฑ โ 5ร.โ
Heavier tails get smaller learning rates; lighter tails get larger ones.
โข Refresh every 100 steps during the first 20% of training, transitioning linearly over 50 steps. Then freeze the multipliers while the base rate continues its cosine decay.
โข Embeddings and the output head use 5ร the base rate.
They report up to 1.5ร training speedup and better generalization.
Moreover, a recent follow-up paper adopts this approach, training a 60M-scale model. They find that they can reduce validation perplexity from 24.727 to 23.751, about 3.9% below uniform learning rates:
When researchers in China start building on your ideas, you know youโve done something right. Those guys are killing it.