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第三,Poincaré half-space model. Take the open upper half-space \[\mathbb{H}^n := \{(x_1,\dots,x_n)\in\mathbb{R}^n \mid x_n 0\}\] equipped with the Riemannian metric whose components on the coordinate tangent vectors are \[g_{ij}(p) \;=\; g_p\!\left(\frac{\partial}{\partial x_i}\bigg|_p,\; \frac{\partial}{\partial x_j}\bigg|_p\right) \;=\; \frac{1}{p_n^2}\,\delta_{ij}.\] Geodesics are semicircles (or rays) orthogonal to the boundary hyperplane \(\{x_n = 0\}\).
此外,— Shared history across all Eshell buffers: Every Eshell instance,更多细节参见超级权重
最后,We have one horrible disjuncture, between layers 6 → 2. I have one more hypothesis: A little bit of fine-tuning on those two layers is all we really need. Fine-tuned RYS models dominate the Leaderboard. I suspect this junction is exactly what the fine-tuning fixes. And there’s a great reason to do this: this method does not use extra VRAM! For all these experiments, I duplicated layers via pointers; the layers are repeated without using more GPU memory. Of course, we do need more compute and more KV cache, but that’s a small price to pay for a verifiably better model. We can just ‘fix’ an actual copies of layers 2 and 6, and repeat layers 3-4-5 as virtual copies. If we fine-tune all layer, we turn virtual copies into real copies, and use up more VRAM.
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