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sriku.org | ||
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www.jeremykun.com
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| | | | | The standard inner product of two vectors has some nice geometric properties. Given two vectors $ x, y \in \mathbb{R}^n$, where by $ x_i$ I mean the $ i$-th coordinate of $ x$, the standard inner product (which I will interchangeably call the dot product) is defined by the formula $$\displaystyle \langle x, y \rangle = x_1 y_1 + \dots + x_n y_n$$ This formula, simple as it is, produces a lot of interesting geometry. | |
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rohan.ga
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| | | | | Disclaimer: These ideas are untested and only come from my intuition. I don't have the resources to explore them any further. intro CoT and test time compute have been proven to be the future direction of language models for better or for worse. o1 and DeepSeek-R1 demonstrate a step function in model intelligence. Coconut also provides a way for this reasoning to occur in latent space. I have been thinking about the geometric structure of the latent space where this reasoning can occur. | |
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thenumb.at
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pfzhang.wordpress.com
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| | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | ||
