انجام پروژه پایتون
پنج سال پیش منتشر شده
تعداد بازدید: 216
کد پروژه: 184105
شرح پروژه
سلام
3073
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توضیحش همونایی که گفتم
یه فیلم هم همکار قبلیتون فرستادن در مورد نحوه اجرای کد،میخواین اون رو هم بهشون بدین
توی کد یک فایل هست به اسم weight_virtualization
مقاله مرتبط به این مطلب هم توی گیت هاب،همون لینکی که گذاشته بودم،هست،هم الان اینجا میفرستم
موضوع این هست که توی مقاله،هر پیج رو با محاسباتی،به پیجی که شبیه ترش هست مپ میکنه،تا به این صورت بتونه اطلاعات کمتری رو ذخیره کنه
حالا میخوایم ببینیم که اگه با استفاده از روش EMD،مقدار lossمحاسبه بشه و اینکه هر صفحه مثلا به چندتا پیج مپ بشه،هر قسمتیش به یکی مثلا،آیا خروجی بهتر میشه یا نه
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P: a vector of pages, P = [p1, p2, …, pn]. P is a d*n matrix, where d is the page size.
Q: a vector of virtual pages, Q = [q1, q2, .., qm], m << n. Q is a d*m matrix, where d is the page size
W: matching matrix, W = [w1, w2, .., wn], each wi is a vector of length m and is a column of the matrix.
Weight page matching problem:
Find Q and a matching matrix W in R^{m*n} so that P = QW.
Implications:
Both Q and W are unknown. To solve the problem, one has to add constraints to derive a solution.
Q is essentially a basis in the d dimension space.
Each real page pi is a weighted summation of virtual pages, pi = Q* wi, where wi is the i-th column in W.
The optimization problem:
Min_{Q, W} ||P - QW||_2 with some constraints
Under the above framework, the algorithm in the weight virtualization paper can be formulated as:
Min_{Q, W} ||P - QW||_2
Subject to the following constraints:
Q is a subset of P. That is, the columns in Q is a subset of columns in P.
Each page is matched to a single virtual page: pi = Q* wi and wi has only one non-zero element (|wi|_0 = 1) and that non-zero element is 1.
Our goal:
Relax the above constraints
New constraints:
Q is a subset of P.
Each page can be matched to multiple virtual pages. The value can be floating point number instead of 1.
For the formulation to the EMD problem:
Each page has a embedding dimension d.
The finite size vocabulary: n.
A sequence of pages P are represented as a normalized BOW vectors, dP= [1, 1, 1, …, 1] of length n.
A sequence of pages Q are represented as dQ = [0, 0, .., 1, ..0] of length n. But the number of 1s are m. To make it shorter, we represent dQ = [1, 1, .., 1] of length m.
The distance between page pi and virtual page qi is: c(pi, qj) = distance(pi, qj)
This implies the cost associated with traveling from a real page to a virtual page.
We allow each virtual page pi in P to be transformed into any virtual page in Q in total or in parts.
Let W be the flow matrix where Tij >= 0.
T.shape = (n, m)
Tij denotes how much of a page pi in P travels to a virtual page qj in Q.
To transform P entirely into Q, we ensure that the entire outgoing flow from page pi equals its frequency. i.e., sum_j(Tij) = 1
Furthermore, the amount of incoming flow to virtual page qj must match its frequency 1 as well. i.e., sum_i (Tij) = 1.
The minimize accumulative cost of moving P to Q is:
T* = argmin sum_{i, }j Tij* c(pi, qj)
S.t.
sum_j(Tij) = 1
sum_i (Tij) = 1
Relexed WMD:
T* = argmin sum_{i, }j Tij* c(pi, qj)
S.t.
sum_{j}(Tij) = 1, for all I = 1, …, n
The optimal solution is for each page in P to move all its probability mass to the most similar virtual page in Q. Precisely,
An optimal T* matrix is:
T_ij = 1 if j = argmin_j c(pi, qj)
T_ij = 0 otherwise.
This optimal solution is equivalent to the weight virtualization paper.
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