Getting back to the original question about backprop, the gradient is a sum of terms computed for each training point. Some problems can be broken into smaller pieces that can be parallelized. For example, sometimes a later part of the computation depends on an earlier result. Not all computations can be parallelized. It would compute dot products without any loops taking place: an analog or digital circuit) with the following logical structure. In the dot product example, imagine we made a custom piece of hardware (e.g. Let's ignore the specifics of existing hardware. So, is it possible to perform the computation without any loops whatsoever? In principle, the answer is yes (for some problems), by using parallelism and executing all operations simultaneously. This can be achieved by taking advantage of special CPU instructions, using multiple CPU cores, or even multiple networked machines or specialized hardware.Īt a fundamental level, we can consider a loop to be the repeated, sequential execution of identical operations in time. The loop(s) won't look exactly like the naive code because much of the efficiency of numerical computing libraries comes from executing multiple operations simultaneously (i.e. as the computer steps through the operations in the linear algebra library's machine code). But, as Matthew Drury pointed out in the comments, looping might still be happening at a lower level (e.g. The vectorized code doesn't explicitly contain loops. BLAS) will still be more efficient than the naive code because it's highly optimized and can accelerate the computation using special features of the hardware. But, using a numerical linear algebra library (e.g. In compiled languages like C, the high level code would be compiled to machine code, avoiding the overhead of an interpreter. In the vectorized code, the interpreter would pass the entire operation to the linear algebra library, which can execute it much more efficiently. Doing this repeatedly over the loop incurs a lot of overhead (but a smarter interpreter might use a JIT compiler to avoid this). To do its job, the interpreter must perform additional computations beyond the mathematical operations we're interested in. In an interpreted language, the naive code would cause the interpreter to repeatedly execute the instructions in the loop. The code we've written no longer contains a loop, although looping might still be happening at a lower level (I'll get to this in a second). In the context of high level, interpreted languages like Python, Matlab, etc. The code might look something like: result = dot(x, y) In pseudo-code: result = 0Ī more efficient approach would be to use numerical linear algebra library that implements dot products. A naive way to do this would be to write a loop in some high level programming language to manually add up the products of the elements. As an example, say we want to compute the dot product between two vectors, $x$ and $y$. But, we can consider a couple possibilities. Reading the quote, it's not clear to me what exactly he means by 'loop'. * for this file see task include a file in language AArch64 assembly */ asciz "Counter = \n" // message resultīl conversion10 // call decimal conversionīl strInsertAtCharInc // insert result at character * for this file see task include a file in language AArch64 assembly*/ * ARM assembly AARCH64 Raspberry PI 3B */ some useful equates - bdos equ 5 h location ofjump to BDOS entry point wboot equ 0 BDOS warm boot function conout equ 2 write character to console - main code - org 100 h lxi sp, stack set up a stack lxi h, 10 starting value for countdown loop: call putdec print it mvi a, ' ' space between numbers call putchr dcx h decrease count by 1 mov a, h are we done (HL = 0)? ora l jnz loop no, so continue with next number jmp wboot otherwise exit to operating system - console output of char in A register preserves BC, DE, HL - putchr: push h push d push b mov e, a mvi c, conout call bdos pop b pop d pop h ret - Decimal output to console routine HL holds 16-bit unsigned binary number to print Preserves BC, DE, HL - putdec: push b push d push h lxi b ,- 10 lxi d ,- 1 putdec2: dad b inx d jc putdec2 lxi b, 10 dad b xchg mov a, h ora l cnz putdec recursive call! mov a, e adi ' 0 ' make printable call putchr pop h pop d pop b ret - data area - stack equ $ 128 64-level stack to support recursion end
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |