By Dr. Amith Singhee, Rob A. Rutenbar (auth.)
As VLSI expertise strikes to the nanometer scale for transistor characteristic sizes, the impression of producing imperfections lead to huge adaptations within the circuit functionality. conventional CAD instruments should not well-equipped to deal with this state of affairs, due to the fact they don't version this statistical nature of the circuit parameters and performances, or in the event that they do, the prevailing recommendations are typically over-simplified or intractably sluggish. Novel Algorithms for quick Statistical research of Scaled Circuits attracts upon rules for attacking parallel difficulties in different technical fields, equivalent to computational finance, computing device studying and actuarial hazard, and synthesizes them with leading edge assaults for the matter area of built-in circuits. the result's a collection of novel recommendations to difficulties of effective statistical research of circuits within the nanometer regime. specifically, Novel Algorithms for speedy Statistical research of Scaled Circuits makes 3 contributions:
1) SiLVR, a nonlinear reaction floor modeling and performance-driven dimensionality relief technique, that instantly captures the designer’s perception into the circuit habit, by means of extracting quantitative measures of relative worldwide sensitivities and nonlinear correlation.
2) quick Monte Carlo simulation of circuits utilizing quasi-Monte Carlo, displaying speedups of two× to 50× over ordinary Monte Carlo.
3) Statistical blockade, a good technique for sampling infrequent occasions and estimating their likelihood distribution utilizing restrict effects from severe worth idea, utilized to excessive replication circuits like SRAM cells.
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Extra resources for Novel Algorithms for Fast Statistical Analysis of Scaled Circuits
Example text
30) we know that w1 = {1, 1} or {1, −1} are two good candidates for the first projection vector. In fact, any {a, b} such that ab = 0 is a good candidate because we can write x1 x2 = (4ab)−1 [(ax1 + bx2 )2 − (ax1 − bx2 )2 ]. 31) Therefore, {1, 0} is a bad projection vector. 5 shows 100 training points as (blue) dots, projected along the projection vectors {1, 0} (Fig. 5(a)) and {1, 1} (Fig. 5(b)). With unrestricted g1 we can find perfect interpolations along both directions, shown as solid lines joining the projected training points.
It is interesting to note the dimensionality-independent 1/ q convergence, similar to the dimensionality-independent convergence of standard Monte Carlo integration, as shown in Sect. 2. According to this result, the more the number of sigmoids the better. However, in a sampling context, where we have only partial information because of a finite number of sampling points, this high model flexibility (complexity) can lead to overfitting problems. This overfitting problem is significantly exacerbated in the context of a PPR model like SiLVR, as discussed in Sect.
58). 80) where pi is one of ak , bk , ck for some k ∈ {1, . . , q }. Note that we have dropped the subscript for the LV here. 58). 61) will drive the search towards a ridge function that exactly fits the sample points along the projection vector. As discussed in Sect. 1, this is not desirable for achieving a generalizable PPR model with low overfitting. Regularization is a standard technique used to constrain the model complexity and reduce this overfitting behavior and involves adding a penalty term to the standard least squared error objective.