1. Montek Singh COMP790-084 Oct 11, 2011

2.  Today’s topics: ◦ more on error metrics ◦ more applications ◦ architectures and design tools ◦ challenges and benefits ◦ open questions

3.  For arithmetic units, error metric based upon an error threshold, δ ◦ errors < δ are tolerable ◦ p δ = prob (err < δ)

4.  Applications which harness probabilistic behavior ◦ algorithms with repeated execution with the same inputs resulting in distinct outcomes (with some prob. distribution)  Separate algorithm into deterministic and probabilistic parts

5.  Bayesian Inference ◦ statistical inference technique mimicking human decision-making process ◦ set of hypotheses and probability weights ◦ each observation leads to a revision of prob weights ◦ Example:

6.  Example ◦ Given  prob of rain  prob of sprinkler being on given rain ◦ Find: prob of rain given that the grass is wet  Implemented using PCMOS

7.  Random Neural Networks ◦ Poisson process models the “firing” of a neuron  Probabilistic Cellular Automata ◦ Each cell’s next state is a function of its neighbors ◦ Next state could be 0 or 1 with certain prob  Hyper Encryption ◦ Random seed generated using PCMOS

9.  Applications that tolerate probabilistic behavior ◦ multimedia mostly ◦ signal processing ◦ others?

10.  Different partitioning of deterministic vs. probabilistic parts of an algorithm

11.  Host (deterministic) vs. coprocessor (probabilistic) partitioning

12.  Comparison ◦ Host = deterministic ◦ without coprocessor: software only ◦ with coprocessor:  using PCMOS  using CMOS

13.  Quality of randomness  using PCMOS vs. pseudo RNG

14.  Benefits ◦ …?  Challenges ◦ …?

15.  Architectural questions ◦ Which design is better in terms of E-p tradeoff? ◦ Example:  Which adder is better: carry-skip or ripple-carry?  carry-skip adder has faster propagation time  ripple-carry adder consumes less energy  But: carry-skip adder may be better when there are delay-induced errors!  Design tools ◦ What type of tool support is needed? ◦ Simulation and validation?