We will design necessary components for an EA to solve the circuit synthesis problem. This includes: 1. A genotype representation for synthesized circuits 2. Appropriate genetic operators (mutation and crossover) for the genotype representation in (1) 3. Fitness functions measuring each objective Furthermore we will need to determine both a single-objective and multi-objective selection strategy for our future use. As part of this work we will also do some preliminary testing of the resulting approaches to see if they are suitable and adjust if they are not. As part of this work we will also define measures of genotypic diversity (dissimilarity measure between genotypes) and phenotypic diversity (dissimilarity measure between tuples of objective scores). Lastly we will implement a multi-objective EA for solving the circuit synthesis problem using the components selected above as well as generating appropriate input data for our two chosen problem instances: - 16-bit population count - 16-bit find-first-set Implementations of the dissimilarity measures described above will be part of this milestone.

1. Design for a genotype representation for synthesized circuits as well as genetic operators for this genotype 2. Choices for a single-objective and multi-objective selection strategy designed to combine with (1) to make two EAs one single-objective the other multi-objective 3. Implementation and preliminary testing of the multi-objective EA described by (1) and (2) 4. Data (in the form of input-output tables) describing the problem instances for circuit synthesis for 16-bit population count and 16-bit find-first set 5. Measures for genotypic dissimilarity and phenotypic dissimilarity based on the choices in (1) and implementations thereof

$15,000 USD

1. Genetic operators for the design are fair (in the EA sense). 2. Single-objective and multi-objective selection strategies are based on current literature and designs. 3. Implementation is a stand-alone executable that can run on problem instances. 4. Measures for genotypic and phenotypic dissimilarity are distance metrics, or as close as possible to this.

We will run our multi-objective EA designed and implemented in Milestone 1 on the input data for our chosen problem instances (also in Milestone 1) to produce synthesized circuits for each of these. We will track the following information for each run: 1. The best overall solution produced for each objective 2. The number of generations required to obtain the solutions in (1) 3. The population size required to obtain the solutions in (1) 4. The genotypic diversity in the final population (how dissimilar the synthesized circuits are using the dissimilarity measures we designed and implemented in Milestone 1). 5. The phenotypic diversity in the final population (what ranges of values for the objective functions we have using the dissimilarity measures we designed and implemented in Milestone 1) 6. Overall running time and memory us 7. PRNG seed(s) used. Furthermore we will collect every generated genotype (both initial population and modified) from each run along with their scores for each objective function. These will be collected together as suitable data sets for LLM training with one such data set per problem instance we are interested in.

1. At least one run using the multi-objective EA designed in Milestone 1 for each of the circuit synthesis problem instances together with the necessary tracked information as per the description above 2. Two data sets one per problem instance containing every generated solution from all runs along with their scores per objective suitable for training an LLM. One data set will be made per problem instance

$15,000 USD

1. The data sets for each problem instance show good diversity (that is, the dissimilarity measures show a large range). 2. The tracked information exists for a large number of runs, with consistently good, but diverse, outcomes.

Using the data sets created in Milestone 2 we will train LLMs designed to act as single-objective scoring functions combining the scoring functions used in the multi-objective EA designed and implemented in Milestone 1. These LLMs will not be generative; instead we will modify an existing open source LLM (like LLaMa or similar) so that the output is a single value in the range 0 to 1. We will train one fitness-LLM for each of the problem instances (and data sets) using whatever architecture fine-tuning methods and hyperparameters produce the best results. We will also implement some means of using these trained fitness-LLMs as scoring functions in the single-objective EA designed and implemented in Milestone 1.

1. A trained LLM designed to act a single-objective scoring function based on the data sets generated in Milestone 2. One LLM will be trained per data set. 2. Implementation of the LLMs from 1 as scoring functions in the single-objective EA designed and implemented in Milestone 1.

$25,000 USD

Each fitness LLM can be used as an objective function from the Milestone 1 executable.

Using the fitness-LLMs trained and adapted for use as scoring functions in Milestone 3 we will run the single-objective EA designed and implemented in Milestone 1. We will run the 16-bit popcount problem instance using the fitness-LLM trained on the 16-bit popcount data from Milestone 2 and analogously for the 16-bit find-first-set. We will use the recorded parameters (population count and generation count) from Milestone 2 and compare the results between the Milestone 2 runs on the same problem instances with the runs using our combined approach. We will note the same information per run as in Milestone 2. Subsequently we will run the single-objective EA designed and implemented in Milestone 1 again on each of the two problem instances but using the fitness-LLM designed for the other problem: thus we will try to solve 16-bit popcount with the fitness-LLM for find-first-set and vice versa. As before we will use the same recorded parameters from Milestone 2 and compare each result with its corresponding one using the correct fitness-LLM. Lastly we will compare the outcomes of the multi-objective EA and our fitness-LLM-using single-objective EA to see whether we can match or improve the performance of the multi-objective approach.

1. For each run of the multi-objective EA from Milestone 2 for the 16-bit popcount and 16-bit find-first-set problem instances a matching run of the single-objective EA from Milestone 1 using the corresponding fitness-LLM from Milestone 3 2. Records of the same information from 1 as for the Milestone 2 runs. 3. For each run from 1 a matching run of the single-objective EA from Milestone 1 using the popcount fitness-LLM for find-first-set and vice versa. 4. A comparison of all outcomes from 1 to 3 with their Milestone 2 counterparts.

$15,000 USD

1. For at least one of the problems, the single-objective EA with a fitness LLM out-performs the same problem with the multi-objective EA. 2. For at least one problem, the single-objective EA is not sensitive to fitness LLM (that is, using the fitness LLM for the other problem doesn’t impact the quality of its results).

Using the work from Milestones 1 through 4 we will integrate the fitness-LLM solution into MOSES and attempt to solve both instances of the circuit synthesis problem used throughout. We will compare the outcomes in MOSES relative the use of only single objectives (agreement with size as a tiebreaker then agreement with depth as a tiebreaker) against each of our fitness-LLMs using the same criteria as in Milestone 2.

1. An implementation of best overall fitness-LLM from Milestone 4 into MOSES as a scoring function. 2. At least one run of MOSES using the single objective of agreement on the circuit synthesis problem instances using size and depth as tiebreakers (six combinations in all). 3. For each run from 2 use the combined implementation from 1 keeping other parameters the same to do a corresponding run on the same problem instance. 4. A comparison of the results from 2 and 3 using the Milestone 2 criteria.

$10,000 USD

The fitness-LLM-using version of MOSES out-performs MOSES without the fitness LLM on at least one problem instance.