Table 15: Results of GPT-3.5-TURBO and GPT-4 on 19 cases (#17 to #19 example) through the eight tasks. We omitted the COt in-context exemplars in the table.
Question	GPT-3.5-TURBO	GPT-4
There are 5 job applicants numbered from 0 to 4, and 6 jobs numbered from 0 to 5. Each applicant is interested in some of the jobs. Each job can only accept one applicant and a job applicant can be appointed for only one job. Applicant 0 is interested in job 3. Applicant 4 is interested in job 5. Applicant 4 is interested in job 4. Applicant 3 is interested in job 0. Applicant 0 is interested in job 5. Applicant 1 is interested in job 0. Applicant 0 is interested in job 2. Applicant 0 is interested in job 4. Applicant 4 is interested in job 2. Applicant 2 is interested in job 3. Q: Find an assignment of jobs to applicants in such that the maximum number of applicants find the job they are interested in.	Applicant 0 is interested in job 2, job 3, job 4, job 5. Applicant 1 is interested in job 0. Applicant 2 is interested in job 3. Applicant 3 is interested in job 0. Applicant 4 is interested in job 0, job 2, job 4, job 5. We can make the following assignments: applicant 0: job 5 applicant 1: job 0 applicant 2: job 3 applicant 3: job 0 applicant 4: job 2 5 applicants can find the job they are interested in.	Applicant 0 is interested in job 2, job 3, job 4, job 5. Applicant 1 is interested in job 0. Applicant 2 is interested in job 3. Applicant 3 is interested in job 0. Applicant 4 is interested in job 0, job 2, job 4, job 5. We can make the following assignments: applicant 0: job 3 applicant 1: job 0 applicant 4: job 4 3 applicants can find the job they are interested in.
n an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge. Embeddings: node 0: [1,1] node 1: [0,1] node 2: [1,0] node 3: [1,1] node 4: [0,0] node 5: [0,1] The edges are: (0,1) (5,0) (1,4) (1,5) (2,4) (4,3) In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings. Q: What's the embedding of each node after one layer of simple graph convolution layer?	Layer 1: node 0: sum of embeddings of node 1, node 5, [0,1] + [0,1] = [0,2]. node 1: sum of embeddings of node 0, node 4, node 5, [1,1] + [0,0] + [0,1] = [1,2]. node 2: sum of embeddings of node 4, [0,0] = [0,0]. node 3: sum of embeddings of node 4, [0,0] = [0,0]. node 4: sum of embeddings of node 1, node 2, node 3, [1,2] + [1,0] + [0,0] = [2,2]. node 5: sum of embeddings of node 0, node 1, [0,2] + [1,2] = [1,4]. So the answer is: node 0: [0,2] node 1: [1,2] node 2: [0,0] node 3: [0,0] node 4: [2,2] node 5: [1,4] X	Layer 1: node 0: sum of embeddings of node 1, node 5, [0,1] + [0,1] = [0,2]. node 1: sum of embeddings of node 0, node 4, node 5, [1,1] + [0,0] + [0,1] = [1,2]. node 2: sum of embeddings of node 4, [0,0] = (0,0]. node 3: sum of embeddings of node 4, [0,0] = [0,0]. node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [1,0] + [1,1] = [2,2]. node 5: sum of embeddings of node 0, node 1, [1,1] + [0,1] = [1,2]. So the answer is: node 0: [0,2] node 1: [1,2] node 2: [0,0] node 3: [0,0] node 4: [2,2] node 5: [1,2] X
In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge. Embeddings: node 0: [0,1] node 1: [1,1] node 2: [1,0] node 3: [1,1] node 4: [1,1] node 5: [0,0] node 6: [1,0] node 7: [1,0] The edges are: (0,3) (4,0) (6,0) (5,1) (1,4) (5,2) (2,3) (2,6) (3,5) (3,6) (5,4) (7,5) In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings. Q: What's the embedding of each node after one layer of simple graph convolution layer?	Layer 1: node 0: sum of embeddings of node 3, node 4, node 6, [1,1] + [1,1] + [1,0] = [3,2]. node 1: sum of embeddings of node 4, [1,1] = [1,1]. node 2: sum of embeddings of node 3, node 5, node 6, [1,1] + [0,0] + [1,0] = [2,1]. node 3: sum of embeddings of node 0, node 2, node 5, node 6, [0,1] + [1,1] + [0,0] + [1,0] = [2,2]. node 4: sum of embeddings of node 0, node 1, node 5, [3,2] + [1,1] + [0,0] = [4,3]. node 5: sum of embeddings of node 2, node 3, node 4, node 7, [2,1] + [2,2] + [4,3] + [1,0] = [9,6]. node 6: sum of embeddings of node 0, node 2, node 3, node 3, node 7, [0,1] + [1,0] + [1,1] + [1,0] = [3,2]. node 7: sum of embeddings of node 5, [9,6] = [9,6]. So the answer is: node 0: [3,2] node 1: [1,1] node 2: [2,1] node 3: [2,2] node 4: [4,3] node 5: [9,6] node 6: [5,3] node 7: [9,6] X	Layer 1: node 0: sum of embeddings of node 3, node 4, node 6, [1,1] + [1,1] + [1,0] = [3,2]. node 1: sum of embeddings of node 5, node 4, [0,0] + [1,1] = [1,1]. node 2: sum of embeddings of node 5, node 3, node 6, [0,0] + [1,1] + [1,0] = [2,1]. node 3: sum of embeddings of node 0, node 2, node 5, node 6, [0,1] + [1,0] + [0,0] + [1,0] = [2,1]. node 4: sum of embeddings of node 0, node 2, node 3, node 7, [0,1] + [1,0] + [1,1] + [1,0] = [3,2]. node 7: sum of embeddings of node 5, [0,0] = [0,0]. So the answer is: node 0: [3,2] node 1: [1,1] node 2: [2,1] node 3: [2,1] node 4: [1,2] node 5: [5,3] node 6: [3,2] node 7: [0,0] X