Task 2: RL4Ising Baseline Benchmark

1D Spin Glass Baseline Benchmark

Instance	# of Spins	ID	Gurobi	MCPG	Ref
Chain	300	ising_2.5_300_5555	-17208224	?	[4]
Chain	300	ising_2.5_300_6666	-17226035	?	[4]
Chain	300	ising_2.5_300_7777	-17114715	?	[4]
Chain	300	ising_3.0_300_5555	-17180221	?	[4]
Chain	300	ising_3.0_300_6666	-17133707	?	[4]
Chain	300	ising_3.0_300_7777	-16974531	?	[4]
Chain	250	ising_2.5_250_5555	-13851379	?	[4]
Chain	250	ising_2.5_250_6666	-14260583	?	[4]
Chain	250	ising_2.5_250_7777	-13083461	?	[4]
Chain	250	ising_3.0_250_5555	-13803242	?	[4]
Chain	250	ising_3.0_250_6666	-14179549	?	[4]
Chain	250	ising_3.0_250_7777	-12857156	?	[4]
Chain	200	ising_2.5_200_5555	-11656902	?	[4]
Chain	200	ising_2.5_200_6666	-11747646	?	[4]
Chain	200	ising_2.5_200_7777	-10862317	?	[4]
Chain	200	ising_3.0_200_5555	-11588805	?	[4]
Chain	200	ising_3.0_200_6666	-11615661	?	[4]
Chain	200	ising_3.0_200_7777	-10706238	?	[4]
Chain	150	ising_2.5_150_5555	-7669451	?	[4]
Chain	150	ising_2.5_150_6666	-8275314	?	[4]
Chain	150	ising_2.5_150_7777	-8653066	?	[4]
Chain	150	ising_3.0_150_5555	-7612796	?	[4]
Chain	150	ising_3.0_150_6666	-8187454	?	[4]
Chain	150	ising_3.0_150_7777	-8585946	?	[4]
Chain	100	ising_2.5_100_5555	-5355449	?	[4]
Chain	100	ising_2.5_100_6666	-5758081	?	[4]
Chain	100	ising_2.5_100_7777	-5845822	?	[4]
Chain	100	ising_3.0_100_5555	-5238757	?	[4]
Chain	100	ising_3.0_100_6666	-5713598	?	[4]
Chain	100	ising_3.0_100_7777	-5784112	?	[4]

2D Spin Glass Baseline Benchmark

Instance	# of Spins	ID	Gurobi	MCPG	Ref
EA	1,600	1	-1234.987698	-1231.095459	[1]
EA	1,600	2	-1262.071521	-1257.488159	[1]
EA	1,600	3	-1253.741406	-1251.403931	[1]
EA	900	0	-1171.015619	-1171.015625	[2]
EA	900	1	-1154.316907	-1154.000122	[2]
EA	900	2	-1173.734263	-1172.162231	[2]
Spin Glass	256	0	-332.0076594	-332.00766	[3]
Spin Glass	256	1	-329.0312525	-329.03125	[3]
Spin Glass	256	2	-345.157069	-345.157074	[3]

3D Spin Glass Baseline Benchmark

Instance	# of Spins	ID	Gurobi	MCPG	Ref
EA	8,000	0	-13396.94785	…	[2]
EA	8,000	1	-13264.95422	…	[2]
EA	8,000	2	-13260.41274	…	[2]
EA	5,730	J_5627	-8547.784703	…	[5]
EA	4,644	J_2084	-3237.933105	-3237.933105	[5]
EA	3,375	0	-5542.208415	-5592.898438	[2]
EA	3,375	1	-5781.360939	-5789.354492	[2]
EA	3,375	2	-5648.926033	-5664.736328	[2]
EA	1,000	0	-1696.610974	-1695.163818	[2]
EA	1,000	1	-1699.175776	-1699.175781	[2]
EA	1,000	2	-1682.087705	-1682.087646	[2]

4D Spin Glass Baseline Benchmark

Instance	# of Spins	ID	Gurobi	MCPG	Ref
EA	4,096	0	?	-8107.549805	[2]
EA	4,096	1	?	-8173.367188	[2]
EA	4,096	2	?	-8228.681641	[2]
EA	2,041	0	?	-4841.733887	[2]
EA	2,041	1	?	-4846.763672	[2]
EA	2,041	2	?	-4790.629883	[2]
EA	1,296	0	-2592.401451	-2592.401367	[2]
EA	1,296	1	-2585.054801	-2618.92334	[2]
EA	1,296	2	-2602.996952	-2609.658936	[2]
EA	625	0	-1263.935083	-1262.323242	[2]
EA	625	1	-1251.184814	-1247.943848	[2]
EA	625	2	-1224.135916	-1230.634399	[2]

References

[1]

Hibat-Allah, M., Inack, E.M., Wiersema, R. et al. Variational neural annealing. Nat Mach Intell 3, 952–961 (2021). https://doi.org/10.1038/s42256-021-00401-3

[2]

Fan, C., Shen, M., Nussinov, Z. et al. Searching for spin glass ground states through deep reinforcement learning. Nat Commun 14, 725 (2023). https://doi.org/10.1038/s41467-023-36363-w

[3]

Mills, K., Ronagh, P. & Tamblyn, I. Finding the ground state of spin Hamiltonians with reinforcement learning. Nat Mach Intell 2, 509–517 (2020). https://doi.org/10.1038/s42256-020-0226-x

[4]

Wiegele, A. (2007, September). Biq Mac Library: A collection of Max-Cut and quadratic 0–1 programming instances of medium size [Data set]. Alpen-Adria-Universität Klagenfurt. http://biqmac.uni-klu.ac.at/biqmaclib.html

[5]

Zhang, H., and Kamenev, A. 2025. On Computational Complexity of 3D Ising Spin Glass: Lessons from D-Wave Annealer. arXiv e-prints, p.arXiv:2501.01107.