Channel Capacity Constrained Estimation (arxiv version: https://arxiv.org/abs/2511.06443)

Example results (no graph rewiring, round to the continuous values to the nearest for implementation)

Cora,

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Depth: 2

• Network channel capacity: 15.9584

• Lower bound: 10.0112 in [7.9040, 17.5644]

• Representation compression: 0.0107

• View Dimensions & Probabilities

  • Hidden dimensions: [1983.0742, 1123.0810]
  • Rounded hidden dims: [1983, 1123]
  • Dropout probabilities: [0.5805, 0.3616]

Depth: 3

• Network channel capacity: 23.4857

• Lower bound: 12.1243 in [7.9040, 17.5644]

• Representation compression: 0.0183

• View Dimensions & Probabilities

  • Hidden dimensions: [1983.0862, 1274.8117, 830.9384]
  • Rounded hidden dims: [1983, 1275, 831]
  • Dropout probabilities: [0.5805, 0.3913, 0.3946]

Depth: 4

• Network channel capacity: 30.9106

• Lower bound: 13.6767 in [7.9040, 17.5644]

• Representation compression: 0.0265

• View Dimensions & Probabilities

  • Hidden dimensions: [1983.0882, 1274.7815, 1038.7230, 701.8598]
  • Rounded hidden dims: [1983, 1275, 1039, 702]
  • Dropout probabilities: [0.5805, 0.3913, 0.4490, 0.4032]

Depth: 5

• Network channel capacity: 38.2757

• Lower bound: 14.8987 in [7.9040, 17.5644]

• Representation compression: 0.0353

• View Dimensions & Probabilities

  • Hidden dimensions: [1983.0854, 1271.3599, 1053.2914, 911.4606, 619.8425]
  • Rounded hidden dims: [1983, 1271, 1053, 911, 620]
  • Dropout probabilities: [0.5805, 0.3907, 0.4531, 0.4639, 0.4048]

Depth: 6

• Network channel capacity: 45.6218

• Lower bound: 15.9161 in [7.9040, 17.5644]

• Representation compression: 0.0443

• View Dimensions & Probabilities

  • Hidden dimensions: [1983.0882, 1277.7392, 1067.4793, 941.0846, 843.7655, 558.0908]
  • Rounded hidden dims: [1983, 1278, 1067, 941, 844, 558]
  • Dropout probabilities: [0.5805, 0.3918, 0.4552, 0.4685, 0.4727, 0.3981]

Depth: 7

• Network channel capacity: 52.9313

• Lower bound: 16.7777 in [7.9040, 17.5644]

• Representation compression: 0.0537

• View Dimensions & Probabilities

  • Hidden dimensions: [1983.0883, 1281.1045, 1072.7756, 949.0070, 865.8996, 790.9780, 511.0134]
  • Rounded hidden dims: [1983, 1281, 1073, 949, 866, 791, 511]
  • Dropout probabilities: [0.5805, 0.3925, 0.4557, 0.4694, 0.4771, 0.4774, 0.3925]

Citeseer,

Depth: 2

• Network channel capacity: 17.2631

• Lower bound: 11.4531 in [8.1098, 18.0218]

• Representation compression: 0.0044

• View Dimensions & Probabilities

  • Hidden dimensions: [5270.4205, 2912.4121]
  • Rounded hidden dims: [5270, 2912]
  • Dropout probabilities: [0.5873, 0.3559]

Depth: 3

• Network channel capacity: 25.3745

• Lower bound: 13.8906 in [8.1098, 18.0218]

• Representation compression: 0.0075

• View Dimensions & Probabilities

  • Hidden dimensions: [5270.4213, 3337.3608, 2178.5658]
  • Rounded hidden dims: [5270, 3337, 2179]
  • Dropout probabilities: [0.5873, 0.3877, 0.3950]

Depth: 4

• Network channel capacity: 33.3886

• Lower bound: 15.6878 in [8.1098, 18.0218]

• Representation compression: 0.0109

• View Dimensions & Probabilities

  • Hidden dimensions: [5270.4219, 3356.2480, 2732.2018, 1845.2651]
  • Rounded hidden dims: [5270, 3356, 2732, 1845]
  • Dropout probabilities: [0.5873, 0.3891, 0.4488, 0.4031]

Depth: 5

• Network channel capacity: 41.3389

• Lower bound: 17.1029 in [8.1098, 18.0218]

• Representation compression: 0.0145

• View Dimensions & Probabilities

  • Hidden dimensions: [5270.4284, 3345.8902, 2767.7160, 2394.2945, 1634.6767]
  • Rounded hidden dims: [5270, 3346, 2768, 2394, 1635]
  • Dropout probabilities: [0.5873, 0.3883, 0.4527, 0.4638, 0.4057]

Depth: 6

• Network channel capacity: 49.2641

• Lower bound: 18.2784 in [8.1098, 18.0218]

• Representation compression: 0.0182

• View Dimensions & Probabilities

  • Hidden dimensions: [5270.4177, 3358.8859, 2798.2368, 2462.5779, 2203.3201, 1476.9303]
  • Rounded hidden dims: [5270, 3359, 2798, 2463, 2203, 1477]
  • Dropout probabilities: [0.5873, 0.3892, 0.4545, 0.4681, 0.4722, 0.4013]