神经网络的收敛标准有最优值吗?

    技术2022-07-31  76

    作一个5分类的三层网络,分类9*9的图片,收敛标准从0.5到6e-8,共47个收敛标准,每个收敛标准收敛199次,共收敛了47*199次。取平均值统计平均性能pave。观察pave是如何随着收敛标准改变的。

     

    得到的表格

    f2[0]

    f2[1]

    f2[2]

    f2[3]

    f2[4]

    迭代次数n

    平均准确率p-ave

    δ

    耗时ms/次

    耗时ms/199次

    耗时 min/199

    最大值p-max

    平均值标准差

    0.4854799

    0.1858553

    0.272492

    0.2602853

    0.2563134

    1084.7739

    0.6110079

    0.5

    70.015075

    13949

    0.2324833

    0.8237011

    0.2530133

    0.5326435

    0.12101

    0.1954744

    0.1860563

    0.1582058

    1643.7136

    0.778164

    0.4

    78.79397

    15680

    0.2613333

    0.8505546

    0.0234568

    0.6958971

    0.0446005

    0.1856664

    0.1821425

    0.1503321

    1914.8794

    0.8280271

    0.3

    83.59799

    16654

    0.2775667

    0.8669002

    0.0191745

    0.7952586

    0.0322357

    0.1595491

    0.1555259

    0.1254544

    2235.7487

    0.8500412

    0.2

    89.135678

    17738

    0.2956333

    0.8898618

    0.0184869

    0.3876615

    0.0156595

    0.0816177

    0.0503286

    0.5872436

    3160.2261

    0.8985676

    0.1

    104.77387

    20850

    0.3475

    0.9208017

    0.0088857

    0.0611409

    0.0047451

    0.0363387

    0.0046498

    0.9119949

    6747.4322

    0.9403243

    0.01

    166.92462

    33218

    0.5536333

    0.9453201

    0.0018007

    0.3821803

    4.17E-04

    0.0911098

    0.0609155

    0.4675613

    28730.467

    0.9551943

    0.001

    550.80905

    109626

    1.8271

    0.9620549

    0.004127

    0.3118726

    3.98E-04

    0.1211546

    0.0457933

    0.5227548

    31145.402

    0.9568312

    9.00E-04

    587.94975

    117033

    1.95055

    0.9624441

    0.0036683

    0.2867465

    3.69E-04

    0.1261143

    0.0858857

    0.5026527

    34822.437

    0.9582198

    8.00E-04

    644.41709

    128254

    2.1375667

    0.963417

    0.0029477

    0.3319181

    3.20E-04

    0.1361159

    0.0406462

    0.4925607

    39842.181

    0.9591331

    7.00E-04

    738.93467

    147048

    2.4508

    0.96439

    0.002471

    0.3067792

    2.99E-04

    0.1159715

    0.0656649

    0.5126319

    45219.985

    0.9600444

    6.00E-04

    814.98995

    162229

    2.7038167

    0.9657521

    0.0024014

    0.3268212

    2.69E-04

    0.1209193

    0.0756559

    0.4774668

    53172.774

    0.9615122

    5.00E-04

    951.00503

    189281

    3.1546833

    0.9675034

    0.0029077

    0.251422

    0.0052492

    0.1811337

    0.0605513

    0.5025688

    63857.302

    0.9637104

    4.00E-04

    1132.3015

    225328

    3.7554667

    0.9696439

    0.0029834

    0.2413307

    0.0102346

    0.2061994

    0.0353675

    0.5075742

    80150.191

    0.9662254

    3.00E-04

    1408.1156

    280231

    4.6705167

    0.9747033

    0.00291

    0.1759618

    1.33E-04

    0.3669061

    0.1257354

    0.3317159

    113404.32

    0.9705993

    2.00E-04

    1971.5276

    392334

    6.5389

    0.9766492

    0.0027735

    0.0301947

    6.71E-05

    0.5176071

    0.1508071

    0.3015366

    178704.5

    0.9755657

    1.00E-04

    3079.9296

    612906

    10.2151

    0.9807356

    0.0020734

    0.0352193

    6.16E-05

    0.5728769

    0.1558284

    0.2362122

    189645.84

    0.9762081

    9.00E-05

    3289.3618

    654583

    10.909717

    0.9801518

    0.0017323

    0.0301881

    5.37E-05

    0.5326786

    0.1708962

    0.2663572

    199240.38

    0.9767577

    8.00E-05

    3124.5779

    621799

    10.363317

    0.980541

    0.0016933

    0.0201314

    4.96E-05

    0.5176013

    0.1909908

    0.2713782

    213000.2

    0.9770862

    7.00E-05

    3870.0804

    770149

    12.835817

    0.9820977

    0.0017903

    0.0201276

    4.13E-05

    0.5377

    0.1608375

    0.2814242

    232538.81

    0.9775898

    6.00E-05

    4183.5427

    832531

    13.875517

    0.9819031

    0.0019222

    0.0251499

    3.54E-05

    0.4321747

    0.2914793

    0.2512723

    261837.84

    0.9784054

    5.00E-05

    4671.7035

    929680

    15.494667

    0.9824869

    0.0017131

    0.020118

    0.0050529

    0.4673476

    0.2864494

    0.2211226

    293045.84

    0.97917

    4.00E-05

    4496.6231

    894833

    14.913883

    0.982876

    0.0017905

    0.0150892

    2.13E-05

    0.5125703

    0.206044

    0.266342

    341946.9

    0.9802202

    3.00E-05

    5834.7286

    1161121

    19.352017

    0.9836544

    0.0016258

    8.67E-06

    0.0050394

    0.467342

    0.2964908

    0.2311632

    408835.39

    0.9810798

    2.00E-05

    6995.1508

    1392042

    23.2007

    0.9846274

    0.0016328

    4.22E-06

    7.36E-06

    0.2663364

    0.4673396

    0.2663348

    576604.23

    0.9824663

    1.00E-05

    9819.1457

    1954028

    32.567133

    0.9856003

    0.0014906

    0.005029

    6.68E-06

    0.3567873

    0.3718623

    0.266335

    590518.09

    0.9824595

    9.00E-06

    10070.03

    2003949

    33.39915

    0.9861841

    0.0016341

    3.66E-06

    6.13E-06

    0.361812

    0.4221129

    0.2160835

    609672.87

    0.9826296

    8.00E-06

    10578.678

    2105158

    35.085967

    0.9854057

    0.0014217

    0.0100532

    5.28E-06

    0.3517614

    0.4321629

    0.206033

    649084.43

    0.9828379

    7.00E-06

    11378.653

    2264389

    37.739817

    0.9863787

    0.0014723

    2.51E-06

    4.55E-06

    0.3919619

    0.402012

    0.2060328

    688141.75

    0.9829699

    6.00E-06

    11112.593

    2211411

    36.85685

    0.9863787

    0.0013737

    0.0050274

    3.74E-06

    0.366836

    0.3919614

    0.2361828

    739405.14

    0.983187

    5.00E-06

    13885.628

    2763247

    46.054117

    0.9863787

    0.0013701

    0.0050268

    2.85E-06

    0.3165845

    0.4221118

    0.2562828

    814895.43

    0.9833523

    4.00E-06

    12441.407

    2475855

    41.26425

    0.9875462

    0.0013463

    0.0100515

    2.26E-06

    0.3115589

    0.4221114

    0.2562826

    898370.47

    0.983451

    3.00E-06

    15068.241

    2998588

    49.976467

    0.9867679

    0.0012352

    0.0100511

    0.0050265

    0.3065335

    0.4422116

    0.2361817

    1018724.4

    0.9834647

    2.00E-06

    17163.116

    3415468

    56.924467

    0.9865733

    0.0014891

    0.0100506

    6.75E-07

    0.2462316

    0.4422113

    0.3015079

    1244358.3

    0.9834852

    1.00E-06

    20607.568

    4100909

    68.348483

    0.9865733

    0.001324

    0.0100506

    6.44E-07

    0.3216084

    0.4522616

    0.2160808

    1291161.7

    0.9834999

    9.00E-07

    21746.186

    4327501

    72.125017

    0.987157

    0.0014341

    0.0050255

    5.71E-07

    0.2512566

    0.432161

    0.311558

    1360011.7

    0.9835537

    8.00E-07

    22496.085

    4476721

    74.612017

    0.9867679

    0.0014877

    0.0050254

    4.83E-07

    0.2412064

    0.432161

    0.3216083

    1402576.1

    0.9834344

    7.00E-07

    24104.799

    4796856

    79.9476

    0.9865733

    0.0014402

    0.0100505

    4.13E-07

    0.3015078

    0.4371861

    0.2512565

    1430741.6

    0.9834246

    6.00E-07

    24127.779

    4801430

    80.023833

    0.987157

    0.0014815

    0.0050253

    0.0100506

    0.3366836

    0.3718594

    0.2763821

    1539160.9

    0.9834148

    5.00E-07

    26017.894

    5177575

    86.292917

    0.9867679

    0.0013904

    0.0100504

    2.66E-07

    0.2964825

    0.4170855

    0.2763821

    1618461.8

    0.983409

    4.00E-07

    27559.96

    5484442

    91.407367

    0.9867679

    0.001473

    0.0100504

    2.00E-07

    0.2864323

    0.4020101

    0.3015076

    1702883.1

    0.9833728

    3.00E-07

    29320.739

    5834845

    97.247417

    0.9867679

    0.0013969

    0.0150755

    1.47E-07

    0.2663317

    0.4221106

    0.2964825

    1843820.1

    0.9831616

    2.00E-07

    31024.427

    6173862

    102.8977

    0.9865733

    0.0013638

    0.0050252

    0.0050252

    0.2763819

    0.3919598

    0.3216081

    2188509.1

    0.9828672

    1.00E-07

    37078.025

    7378528

    122.97547

    0.98813

    0.0015414

    0.0150754

    0.0100503

    0.2914573

    0.3517588

    0.3316583

    2266508.3

    0.9827519

    9.00E-08

    38511.402

    7663774

    127.72957

    0.9875462

    0.0015187

    0.0201005

    5.58E-08

    0.2964824

    0.3567839

    0.3266332

    2273906.5

    0.9828144

    8.00E-08

    38618.528

    7685090

    128.08483

    0.9861841

    0.0014832

    0.0100503

    4.94E-08

    0.2713568

    0.3969849

    0.3216081

    2310469.9

    0.9827157

    7.00E-08

    39082.382

    7777409

    129.62348

    0.9867679

    0.0014673

    0.0150754

    0.0100503

    0.2512563

    0.3668342

    0.3567839

    2424313.6

    0.9827822

    6.00E-08

    42822.03

    8521589

    142.02648

    0.9863787

    0.0015439

     

     

    这张图是δ=5e-5到δ=6e-8的pave曲线,相当直观当δ=8e-7时网络达到峰值,峰值是0.983554。

    这张图是δ=1e-5到δ=6e-8的pave曲线,表明对三层网络收敛标准是有最优值的,超过最优值以后网络性能是下降的。

    《估算卷积核数量的近似方法》实验表明卷积核数量是有最优值的

    《平均分辨准确率对网络隐藏层节点数的非线性变化关系03》实验表明隐藏层节点数是有最优值的。

    因为有最优值的存在,如果将网络的收敛标准设定为某一迭代次数,则将迭代次数调大并不必然导致网络的性能改善。如将收敛标准设为6e-8,平均性能只有峰值δ=8e-7的0.999216.但迭代次数却是峰值的1.78倍,耗时是峰值的1.9倍,也就是用了1.9倍的时间却换来性能下降万分之8.或者也可以解释成导致网络性能下降的一个原因恰恰是迭代次数过多了。

     

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