File size: 28,880 Bytes
e2e06a3
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
{
  "best_metric": null,
  "best_model_checkpoint": null,
  "epoch": 1.0,
  "eval_steps": 100,
  "global_step": 67,
  "is_hyper_param_search": false,
  "is_local_process_zero": true,
  "is_world_process_zero": true,
  "log_history": [
    {
      "completion_length": 588.9654293060303,
      "epoch": 0.014925373134328358,
      "grad_norm": 2.6534500122070312,
      "kl": 0.0,
      "learning_rate": 4.2857142857142857e-07,
      "loss": 0.0,
      "reward": 0.6618303954601288,
      "reward_std": 0.3340754471719265,
      "rewards/accuracy_reward": 0.6618303954601288,
      "rewards/format_reward": 0.0,
      "step": 1
    },
    {
      "completion_length": 574.2835121154785,
      "epoch": 0.029850746268656716,
      "grad_norm": 1.5236740112304688,
      "kl": 0.0,
      "learning_rate": 8.571428571428571e-07,
      "loss": 0.0,
      "reward": 0.6640625298023224,
      "reward_std": 0.35328569635748863,
      "rewards/accuracy_reward": 0.6640625298023224,
      "rewards/format_reward": 0.0,
      "step": 2
    },
    {
      "completion_length": 603.0803833007812,
      "epoch": 0.04477611940298507,
      "grad_norm": 1.810470461845398,
      "kl": 0.00018996000289916992,
      "learning_rate": 1.2857142857142856e-06,
      "loss": 0.0,
      "reward": 0.6685268227010965,
      "reward_std": 0.3423070926219225,
      "rewards/accuracy_reward": 0.6685268227010965,
      "rewards/format_reward": 0.0,
      "step": 3
    },
    {
      "completion_length": 662.1841831207275,
      "epoch": 0.05970149253731343,
      "grad_norm": 2.944155693054199,
      "kl": 0.00020492076873779297,
      "learning_rate": 1.7142857142857143e-06,
      "loss": 0.0,
      "reward": 0.6506696715950966,
      "reward_std": 0.3272070288658142,
      "rewards/accuracy_reward": 0.6506696715950966,
      "rewards/format_reward": 0.0,
      "step": 4
    },
    {
      "completion_length": 611.7890968322754,
      "epoch": 0.07462686567164178,
      "grad_norm": 0.5025805234909058,
      "kl": 0.00025087594985961914,
      "learning_rate": 2.142857142857143e-06,
      "loss": 0.0,
      "reward": 0.6216518208384514,
      "reward_std": 0.2848156485706568,
      "rewards/accuracy_reward": 0.6216518208384514,
      "rewards/format_reward": 0.0,
      "step": 5
    },
    {
      "completion_length": 606.5625228881836,
      "epoch": 0.08955223880597014,
      "grad_norm": 1.21269953250885,
      "kl": 0.0005187392234802246,
      "learning_rate": 2.571428571428571e-06,
      "loss": 0.0,
      "reward": 0.683035746216774,
      "reward_std": 0.3044421002268791,
      "rewards/accuracy_reward": 0.683035746216774,
      "rewards/format_reward": 0.0,
      "step": 6
    },
    {
      "completion_length": 600.8437728881836,
      "epoch": 0.1044776119402985,
      "grad_norm": 0.5010935664176941,
      "kl": 0.0006451606750488281,
      "learning_rate": 3e-06,
      "loss": 0.0,
      "reward": 0.7120536044239998,
      "reward_std": 0.27275579422712326,
      "rewards/accuracy_reward": 0.7120536044239998,
      "rewards/format_reward": 0.0,
      "step": 7
    },
    {
      "completion_length": 604.5390853881836,
      "epoch": 0.11940298507462686,
      "grad_norm": 1.0228732824325562,
      "kl": 0.0014821290969848633,
      "learning_rate": 2.9979443021318607e-06,
      "loss": 0.0001,
      "reward": 0.7533482499420643,
      "reward_std": 0.26047475449740887,
      "rewards/accuracy_reward": 0.7533482499420643,
      "rewards/format_reward": 0.0,
      "step": 8
    },
    {
      "completion_length": 628.8348484039307,
      "epoch": 0.13432835820895522,
      "grad_norm": 0.6632704734802246,
      "kl": 0.0016405582427978516,
      "learning_rate": 2.99178284305241e-06,
      "loss": 0.0001,
      "reward": 0.6897321715950966,
      "reward_std": 0.2548013962805271,
      "rewards/accuracy_reward": 0.6897321715950966,
      "rewards/format_reward": 0.0,
      "step": 9
    },
    {
      "completion_length": 626.3750247955322,
      "epoch": 0.14925373134328357,
      "grad_norm": 1.5124034881591797,
      "kl": 0.0020029544830322266,
      "learning_rate": 2.981532510892707e-06,
      "loss": 0.0001,
      "reward": 0.7689732499420643,
      "reward_std": 0.2507007820531726,
      "rewards/accuracy_reward": 0.7689732499420643,
      "rewards/format_reward": 0.0,
      "step": 10
    },
    {
      "completion_length": 653.0457916259766,
      "epoch": 0.16417910447761194,
      "grad_norm": 0.3473568558692932,
      "kl": 0.0020618438720703125,
      "learning_rate": 2.9672214011007086e-06,
      "loss": 0.0001,
      "reward": 0.7109375335276127,
      "reward_std": 0.24070814065635204,
      "rewards/accuracy_reward": 0.7109375335276127,
      "rewards/format_reward": 0.0,
      "step": 11
    },
    {
      "completion_length": 624.7511444091797,
      "epoch": 0.1791044776119403,
      "grad_norm": 4.333103656768799,
      "kl": 0.006229400634765625,
      "learning_rate": 2.9488887394336023e-06,
      "loss": 0.0002,
      "reward": 0.6964286062866449,
      "reward_std": 0.25179733615368605,
      "rewards/accuracy_reward": 0.6964286062866449,
      "rewards/format_reward": 0.0,
      "step": 12
    },
    {
      "completion_length": 638.3526973724365,
      "epoch": 0.19402985074626866,
      "grad_norm": 0.12630324065685272,
      "kl": 0.0025043487548828125,
      "learning_rate": 2.9265847744427307e-06,
      "loss": 0.0001,
      "reward": 0.7578125335276127,
      "reward_std": 0.2057263469323516,
      "rewards/accuracy_reward": 0.7578125335276127,
      "rewards/format_reward": 0.0,
      "step": 13
    },
    {
      "completion_length": 594.9152069091797,
      "epoch": 0.208955223880597,
      "grad_norm": 0.1356700211763382,
      "kl": 0.002197265625,
      "learning_rate": 2.9003706397458025e-06,
      "loss": 0.0001,
      "reward": 0.7857143208384514,
      "reward_std": 0.16860559629276395,
      "rewards/accuracy_reward": 0.7857143208384514,
      "rewards/format_reward": 0.0,
      "step": 14
    },
    {
      "completion_length": 577.4933338165283,
      "epoch": 0.22388059701492538,
      "grad_norm": 0.12567110359668732,
      "kl": 0.0028967857360839844,
      "learning_rate": 2.8703181864639013e-06,
      "loss": 0.0001,
      "reward": 0.820312537252903,
      "reward_std": 0.17374721262603998,
      "rewards/accuracy_reward": 0.820312537252903,
      "rewards/format_reward": 0.0,
      "step": 15
    },
    {
      "completion_length": 593.5212230682373,
      "epoch": 0.23880597014925373,
      "grad_norm": 0.1694745570421219,
      "kl": 0.0028734207153320312,
      "learning_rate": 2.8365097862825516e-06,
      "loss": 0.0001,
      "reward": 0.7645089589059353,
      "reward_std": 0.2047506500966847,
      "rewards/accuracy_reward": 0.7645089589059353,
      "rewards/format_reward": 0.0,
      "step": 16
    },
    {
      "completion_length": 585.3772563934326,
      "epoch": 0.2537313432835821,
      "grad_norm": 0.23806491494178772,
      "kl": 0.0028820037841796875,
      "learning_rate": 2.7990381056766585e-06,
      "loss": 0.0001,
      "reward": 0.7645089663565159,
      "reward_std": 0.2365775415673852,
      "rewards/accuracy_reward": 0.7645089663565159,
      "rewards/format_reward": 0.0,
      "step": 17
    },
    {
      "completion_length": 589.7611808776855,
      "epoch": 0.26865671641791045,
      "grad_norm": 0.15571320056915283,
      "kl": 0.002490997314453125,
      "learning_rate": 2.758005851918136e-06,
      "loss": 0.0001,
      "reward": 0.7544643264263868,
      "reward_std": 0.21331929927691817,
      "rewards/accuracy_reward": 0.7544643264263868,
      "rewards/format_reward": 0.0,
      "step": 18
    },
    {
      "completion_length": 603.9732398986816,
      "epoch": 0.2835820895522388,
      "grad_norm": 0.20735572278499603,
      "kl": 0.0032434463500976562,
      "learning_rate": 2.713525491562421e-06,
      "loss": 0.0001,
      "reward": 0.7667411062866449,
      "reward_std": 0.17671918543055654,
      "rewards/accuracy_reward": 0.7667411062866449,
      "rewards/format_reward": 0.0,
      "step": 19
    },
    {
      "completion_length": 608.0290489196777,
      "epoch": 0.29850746268656714,
      "grad_norm": 0.3643544912338257,
      "kl": 0.0036559104919433594,
      "learning_rate": 2.6657189421854562e-06,
      "loss": 0.0001,
      "reward": 0.7645089607685804,
      "reward_std": 0.16924317786470056,
      "rewards/accuracy_reward": 0.7645089607685804,
      "rewards/format_reward": 0.0,
      "step": 20
    },
    {
      "completion_length": 604.2723560333252,
      "epoch": 0.31343283582089554,
      "grad_norm": 0.22008363902568817,
      "kl": 0.0029211044311523438,
      "learning_rate": 2.6147172382160914e-06,
      "loss": 0.0001,
      "reward": 0.7466518208384514,
      "reward_std": 0.14925407292321324,
      "rewards/accuracy_reward": 0.7466518208384514,
      "rewards/format_reward": 0.0,
      "step": 21
    },
    {
      "completion_length": 604.7009181976318,
      "epoch": 0.3283582089552239,
      "grad_norm": 0.5150439739227295,
      "kl": 0.0036449432373046875,
      "learning_rate": 2.5606601717798212e-06,
      "loss": 0.0001,
      "reward": 0.7466518171131611,
      "reward_std": 0.20275325747206807,
      "rewards/accuracy_reward": 0.7466518171131611,
      "rewards/format_reward": 0.0,
      "step": 22
    },
    {
      "completion_length": 539.8783779144287,
      "epoch": 0.34328358208955223,
      "grad_norm": 0.08835027366876602,
      "kl": 0.0028405189514160156,
      "learning_rate": 2.5036959095382875e-06,
      "loss": 0.0001,
      "reward": 0.8080357424914837,
      "reward_std": 0.151585946790874,
      "rewards/accuracy_reward": 0.8080357424914837,
      "rewards/format_reward": 0.0,
      "step": 23
    },
    {
      "completion_length": 617.0491275787354,
      "epoch": 0.3582089552238806,
      "grad_norm": 0.11819685250520706,
      "kl": 0.0034465789794921875,
      "learning_rate": 2.4439805865747562e-06,
      "loss": 0.0001,
      "reward": 0.7209821790456772,
      "reward_std": 0.20670274924486876,
      "rewards/accuracy_reward": 0.7209821790456772,
      "rewards/format_reward": 0.0,
      "step": 24
    },
    {
      "completion_length": 561.9810562133789,
      "epoch": 0.373134328358209,
      "grad_norm": 0.1162777692079544,
      "kl": 0.0033864974975585938,
      "learning_rate": 2.3816778784387097e-06,
      "loss": 0.0001,
      "reward": 0.8359375335276127,
      "reward_std": 0.12302456051111221,
      "rewards/accuracy_reward": 0.8359375335276127,
      "rewards/format_reward": 0.0,
      "step": 25
    },
    {
      "completion_length": 603.2611846923828,
      "epoch": 0.3880597014925373,
      "grad_norm": 0.11348129063844681,
      "kl": 0.003231048583984375,
      "learning_rate": 2.316958552522541e-06,
      "loss": 0.0001,
      "reward": 0.7555803954601288,
      "reward_std": 0.19700363464653492,
      "rewards/accuracy_reward": 0.7555803954601288,
      "rewards/format_reward": 0.0,
      "step": 26
    },
    {
      "completion_length": 576.3515892028809,
      "epoch": 0.40298507462686567,
      "grad_norm": 0.10333164781332016,
      "kl": 0.003551483154296875,
      "learning_rate": 2.25e-06,
      "loss": 0.0001,
      "reward": 0.7332589626312256,
      "reward_std": 0.16596951289102435,
      "rewards/accuracy_reward": 0.7332589626312256,
      "rewards/format_reward": 0.0,
      "step": 27
    },
    {
      "completion_length": 576.9352893829346,
      "epoch": 0.417910447761194,
      "grad_norm": 0.08400996029376984,
      "kl": 0.003052234649658203,
      "learning_rate": 2.18098574960932e-06,
      "loss": 0.0001,
      "reward": 0.7656250335276127,
      "reward_std": 0.16529620438814163,
      "rewards/accuracy_reward": 0.7656250335276127,
      "rewards/format_reward": 0.0,
      "step": 28
    },
    {
      "completion_length": 572.9832820892334,
      "epoch": 0.43283582089552236,
      "grad_norm": 0.09134360402822495,
      "kl": 0.0033164024353027344,
      "learning_rate": 2.1101049646137005e-06,
      "loss": 0.0001,
      "reward": 0.7243303973227739,
      "reward_std": 0.18314252886921167,
      "rewards/accuracy_reward": 0.7243303973227739,
      "rewards/format_reward": 0.0,
      "step": 29
    },
    {
      "completion_length": 598.8917636871338,
      "epoch": 0.44776119402985076,
      "grad_norm": 0.0819033682346344,
      "kl": 0.003021240234375,
      "learning_rate": 2.03755192431795e-06,
      "loss": 0.0001,
      "reward": 0.772321455180645,
      "reward_std": 0.20655824523419142,
      "rewards/accuracy_reward": 0.772321455180645,
      "rewards/format_reward": 0.0,
      "step": 30
    },
    {
      "completion_length": 568.7176551818848,
      "epoch": 0.4626865671641791,
      "grad_norm": 0.1345580369234085,
      "kl": 0.004252433776855469,
      "learning_rate": 1.963525491562421e-06,
      "loss": 0.0002,
      "reward": 0.7767857536673546,
      "reward_std": 0.18306655017659068,
      "rewards/accuracy_reward": 0.7767857536673546,
      "rewards/format_reward": 0.0,
      "step": 31
    },
    {
      "completion_length": 579.5647583007812,
      "epoch": 0.47761194029850745,
      "grad_norm": 0.08470705151557922,
      "kl": 0.0035343170166015625,
      "learning_rate": 1.888228567653781e-06,
      "loss": 0.0001,
      "reward": 0.7957589663565159,
      "reward_std": 0.17081871908158064,
      "rewards/accuracy_reward": 0.7957589663565159,
      "rewards/format_reward": 0.0,
      "step": 32
    },
    {
      "completion_length": 609.633955001831,
      "epoch": 0.4925373134328358,
      "grad_norm": 0.07784049212932587,
      "kl": 0.0028290748596191406,
      "learning_rate": 1.8118675362266389e-06,
      "loss": 0.0001,
      "reward": 0.7578125335276127,
      "reward_std": 0.1949409432709217,
      "rewards/accuracy_reward": 0.7578125335276127,
      "rewards/format_reward": 0.0,
      "step": 33
    },
    {
      "completion_length": 622.8817157745361,
      "epoch": 0.5074626865671642,
      "grad_norm": 0.08559560030698776,
      "kl": 0.0029349327087402344,
      "learning_rate": 1.7346516975603465e-06,
      "loss": 0.0001,
      "reward": 0.7488839663565159,
      "reward_std": 0.19219930842518806,
      "rewards/accuracy_reward": 0.7488839663565159,
      "rewards/format_reward": 0.0,
      "step": 34
    },
    {
      "completion_length": 612.6897583007812,
      "epoch": 0.5223880597014925,
      "grad_norm": 0.07799447327852249,
      "kl": 0.002971649169921875,
      "learning_rate": 1.6567926949014804e-06,
      "loss": 0.0001,
      "reward": 0.7533482573926449,
      "reward_std": 0.1705156215466559,
      "rewards/accuracy_reward": 0.7533482573926449,
      "rewards/format_reward": 0.0,
      "step": 35
    },
    {
      "completion_length": 575.945333480835,
      "epoch": 0.5373134328358209,
      "grad_norm": 0.11088297516107559,
      "kl": 0.00347900390625,
      "learning_rate": 1.578503934364416e-06,
      "loss": 0.0001,
      "reward": 0.753348246216774,
      "reward_std": 0.18251199880614877,
      "rewards/accuracy_reward": 0.753348246216774,
      "rewards/format_reward": 0.0,
      "step": 36
    },
    {
      "completion_length": 575.522346496582,
      "epoch": 0.5522388059701493,
      "grad_norm": 0.07977250218391418,
      "kl": 0.003589630126953125,
      "learning_rate": 1.5e-06,
      "loss": 0.0001,
      "reward": 0.768973246216774,
      "reward_std": 0.172359649091959,
      "rewards/accuracy_reward": 0.768973246216774,
      "rewards/format_reward": 0.0,
      "step": 37
    },
    {
      "completion_length": 574.8672142028809,
      "epoch": 0.5671641791044776,
      "grad_norm": 0.07976463437080383,
      "kl": 0.0032825469970703125,
      "learning_rate": 1.4214960656355842e-06,
      "loss": 0.0001,
      "reward": 0.8125000409781933,
      "reward_std": 0.12335904035717249,
      "rewards/accuracy_reward": 0.8125000409781933,
      "rewards/format_reward": 0.0,
      "step": 38
    },
    {
      "completion_length": 568.9866352081299,
      "epoch": 0.582089552238806,
      "grad_norm": 0.11306460946798325,
      "kl": 0.004673480987548828,
      "learning_rate": 1.3432073050985201e-06,
      "loss": 0.0002,
      "reward": 0.7723214589059353,
      "reward_std": 0.15484962752088904,
      "rewards/accuracy_reward": 0.7723214589059353,
      "rewards/format_reward": 0.0,
      "step": 39
    },
    {
      "completion_length": 607.1752510070801,
      "epoch": 0.5970149253731343,
      "grad_norm": 0.1425676792860031,
      "kl": 0.0033125877380371094,
      "learning_rate": 1.2653483024396534e-06,
      "loss": 0.0001,
      "reward": 0.772321455180645,
      "reward_std": 0.17449467908591032,
      "rewards/accuracy_reward": 0.772321455180645,
      "rewards/format_reward": 0.0,
      "step": 40
    },
    {
      "completion_length": 534.8303833007812,
      "epoch": 0.6119402985074627,
      "grad_norm": 0.0919041708111763,
      "kl": 0.004061698913574219,
      "learning_rate": 1.1881324637733612e-06,
      "loss": 0.0002,
      "reward": 0.7745536006987095,
      "reward_std": 0.16172579256817698,
      "rewards/accuracy_reward": 0.7745536006987095,
      "rewards/format_reward": 0.0,
      "step": 41
    },
    {
      "completion_length": 560.0078372955322,
      "epoch": 0.6268656716417911,
      "grad_norm": 0.0930609181523323,
      "kl": 0.0036792755126953125,
      "learning_rate": 1.1117714323462188e-06,
      "loss": 0.0001,
      "reward": 0.8158482536673546,
      "reward_std": 0.170708823017776,
      "rewards/accuracy_reward": 0.8158482536673546,
      "rewards/format_reward": 0.0,
      "step": 42
    },
    {
      "completion_length": 601.4565029144287,
      "epoch": 0.6417910447761194,
      "grad_norm": 0.08595103770494461,
      "kl": 0.0032434463500976562,
      "learning_rate": 1.036474508437579e-06,
      "loss": 0.0001,
      "reward": 0.7522321753203869,
      "reward_std": 0.16597021045163274,
      "rewards/accuracy_reward": 0.7522321753203869,
      "rewards/format_reward": 0.0,
      "step": 43
    },
    {
      "completion_length": 553.7667694091797,
      "epoch": 0.6567164179104478,
      "grad_norm": 0.09559870511293411,
      "kl": 0.004054069519042969,
      "learning_rate": 9.624480756820497e-07,
      "loss": 0.0002,
      "reward": 0.7767857499420643,
      "reward_std": 0.14699635887518525,
      "rewards/accuracy_reward": 0.7767857499420643,
      "rewards/format_reward": 0.0,
      "step": 44
    },
    {
      "completion_length": 572.5535984039307,
      "epoch": 0.6716417910447762,
      "grad_norm": 0.07558111101388931,
      "kl": 0.0035276412963867188,
      "learning_rate": 8.898950353863e-07,
      "loss": 0.0001,
      "reward": 0.7901786155998707,
      "reward_std": 0.15063981525599957,
      "rewards/accuracy_reward": 0.7901786155998707,
      "rewards/format_reward": 0.0,
      "step": 45
    },
    {
      "completion_length": 627.7455635070801,
      "epoch": 0.6865671641791045,
      "grad_norm": 0.08073041588068008,
      "kl": 0.0030755996704101562,
      "learning_rate": 8.190142503906799e-07,
      "loss": 0.0001,
      "reward": 0.7421875447034836,
      "reward_std": 0.19877350237220526,
      "rewards/accuracy_reward": 0.7421875447034836,
      "rewards/format_reward": 0.0,
      "step": 46
    },
    {
      "completion_length": 561.7902069091797,
      "epoch": 0.7014925373134329,
      "grad_norm": 0.08770101517438889,
      "kl": 0.0040454864501953125,
      "learning_rate": 7.500000000000003e-07,
      "loss": 0.0002,
      "reward": 0.812500037252903,
      "reward_std": 0.18986603012308478,
      "rewards/accuracy_reward": 0.812500037252903,
      "rewards/format_reward": 0.0,
      "step": 47
    },
    {
      "completion_length": 582.2556076049805,
      "epoch": 0.7164179104477612,
      "grad_norm": 0.08533724397420883,
      "kl": 0.0029554367065429688,
      "learning_rate": 6.830414474774594e-07,
      "loss": 0.0001,
      "reward": 0.8058036006987095,
      "reward_std": 0.1576297921128571,
      "rewards/accuracy_reward": 0.8058036006987095,
      "rewards/format_reward": 0.0,
      "step": 48
    },
    {
      "completion_length": 613.2410888671875,
      "epoch": 0.7313432835820896,
      "grad_norm": 0.08394148200750351,
      "kl": 0.0036144256591796875,
      "learning_rate": 6.183221215612905e-07,
      "loss": 0.0001,
      "reward": 0.7667411081492901,
      "reward_std": 0.20444503612816334,
      "rewards/accuracy_reward": 0.7667411081492901,
      "rewards/format_reward": 0.0,
      "step": 49
    },
    {
      "completion_length": 596.3806076049805,
      "epoch": 0.746268656716418,
      "grad_norm": 0.09445685148239136,
      "kl": 0.0038156509399414062,
      "learning_rate": 5.560194134252441e-07,
      "loss": 0.0002,
      "reward": 0.7154018096625805,
      "reward_std": 0.16886480245739222,
      "rewards/accuracy_reward": 0.7154018096625805,
      "rewards/format_reward": 0.0,
      "step": 50
    },
    {
      "completion_length": 588.2489070892334,
      "epoch": 0.7611940298507462,
      "grad_norm": 0.1409761756658554,
      "kl": 0.0034036636352539062,
      "learning_rate": 4.963040904617131e-07,
      "loss": 0.0001,
      "reward": 0.7779018171131611,
      "reward_std": 0.15530426986515522,
      "rewards/accuracy_reward": 0.7779018171131611,
      "rewards/format_reward": 0.0,
      "step": 51
    },
    {
      "completion_length": 582.168550491333,
      "epoch": 0.7761194029850746,
      "grad_norm": 0.08169642090797424,
      "kl": 0.0034346580505371094,
      "learning_rate": 4.3933982822017883e-07,
      "loss": 0.0001,
      "reward": 0.7421875409781933,
      "reward_std": 0.17119849054142833,
      "rewards/accuracy_reward": 0.7421875409781933,
      "rewards/format_reward": 0.0,
      "step": 52
    },
    {
      "completion_length": 590.315881729126,
      "epoch": 0.7910447761194029,
      "grad_norm": 0.09575485438108444,
      "kl": 0.0036096572875976562,
      "learning_rate": 3.852827617839085e-07,
      "loss": 0.0001,
      "reward": 0.776785746216774,
      "reward_std": 0.20339447353035212,
      "rewards/accuracy_reward": 0.776785746216774,
      "rewards/format_reward": 0.0,
      "step": 53
    },
    {
      "completion_length": 571.912971496582,
      "epoch": 0.8059701492537313,
      "grad_norm": 0.07775302976369858,
      "kl": 0.0041255950927734375,
      "learning_rate": 3.3428105781454364e-07,
      "loss": 0.0002,
      "reward": 0.7544643320143223,
      "reward_std": 0.14612831640988588,
      "rewards/accuracy_reward": 0.7544643320143223,
      "rewards/format_reward": 0.0,
      "step": 54
    },
    {
      "completion_length": 575.9989128112793,
      "epoch": 0.8208955223880597,
      "grad_norm": 0.13639913499355316,
      "kl": 0.0060577392578125,
      "learning_rate": 2.86474508437579e-07,
      "loss": 0.0002,
      "reward": 0.7745536118745804,
      "reward_std": 0.1799168661236763,
      "rewards/accuracy_reward": 0.7745536118745804,
      "rewards/format_reward": 0.0,
      "step": 55
    },
    {
      "completion_length": 595.2321643829346,
      "epoch": 0.835820895522388,
      "grad_norm": 0.09935541450977325,
      "kl": 0.0034551620483398438,
      "learning_rate": 2.419941480818641e-07,
      "loss": 0.0001,
      "reward": 0.7566964663565159,
      "reward_std": 0.1705572777427733,
      "rewards/accuracy_reward": 0.7566964663565159,
      "rewards/format_reward": 0.0,
      "step": 56
    },
    {
      "completion_length": 578.415205001831,
      "epoch": 0.8507462686567164,
      "grad_norm": 0.08712073415517807,
      "kl": 0.0035562515258789062,
      "learning_rate": 2.0096189432334195e-07,
      "loss": 0.0001,
      "reward": 0.7868303917348385,
      "reward_std": 0.1490265424363315,
      "rewards/accuracy_reward": 0.7868303917348385,
      "rewards/format_reward": 0.0,
      "step": 57
    },
    {
      "completion_length": 570.0915451049805,
      "epoch": 0.8656716417910447,
      "grad_norm": 0.08893033117055893,
      "kl": 0.003448486328125,
      "learning_rate": 1.634902137174483e-07,
      "loss": 0.0001,
      "reward": 0.7868303954601288,
      "reward_std": 0.13831894285976887,
      "rewards/accuracy_reward": 0.7868303954601288,
      "rewards/format_reward": 0.0,
      "step": 58
    },
    {
      "completion_length": 570.3884201049805,
      "epoch": 0.8805970149253731,
      "grad_norm": 0.0921068862080574,
      "kl": 0.0033750534057617188,
      "learning_rate": 1.2968181353609853e-07,
      "loss": 0.0001,
      "reward": 0.8102678991854191,
      "reward_std": 0.15646472247317433,
      "rewards/accuracy_reward": 0.8102678991854191,
      "rewards/format_reward": 0.0,
      "step": 59
    },
    {
      "completion_length": 562.8716716766357,
      "epoch": 0.8955223880597015,
      "grad_norm": 0.06974907219409943,
      "kl": 0.0035638809204101562,
      "learning_rate": 9.962936025419756e-08,
      "loss": 0.0001,
      "reward": 0.7857143245637417,
      "reward_std": 0.1675086230970919,
      "rewards/accuracy_reward": 0.7857143245637417,
      "rewards/format_reward": 0.0,
      "step": 60
    },
    {
      "completion_length": 584.5279273986816,
      "epoch": 0.9104477611940298,
      "grad_norm": 0.13824282586574554,
      "kl": 0.003696441650390625,
      "learning_rate": 7.341522555726971e-08,
      "loss": 0.0001,
      "reward": 0.7511161006987095,
      "reward_std": 0.19415182201191783,
      "rewards/accuracy_reward": 0.7511161006987095,
      "rewards/format_reward": 0.0,
      "step": 61
    },
    {
      "completion_length": 549.1629695892334,
      "epoch": 0.9253731343283582,
      "grad_norm": 0.10054602473974228,
      "kl": 0.004033088684082031,
      "learning_rate": 5.11112605663977e-08,
      "loss": 0.0002,
      "reward": 0.8381696827709675,
      "reward_std": 0.1603721366263926,
      "rewards/accuracy_reward": 0.8381696827709675,
      "rewards/format_reward": 0.0,
      "step": 62
    },
    {
      "completion_length": 593.0893096923828,
      "epoch": 0.9402985074626866,
      "grad_norm": 0.08826031535863876,
      "kl": 0.0032329559326171875,
      "learning_rate": 3.277859889929147e-08,
      "loss": 0.0001,
      "reward": 0.812500037252903,
      "reward_std": 0.1807763264514506,
      "rewards/accuracy_reward": 0.812500037252903,
      "rewards/format_reward": 0.0,
      "step": 63
    },
    {
      "completion_length": 549.9207801818848,
      "epoch": 0.9552238805970149,
      "grad_norm": 0.0768972784280777,
      "kl": 0.0036096572875976562,
      "learning_rate": 1.846748910729351e-08,
      "loss": 0.0001,
      "reward": 0.8225446753203869,
      "reward_std": 0.12298994930461049,
      "rewards/accuracy_reward": 0.8225446753203869,
      "rewards/format_reward": 0.0,
      "step": 64
    },
    {
      "completion_length": 544.910737991333,
      "epoch": 0.9701492537313433,
      "grad_norm": 0.07084512710571289,
      "kl": 0.0035963058471679688,
      "learning_rate": 8.217156947590065e-09,
      "loss": 0.0001,
      "reward": 0.8169643096625805,
      "reward_std": 0.12426057457923889,
      "rewards/accuracy_reward": 0.8169643096625805,
      "rewards/format_reward": 0.0,
      "step": 65
    },
    {
      "completion_length": 587.8024768829346,
      "epoch": 0.9850746268656716,
      "grad_norm": 0.08717910200357437,
      "kl": 0.003803253173828125,
      "learning_rate": 2.0556978681392503e-09,
      "loss": 0.0002,
      "reward": 0.7444196753203869,
      "reward_std": 0.17243521055206656,
      "rewards/accuracy_reward": 0.7444196753203869,
      "rewards/format_reward": 0.0,
      "step": 66
    },
    {
      "completion_length": 574.7916831970215,
      "epoch": 1.0,
      "grad_norm": 0.0701616182923317,
      "kl": 0.0031533241271972656,
      "learning_rate": 0.0,
      "loss": 0.0001,
      "reward": 0.7291666679084301,
      "reward_std": 0.0578637570142746,
      "rewards/accuracy_reward": 0.7291666679084301,
      "rewards/format_reward": 0.0,
      "step": 67
    },
    {
      "epoch": 1.0,
      "step": 67,
      "total_flos": 0.0,
      "train_loss": 0.00012216681254848273,
      "train_runtime": 12383.6526,
      "train_samples_per_second": 0.606,
      "train_steps_per_second": 0.005
    }
  ],
  "logging_steps": 1,
  "max_steps": 67,
  "num_input_tokens_seen": 0,
  "num_train_epochs": 1,
  "save_steps": 500,
  "stateful_callbacks": {
    "TrainerControl": {
      "args": {
        "should_epoch_stop": false,
        "should_evaluate": false,
        "should_log": false,
        "should_save": false,
        "should_training_stop": false
      },
      "attributes": {}
    }
  },
  "total_flos": 0.0,
  "train_batch_size": 1,
  "trial_name": null,
  "trial_params": null
}