1
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Imagine a model choosing its next word, with several
continuations that fit the same context.

2
00:00:06,160 --> 00:00:11,340
Our first bar is the observed label; the others are alternatives
in this original teaching example.

3
00:00:12,340 --> 00:00:18,600
A training example records one continuation, without proving
that every other plausible continuation is wrong.

4
00:00:19,560 --> 00:00:25,440
Imagine an update pushing nearly all probability onto the label,
making the alternatives difficult to sample.

5
00:00:26,400 --> 00:00:32,500
These probabilities are illustrative, but increasing target
confidence can also erase other useful possibilities.

6
00:00:33,520 --> 00:00:40,080
Can supervised adaptation learn the observed answer while
preserving useful relationships among the other possibilities?

7
00:00:40,900 --> 00:00:47,620
The paper studies pretrained distributions, rather than treating
every non-label token as uninformative tail noise.

8
00:00:48,820 --> 00:00:54,380
Entropy analysis finds comparable candidate probabilities,
corresponding to different effective support sizes.

9
00:00:55,560 --> 00:01:01,560
Shannon and Renyi entropies describe effective support size and
how close the normalized profile is to uniform.

10
00:01:02,680 --> 00:01:08,880
Small groups can reflect semantic branching; larger groups can
reflect structural ambiguity among plausible digits.

11
00:01:10,240 --> 00:01:16,640
Reported patterns span instruction, code, and mathematics
datasets across different model families and architectures.

12
00:01:17,840 --> 00:01:22,940
The goal preserves plausible alternative structure, while
allowing their absolute probabilities to change.

13
00:01:23,767 --> 00:01:31,027
LP-SFT selects local candidates from the frozen base model,
using its highest ranked next-token possibilities.

14
00:01:31,967 --> 00:01:38,307
It removes the supervised label, leaving only non-label
candidates as the explicit objects of preservation.

15
00:01:39,307 --> 00:01:45,247
Cross-entropy pushes the label upward; preserving that same
label could directly oppose its supervision.

16
00:01:46,167 --> 00:01:51,827
The target learns from the example, while the preservation term
protects relationships among the alternatives.

17
00:01:52,707 --> 00:01:59,507
The default uses ten base candidates, covering several plausible
regimes without a separate per-token schedule.

18
00:02:00,287 --> 00:02:05,567
This is a training objective, rather than an inference-time
requirement to filter generated words.

19
00:02:06,233 --> 00:02:12,033
Return to the toy distribution, with an update raising the label
while retaining alternative proportions.

20
00:02:13,013 --> 00:02:20,073
The alternatives start at thirty, twenty, and ten percent:
relative proportions of three to two to one.

21
00:02:20,833 --> 00:02:27,473
Their updated probabilities are fifteen, ten, and five percent,
so their combined mass falls by half.

22
00:02:28,513 --> 00:02:35,513
Inside the non-label set, the relative profile remains;
meanwhile, the supervised label gains probability.

23
00:02:36,553 --> 00:02:42,473
Local normalization compares the alternative set shape,
independently of the total probability assigned to it.

24
00:02:43,513 --> 00:02:50,253
These ratios illustrate the goal; real training encourages
preservation through a loss, rather than invented values.

25
00:02:50,860 --> 00:02:57,780
The objective combines target cross-entropy with KL over locally
normalized non-label candidate distributions.

26
00:02:58,880 --> 00:03:03,960
Cross-entropy learns observed response tokens from supervised
instruction and response examples.

27
00:03:04,940 --> 00:03:10,520
The second term uses fixed base information to protect relative
preferences among selected alternatives.

28
00:03:11,720 --> 00:03:18,260
Gradient analysis explains why unnormalized matching instead
pushes more probability mass toward the alternatives.

29
00:03:19,380 --> 00:03:25,620
Local normalization removes that pressure; target exclusion
prevents direct conflict with the label supervision.

30
00:03:26,580 --> 00:03:31,720
The frozen base is a local structural reference, rather than a
stronger teacher producing new answers.

31
00:03:32,347 --> 00:03:37,687
A naive implementation would keep both models in memory and run
the frozen base at each step.

32
00:03:38,427 --> 00:03:44,847
LP-SFT uses the fact that its base model and training examples
are fixed before optimization begins.

33
00:03:45,507 --> 00:03:51,947
An offline pass computes base candidate logits and caches the
information needed for local preservation sets.

34
00:03:52,827 --> 00:04:00,027
Fine-tuning compares current model logits with that cache,
restricting the comparison to relevant non-label candidates.

35
00:04:00,727 --> 00:04:06,687
This avoids an extra frozen-model forward pass at each step
while retaining the local base preferences.

36
00:04:07,707 --> 00:04:13,887
Cache construction remains a separate, one-time preparation cost
alongside the ongoing fine-tuning computation.

37
00:04:14,507 --> 00:04:18,847
Table one uses Qwen version three, with fourteen billion
parameters.

38
00:04:19,667 --> 00:04:24,067
It is fine-tuned on mixed mathematics, code, and general
instruction data.

39
00:04:24,947 --> 00:04:29,987
The aggregate averages displayed single-sample, finite-budget,
and general knowledge metrics.

40
00:04:30,847 --> 00:04:37,467
The base scores sixty-six point seven nine; cross-entropy
fine-tuning reaches fifty-eight point five five.

41
00:04:38,287 --> 00:04:45,867
LP-SFT reaches sixty-five point three two, reducing the gap
while remaining below this configuration base average.

42
00:04:46,926 --> 00:04:54,327
MMLU accuracy likewise stays closer to the base under LP-SFT
than cross-entropy in this matched comparison.

43
00:04:55,127 --> 00:05:01,167
These scoped retention results use a mean of displayed metrics,
rather than pooled benchmark task accuracy.

44
00:05:01,773 --> 00:05:08,093
Separate the supervised lesson from the alternative structure
that the pretrained model already considers plausible.

45
00:05:09,073 --> 00:05:16,733
Target exclusion protects supervision; local normalization
preserves relationships without fixing alternative mass.

46
00:05:17,873 --> 00:05:23,953
These choices strengthen the label while encouraging non-label
preferences to survive domain adaptation.

47
00:05:25,153 --> 00:05:31,153
Evaluation tests one sampled answer and access to correct
solutions within a finite sampling budget.

48
00:05:32,153 --> 00:05:38,353
Matched results support preservation, while the objective
specifies which relationships receive protection.

49
00:05:39,353 --> 00:05:47,093
As the observed answer improves, LP-SFT asks which other
plausible continuations should remain possible after training.