What Does Post-training Change?

Task and Starting Point

This course looks at a specific question: how to change its behavior with demonstration and preference after a conditional probabilities strategy is in place, and knowing what is best for itself. Readers should learn the Python list and function, limited probability, logarithm, lead numbers and chain rules; softmax and cross-entropy will be rolled out in the next chapter. SFT/DPO, all of the parameters are actually learned. It is not a commercial large model, and it has no pre-training language or online model interface; limited tasks allow preferences, probabilities and KL to be checked exhaustively, and then the mechanisms are mapped to language models to identify additional assumptions.

In the language model, pre-training is usually tasked with a large number of text next totoken forecasts, monitoring fine-tuning is directed at the model answer given by the given reminder, and learning preferences are based on two of the same hints for better comparison. The three data objects are not equal. The demonstration provides an apparent specific answer, but does not indicate who is worse; comparisons are given in relative order, but do not normally give absolute quality values. This course builds SFT, data preferences, Bradley-Terry Award Model, KL Best Strategies and DPOs, and ultimately measures behavior in an independent context. A demonstration incentive model is used to understand and contrast, and is not a component that DPO training must use.

An Exhaustively Enumerable Post-training Environment

The project hint is non-zero X, the task being to judge positives and negatives and to be as brief as possible. Four response numbers are fixed: zero “Negative，Short”, one “Positive，Short”, two “Negative，Long” and three “Positive，Long”. Each number here represents a complete answer, not the first word of an answer. Only once is the action generated, so the condition response distribution is equal to a single four-class Softmax. We will not describe this simplified as a fully trained self-return language model; and many token answers appear and hides are specifically deproveded in chapter II.

Bring the action together into an A, strategy writing. $\pi_\theta(a\mid x)$ and a is in four numbers, $\theta$ is a training parameter. Each action has two parameters: the slope between bias and x, logit is $z_a=b_a+w_ax$, which is eight metrics. Softmax turns the real logit into a strict positive, and one probability. This parameter is an expression of linear trends associated with positives and negatives, and does not express any mandate. To be able to observe all errors, we keep four actions, and training does not obscure the wrong categories; the correctness must come from learning rather than deleting errors from the pool of candidates.

The context of training is negative three, negative two, negative one, positive one, positive two, positive three; validation is positive one five and negative one five; testing is positive one five five five and three five. There are no overlaps in the three aggregate values, but the rules for sharing “Look at the symbols.” test range from close to zero and beyond absolute training value. It is not a new task distribution, much less a proof range that natural language understands. The project uses fixed data summaries to cover both action definition, division, demonstration and comparison generation rules; and any change to either is considered a new experiment and the old state entry will reject the digest.

Examples, Preferences, and Evaluation Functions

There are three models for each training x: two correct shorts and one correct and lengthy. So the experience of the same context shows a ratio of two-thirds to one-third, and the wrong action zeroes. Repeated samples are intentional weights, not three different people who actually write these words. If the model is free to assign probabilities to each context, SFT best works to match them; our shared linear parameters and limited step optimizations can only approximate it. Keeping the long demonstration allows for an extraordinary goal of behavior adjustment to follow-up preferences, rather than SFT has already pushed the short probability to one.

The preferences set gives a short answer to each X selection correctly: Winner, paired with three other responses, and compared to 18 trainings. It clearly prefers the correct and short, but does not directly compare the order between two failed answers. The labels are entirely produced by public rules and are not from human labelers; they are called “Human Value Aligning Data” over evidence. We use an independent defined inspection function. $u(x,a)=\mathbf1[\operatorname{sign}(a)x>0]-0.2(1-\operatorname{brief}(a))$ Assessments that the previous reward is correct and the subsequent punishment is lengthy. This function is not a BT score in training, nor is it a DPO hidden reward.

Example 1: Complete Behavioral Accounting for a Uniform Policy

The correct action is one to three, the total correct quality is one; and the short action is zero to one, and the total short quality is one. The four effects are zero, one, negative zero two, zero eight, so the expected effect is four by four, equal to zero four. Even if greedy chooses zero and wrongly answers the correct quality of the probability distribution is one in two; “greedyAccuracy” is not the same as the "Red-in rate for random sampling of tactics".

Now change the probability to [0.05,0.60,0.05,0.30]. The total correct quality is 0. 90 Short mass. 65 The expected utility is 0.60 plus 0.30 times 0.8 minus 0.05 times 0. 2 equals 0. 83. The other route is checked by "the correct quality minus two times the long quality" and gets 0.90−0.2 × 0.35 Also, it's 0. 83. This is the first independent, permanent equivalent verification to detect the realization of a failed, lengthy action that mixes shortness with the correct axis or leaves it.

Example 2: SFT Fit Does Not Imply Preference Optimality

The ideal model distribution gives two-thirds of the probability to the right shortness, one-third to the right length, one-third to the right quality, and one-two-thirds to the desired effect of zero-two times one-third, or fourteen-fifths. If the preference phase moves the probability to the right size, the expectation is one, but the SFT model cross-alcerium will change, because there are indeed lengthy answers. No separate “TraininglossDrop” can substitute for behavioural objectives: different loss scenarios must first say whether it wishes to imitate the frequency of the demonstration or change preferences.

This example also reveals support conditions. Limited logit softmax gives each action a positive probability that it cannot accurately achieve zero probability of error action in a limited parameter; the ideal distribution is merely an unlimited expression of boundary resolution in space, not the precise end point for 200-step training. If the probability of certain actions is hardened to zero, then the relative reference probability may not be defined with KL. The project retains support, uses stable log probabilities, independently checks the probability of each context and one, and checks all log losses are limited.

Data Boundaries and Identifiable Content

The preference label does not determine absolute zero: all responses are given a constant number under the same x, and all two wins remain unchanged. It also does not determine the behaviour of uncomparisoned answers in all new contexts. Filling these gaps with a simple parameter group is a model hypothesis, not proof of the label itself. The project incentive uses two observable features: action symbols multiplied by x, and whether it is short; it shares cross context information in a linear manner.

The data check must confirm that Winner shares the same x with Loser, that both are legal moves and context-based by training. The same Pair repeats changes the weight of experience, and reverse repeats indicate differences in labelling, which cannot always be deleted. The current rule is to determine no noise comparisons, so then the BT at the back will have a pressure on the parameter scale of scalable data; the course will use this failure mechanism to explain whether the correct ranking accuracy rate has been calibrated as an incentive probability.

In addition to the context partitions, the candidate generation process should be frozen. Realistic preferences, if they contain only answers that are easily generated by an old strategy, do not have direct label support for incentives or DPO constraints when a new strategy moves to an uncovered area. The Winner of this project, who has four candidates out of three, has a clear and narrow coverage; there is no simulation of unlimited candidate space in open text.

Project State and This Lesson's Validation

The initial base is a random eight-parameter strategy, which does not pretend to be a basic model from pre-training in large languages. SFT ends by copying reference; subsequent DPOs only update independent copies and reference remains frozen. The reward model has two other parameters that are not shared with the strategy. A clear target identity prevents “References are updated.”, a loss that can still run but changes the mathematical target. JSON saves the summary of data, phase parameters,seed,seed, $\beta$ With the complete check point history, standard library training does not hide online services or external random output.

This chapter delivers as a compact of tasks, action sequences, data partitions and three evaluation volumes. Chapter II provides evidence that all eight strategic parameters are actually updated from the demonstration simulating the SFT gradient; and chapter III addresses how comparisons can enter statistical models. Before moving forward, readers should be able to calculate the correct quality, short quality and desired utility of any four probability vectors on paper, noting that these values describe only this limited task and cannot be renamed generic security, factual or commercial large model capabilities.

This course ends with a complete decoder sequence feed, which continues to be on four categories. It answers with ASCII tips and multibytes, response-only SFT from random parameters, and then responds to the full logprob for DPOs; embedding, attention, location, foreplay, reclassification, and output head all updated. It can count each formula against the limited range, and it is responsible for checking the real sequence link from a full decoder. Chapter VII would correspond to the probabilities of each of the two, and chapter VIII would retain the standard format successfully and the format migration failed.

The task clearly excludes X, because the four responses do not have “nil” as a category. For zero input to be rated by force, only undefined problems are packaged into model errors; action and rules should be expanded before data summaries should be updated. Positive + + +05 in the test is still defined as non-zero, but close to the boundary. A model that does not perform well at this border is a legitimate failure to observe, and it is not the same thing to ask it about zero without a defined label.

p=[.05,.60,.05,.30]
u=[0.,1.,-.2,.8]
assert abs(sum(p)-1)<1e-12
correct=p[1]+p[3]; brief=p[0]+p[1]
expected=sum(a*b for a,b in zip(p,u))
assert abs(expected-(correct-.2*(1-brief)))<1e-12
ideal=1-.2/3
print('correct mass',correct,'brief mass',brief,'expected utility',expected,'ideal SFT utility',ideal)