Define Tasks, Trajectories and Rewards

What You Will Build in This Course

The course links all the key elements of intensive learning to a laboratory that can be downloaded, run, checked and rebutted. Readers need Python functions, lists, limited summation, logarithm and basic orientation; when it comes to probability of conditions, variation, strategy gradients, group baselines and relative entropy, instructions are pre-used. The end point is to explain why an update was created, what was verified and which tasks failed, rather than to call several lines as “Big model reasoning training”.

The entire book uses the same original algorithm protocol. $x=(a,b)$, two of which are in the range of zero to four, with 25 questions. $y=(u,v,e)$: Write integer and $u=a+b$ I'll write this and double it to ten. $v=(2u)\bmod 10$, end-of-word character $e$. The remainder is divided by non-negative after ten years, for example 12 divided by more than ten. The first step is not a natural language interpretation, but a verifiable intermediate state; the second step must be consistent with it. Nor can it be demonstrated that the network has followed this algorithm sequentially in human terms.

Separate the Object from Its Encoding

Math numbers, integer numbers in models and display characters are three things. This item just sets the numbering of ten numbers to zero to nine, but plus number 10, equal number 11, start BOS XII, terminate task EOS 13. $(2,2)$ Sequentialized as [12,2,10,2,11], responding correctly to [4,8,13]. The size of 14 does not mean that 14 moves are allowed at each step; training and sampling are jointly bound by clear grammar, with the first two steps allowing only 10 numbers and the third is terminated by force.

The random sample space given for the given input is therefore all 100 two digital tracks, each of which is finally joined to the same EOS. The event is a random subset of these tracks. The strategy gives each track a non-negative probability, with all probability added to one. The training distribution of the input task is evenly distributed on 20 training topics, with a separate test distribution; the two cannot be confused with the same undefined “Data distribution”. All logarithmics are natural and the probabilities are relative to Nat, with no incentive for physical units.

The original 14-dimensional logits for model output are not yet re-aligned. Take the first 10-dimensional softmax and get the current restricted action distribution; this is the equivalent of setting the score of other actions to a negative and then to a single one. The probability cannot be taken first on fourteen actions, and then deleted four as a new probability, which is always less than one. The support restriction here is already preventing free format failure, and the report must state that “The rate of correctness in restricted grammar” cannot be promoted as a free text output reliability.

Reward as the Task Contract

Certifier is a sure function that receives tasks and complete responses, returns the incentive zero or one and the reason for failure. Use the indicator function $\mathbf1\{C\}$ This means that condition C is established as one, or zero. Checks the type, length and range of tasks, and then the response is exactly three real integer numbers. The boolean value in Python is an integer subcategory, so it must be checked to reject True assuming numbers with a strict type. Then check the first two at zero to nine, the last one just happens to be EOS, and finally check the middle and final number in order. Any excess, little step or invalid number fails.

Stinging this order will separate the three failures of formatting, intermediate steps, and final steps, but the diagnostic label is not an additional reward. Adding the correct format to zero two and the right middle to zero three is another plastic set of rewards that may be useful or induces only easy-to-scoring steps. We first use rigorous incentives, using “Mission successful.” as the only training feedback; the later comparison discusses how to change the target.

Example 1: Every Check on a Correct Trajectory

Enter $(3,4)$ The response should be [7,4,13]. The check length of three, each element type, int, two numbers is legal, the end stop is legal, the check seven equals three plus four and four equals 14 more. If the network exports [7,14,13], the intention to double may be correct, but the number XIV is not supported by the action and has not been taken, the format should fail and cannot be given a full score based on subjective understanding.

Output with the same theme [4,8,13] The second step is indeed double the first step, but it is wrong to enter and calculate; the reward is still zero. “It's internal.” and “Complete original task” Not the same condition. Output. [7,4] without an end mark; output [7,4,13,13] It's a lot of markers. We'd rather define these boundaries in a contract ahead of time, rather than make provisional changes to the rules after the result, so as to preserve the seemingly good curve.

Example 2: A Uniform Policy Provides Positive and Negative Controls

If each step is independent and evenly balanced for 10 figures, the probability of any trajectory is 1%. With only one track that has been strictly tested, the probability of success is 1% rather than 1/10%. The first step is one tenth, and the second step is one tenth, with one percent of the right number, under which conditions. If you look at the final balance, sometimes the same amount is given in the middle of the error and happens to be given; and the strict reward is deliberately not calculated as a short cut.

The probability of a complete failure when the model sampled a set of eight separate tracks is $0.99^8$ About 92%, 27%; at least one success is about 7.73%. This explains why the reward for many groups is zero, starting with random tactics.

A Data Split That Exposes a Difficult Generalization Gap

The project leaves all five inputs equal to and equal to four for testing: zero plus four, one plus three, two plus two, three plus one, four plus zero. The training collection contains the remaining 20 questions. This is not a five-point combination extrapolation test from random sampling of the same distribution, but rather a combined extrapolation pressure test without an intermediate result. If the test fails, we can only say that this experiment has not learned the extrapolation; it does not prove that all intensive learning is indisputable.

Split files are locked by the constants and data summaries in the code. Topics, protocols, rewards and sequenced entry into the SHA-256 digest, rechecking when loading check points to avoid using new rules to explain old weights. The summary detects byte changes and does not prove that there is no statistical correlation between the data; training and testing of shared add-up structures are part of the design. We do not mix test topics into monitoring models, nor select training steps based on test performance, and fixed budgets are fully recorded in chapters V to VIII.

From This Lesson to Subsequent Updates

This chapter only defines the environment and does not allow the existence of incentives to be considered as learning. Chapter II begins with a precise strategic gradient on three limited actions, chapter III proves when the group baseline will be maintained, chapter IV adds a reference distribution constraint, chapter V provides a full trajectory probability to a real decoder, chapter VI takes samples and updates all parameters. Chapter VII compares training gains, testing degradation, and extra sampling budgets, and chapter VIII rebuilds the entire evidence chain. Each step depends on the same previous contract, and cannot be evaluated by evading success criteria.

The first action should be to run the tests.py authenticator and attack counter-cases, and then to observe the 100 path counts of random tactics. All cases are passed but the attack is also passed; the full rejection is too wide; the rejection of all attacks but the rejection is a failure of the authentication. In both cases, the incentive curve is lost. The resource boundaries of the actual software are also clear: this protocol only handles small integer sequences of fixed lengths, no eval, any code execution or long expression, so the cost of verification is constant size; it is not a generic mathematical proof checker.

from run import verify, target
assert verify((3,4), target((3,4)))["reward"] == 1
assert verify((3,4), [4,8,13])["reason"] == "intermediate"
assert verify((2,2), [4,8,True])["reward"] == 0
print("contract checks pass")