From Small-scale Comparisons to Credible Budget Conclusions

Task and Prerequisites: Investigate Trends Without Inventing Laws

The last chapter treats the entire project as a pilot system. Readers need to have fixed language, training budgets, parameter accounts and set indicators for the first seven chapters, and to be able to see numbers, mean values, and simple algebras. The objective of this chapter is to learn to raise questions of size that can be rebutted by data, not to announce the law of large-scale scalding after a few seconds of CPU operation. The official curriculum separates parameters, data, calculations; we do only a very small controlled version of the original paper; we use it to practice experimental logic.

Without changing the 32 BPE rules, 24 largest windows, single layers four, front-hand width double the hidden width, and learning rates and data protocols, a comparison of 16 and 32 degrees of width. Seven and eleven random seeds for each width run, the same group is evaluated at 20, 40 and 80 updates, with a total of 12 points in four tracks. The two widths use the same independent sampler set under the same torrent, the same window order; the model is initialized in different shapes, and cannot be said to have the initial weighting of elements. The test maintains a final assessment of the fixed configuration and does not participate in this grid selection point.

Four Budget Quantities That Cannot Substitute for One Another

The parameters are recorded as P and the number of valid targets for unique training data is recorded as P $D_{unique}$, the number of valid targets for cumulative participation in the update is recorded as $D_{seen}$, calculate resources as F. Here. $D_{unique}=690$, 80-update with two widths below Seed $D_{seen}$ Same, but slightly changed the order of long windows after the change. The addition of updates mainly repeats the same document in no way amounts to adding a unique language. The parameter width also increases the output head and position items, which cannot be estimated at the entire P by using only d-square ratios, and must use the exact formula of chapter V.

The same update and the same target budget can be compared to sample efficiency, but not the same calculation: the broad model is more expensive every step. The same wall clock time is not the same calculation as the clean, because this tiny CPU project has a framework fixed charge, a cache and a timing shake. The four tracks of the project run with a clear budget update and are not disguised as precise compute-matched experiments. If the best distribution of calculations is to be tested in the future, the calculation measurement and cessation strategy should first be frozen, no synchronization assigned to each model, and then run independently rather than randomly intercept the best points from the existing curves.

Example 1: Recomputing Every Entry in the Budget Table

The width 16 has 11856 parameters and the width 32 has 27808 parameters, which is about 2 34548 instead of exactly 4 times the value, because the vocabulary matrix is larger. The 20th, 40th, and 80th updates to the Seed 7 see 1170, 2328, 4585 active targets; the two widths are identical. At the time of the 80th update, Agent F was provided by the number of six-fold parameters multiplied by 4585. This number is a volume agent, not an FLOPs measured by a timer or hardware counter; the original factors are listed to allow readers to recover independently.

Seed XI corresponds to cumulative targets of 1130, 2291, 4638; synchronization does not ensure that the cumulative target is equal by value compared with the Seed VII, but it remains the same as the Seed width. Independent inspection is based on the determination of two widths of targets_seen according to the Seed and Step groups; independent inspection is based on the re-establishment of the checkpoint budget using the receipt towers per step. If two different Seed tracks are collated into a “Continuous Best Curve”, this will undermine consistency; Each curve should retain its own kind, source configuration and all points, including the weaker.

The observations of these 12 points are that, under this data, learning rates, seeds and updated budgets, the validation of NLs per trajectory decreases with three checkpoints; the same width of 32 below 16 under the same Seed and Step. It does not prove that all Seeds are so, much less that they still exist under the equivalent calculation of budgets, more data or deeper numbers. The two Seeds provide only a very small robust examination and do not provide a reliable estimate of the overall distribution of errors. The trend in the tables is an empirical statement within the measured range, rather than a theory introduced by model definitions.

Example 2: Why Two Points Can Fit Many Apparent Laws

Common experiential form can be written $L(P)=E+A P^{-\alpha}$, of which E is the model item with the lower limit of improbable loss, A and Alpha are positive. If you know only two parameters and two losses, there are three unknowns even if there is no noise in the observations; if you choose an E less than two losses, you can calculate a alpha to A. $\alpha=\log[(L_1-E)/(L_2-E)]/\log(P_2/P_1)$. So, you take only two widths as a two-logar straight line, essentially snuck down the floor, and the slope is not recognized as a natural constant.

Use pure teaching values P1=100 、 P2=400 、 L1=3 、 L2=2 If E=0 All right, all right, all right. 292481;if E=1 ， alpha=0.5;if E=1.9 I'm going to go to the hospital. 729716. All three curves go through the same two points, but right. P=1600 The independent inspection is a recollection of A and two Ps for 3 and 2, and then compares the third difference in prediction. The ambiguity between the unknown lower limit and the limited span is more fundamental than the decimal accuracy of the drawings; when training is not collected, the additional optimisation errors are also mis absorbed into alpha.

import math
P1,P2=11856,27808
seen=4585
print('parameter ratio',P2/P1,'proxy budgets',6*P1*seen,6*P2*seen)
for floor in [0.,1.,1.9]:
    p1,p2,l1,l2=100.,400.,3.,2.
    alpha=math.log((l1-floor)/(l2-floor))/math.log(p2/p1)
    A=(l1-floor)*p1**alpha
    predicted=lambda p: floor+A*p**(-alpha)
    assert abs(predicted(p1)-l1)<1e-12 and abs(predicted(p2)-l2)<1e-12
    print('assumed floor',floor,'alpha',round(alpha,6),'third point',round(predicted(1600),6))
small=[3.5288419142490675,3.5576071979618873]
large=[3.0369303862587747,2.957531113083623]
deltas=[a-b for a,b in zip(small,large)]
assert all(d>0 for d in deltas)
print('paired NLL gains',deltas,'mean gain',sum(deltas)/2)

What the Control Must Specify in Advance

A rebuttable question could be: “Standing codes, data, layer numbers, learning rates and effective target budget updates, does the width reduce the validation of NL in seeds 7 and 11?” It gives early conditions for failure: any non-upgrading should be retained and marked, and cannot be replaced until twice. The main indicator, check point, and operation failure should also be defined in advance. If there is a non-limited loss of resources at one point, the recording failure and the budget used are not filled with the other. The current grid did not have these failures, but the receipt design retained all points without filtering.

Tokenizers are introduced when the model size is increased; data mixing is introduced when the difficult files are removed from the budget increase; different models read different catch sequences increase sampling noise; and selection deviations are introduced when reporting only the best validation points in each trajectory without recording the number of searches. These are specific mechanisms that make it difficult to explain “Benefits of scale”. The first two items are fixed and match samples under the same category, while the remaining initializations are clearly retained with the effects of the limited sample. We have not claimed to control all the underlying factors, nor have we attributed any improvement in experience to a single focus.

To study unique data sizes, multiple nested subsets must be defined in advance from the training group, and tokenizer must decide whether to freeze or re-height with sub-coding; otherwise, new data should change at the same time as new codes. To study repeated training, unique pools should be fixed, with only Dseen changed. To study the best of calculations, different P-Dseen combinations need to be covered, and budget agent errors should be estimated. Three questions are designed differently and cannot be called data size by the same “Run a few more steps.” curve. This course is intended to support the closed circle of follow-up research, not all of which have been completed.

Final Project Validation and Course Scope

The compressed package contains original synthetics and cut-off, reversible byte-BPE, precise windows, complete self-written decoder, single-line training, freeze assessment, checkpoint recovery testing, reliance on source and live receipts. The source code does not import other course paths, the model is updated with all parameters from random initialization; the standard library segments are used to explain values item by item, and the project code is responsible for real training. The acceptance should first perform 13 tests in the decompression directory and then re-establish training and grids according to fixed orders; The results of the current decimal shall be subject to environmental review and time taken as observations of possible change.

The course is closed here by “given small words, define tasks and expressions, train a complete micro-language model and judge what evidence supports.” Unfinished and unintentional elements include large-scale language cleansing, distributional and intranuclear GPUs, real compressors, cross-cutting competency assessment and formal scaling law validation. The preservation of these boundaries is not to deny small experiments, but to allow each completed component to have traceable input, output and independent testing. The follow-up improvement should start with a clear new issue and re-freeze the agreement without aggregating the best local results of multiple operations into a model that has never existed.

When reading the diagrams, you must also distinguish between plug value and extrapolation. An estimate of a trend between the two measured widths has already relied on smooth assumptions; it extends to millions of parameters and includes a large number of assumptions such as optimization, data and structural behaviour. The extensive experimental evidence of the original paper may inspire new designs, but it cannot replace the measurement of the current system in the new range. We therefore do not draw up an indicator that appears to be accurate to be attached to a small map, nor does it directly fit the best data quota in the paper into a single-layer model with a higher proportion of the table.

For each target, the two Seed pairs are about 0.49112 and 0. 600076 nats, respectively, on average about 0. 545994. This mean describes the two running pairs, not the overall lower limit of confidence; a positive average when too few samples is written does not prove that arbitrary new seed would improve. If you add the Seed, then the original pair should be retained and the aggregation predefined, not just the positive margin. The parameters, target budget, wall clocks and failure need to be linked to the same operational identity so that local victories of different experiments are not combined into stable patterns.

The project grid shares training status within each trajectory, from 20 to 40 and 80, not re-introduction. The curve is a practical continuous learning process. The path between the Seeds is separate, and does not link the sequence of records to a longer training; the checkpoints in the same original log can compare trends, but they are not strong enough to be trusted by 12 independent samples. The difference between the four tracks and the 12 observations is the level that must be explained before any statistical aggregation is performed.

The contrast variable also includes layers. The current width changes both the dimensions of each layer and the exterior feed, but it is fixed to only one layer; “There's a similar share of the gain from deepening.” cannot be deduced from it. If the depth of later comparisons is greater, the normalized and projected parameters should be recalculated to match the total parameter or budget, and the difficulty of recording possible differences in optimization may be different. The vocabulary matrix takes a large head of very small models, making the width experiment different from the typical large model parameter; this structural difference is itself sufficient to prevent local slopes from being brought directly into large-scale resource planning.

python run.py grid
python -m unittest -v tests.test_pipeline