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When an objective sums per-example losses from a main dataset and a larger auxiliary dataset, a coefficient $$\beta$$ can scale the auxiliary losses. To give both datasets equal aggregate weight, set $$\beta=N_{\mathrm{main}}/N_{\mathrm{aux}}$$. Thus, for 6,000 labeled storefront images and 144,000 auxiliary web images, $$\beta=6000/144000=1/24$$. Treat this ratio as an initial choice, then compare candidate values using development-set performance.

Choosing the Weight for Auxiliary Data

Which beta value gives the two image collections equal total weight?

Does beta set how much the auxiliary image set influences the total loss?

Match each part of the weighted loss to its role.

Order the steps for setting the auxiliary-data weight.

Question:
In a concise analytical response, explain what beta = 1/40 changes in the training objective and why the dev set still matters when choosing beta.

Sample answer:
Beta controls the contribution of a supplemental collection of 160,000 examples in the loss. In an objective that also uses 4,000 core examples, setting beta = 1/40 gives the supplemental collection the same total weight as the core collection, because 160,000 × 1/40 = 4,000. That is only one possible setting; beta should still be treated as a tunable hyperparameter and chosen using dev-set performance.

Key points:
- Beta scales the contribution of the supplemental data.
- The example compares 4,000 core examples with 160,000 supplemental examples.
- Beta = 1/40 makes the two collections equal in total influence.
- Beta is still selected by checking which value works best on the dev set.

Rubric:
A strong response identifies what beta weights, explains why 1/40 equalizes the total contribution in this example, and states that beta should be tuned on the dev set rather than assumed to be fixed.


Explain what beta = 1/40 does when mixing two training pools

Case context:
A training objective combines 5,000 clinic photos with 200,000 web-scraped reference images. The current setting is beta = 1/40, and the team is considering whether another setting would work better.

Question:
What does beta = 1/40 do in this setup, and how should the team choose among other beta settings?

Sample answer:
With beta = 1/40, the smaller clinic-photo set and the much larger web-image set contribute the same overall amount to the objective, even though one set has far fewer examples. If the team wants a different tradeoff, it should compare other beta values on the development set and select the one that performs best there.

Key points:
- Beta = 1/40 makes the two groups contribute equally in aggregate.
- The 200,000-image set is the auxiliary web-image source.
- Other beta settings can be tried.
- The development set should decide which setting to keep.

Rubric:
The response should state the effect of beta = 1/40 and say that candidate beta values are chosen using the development set. It should associate beta with the auxiliary web-image data.

Interpreting beta when two data sources differ in size

Question:
In one to three sentences, explain the total-weight effect of beta = 1/25 on 2,400 clinic notes and 60,000 web notes.

Sample answer:
Beta = 1/25 reduces the contribution of the auxiliary web-note set so that the 60,000 web notes carry the same total weight as the 2,400 clinic notes.

Key points:
- The two collections end up with equal total weight.
- Beta is applied to the auxiliary web-note data.

Rubric:
The answer must state that beta = 1/25 makes the total weight of the two collections equal and identify the web notes as the auxiliary data.

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