Datasets:

Elliot-Data
/

latexformulas_cleaned

---
license: other
task_categories:
- visual-question-answering
language:
- en
---
# latexformulas_cleaned
The **latexformulas__x** family of the ElliotVL supervised-fine-tuning pool, **after VLM cleaning**.
| | |
|---|---|
| images | 532,565 |
| QA turns | 987,821 |
| answers rewritten by the cleaning pass | 63,612 |
| QA created by the cleaning pass (`new_qa`) | 467,660 (47.3%) |
| shards | 12 |

## How this was cleaned

A vision-language model read each image together with its QA and judged the item. The pass is
**not a filter that only removes rows** — it rewrites answers it finds wrong but salvageable,
drops what it cannot salvage, and adds QA where the image supports more than the source provided.
Each row carries the judge's own record in `clean_meta`, including the cleaner identity, the
policy it applied, and its per-item scores for legibility, richness and coverage.

**A large share of the QA here was written by the cleaning pass, not by the original dataset.**
Across the pool that share runs from roughly half to over 80% of a family's turns, and it is
reported in the table above. Those rows have an empty `org_answer` because no pre-clean original
exists. Treat them as model-generated supervision: they were judged against the image, but they
are not human annotation, and model-written QA is where formatting defects are most likely.

The effect on the answers that *were* carried over is substantive rather than cosmetic. In this pool the pass corrects values, not just
wording — a curve's critical point restated from `4.00` to `2.00`, a computed ratio from `1` to
`Approximately 1.33` — and for some families it removed the content entirely, which is why those
families are absent here rather than published empty.

## `answer` vs `org_answer`
- `answer` — the cleaned answer. **Train on this.**
- `org_answer` — the pre-cleaning answer from the same `(image, question)` in the uncleaned pool.
  It is empty for QA the cleaning pass added, which have no original.

Where the two differ, the difference is the correction. Keeping both makes every edit auditable
instead of asking you to take the cleaning on trust.



## Schema

- `image` — HF `Image()`, renders directly in the dataset viewer
- `image_sha256` — content hash of the image
- `n_qa` — number of turns attached to this image
- `qa` — list of {`question`, `answer`, `org_answer`}, **in source order**
- `family` / `clean_meta` — provenance and the judge's per-row record

A row with more than one entry in `qa` is a **conversation over a single image**, not a set of
independent questions — the turns depend on each other and the image belongs to all of them.
Keep them together and in order when training.

Parquet row groups are written at ~32 MB so the dataset viewer pages without stalling.

## What is NOT claimed

No rejection sampling was run against this family: there is no accept/reject verdict per row, and
`answer` is the cleaned reference rather than a model generation that a string verifier confirmed.
For that, use the `*_RS_think` / `*_rejected` datasets in [elliot-mllm](https://huggingface.co/elliot-mllm).


## Examples
10 rows taken straight from this dataset. Images are the **original files** as stored here - no downscaling, no recompression - and every turn is shown in full.

### Example 1 — 2 turns on one image

![case1](samples/case1.png)

| # | question | answer (cleaned) | org_answer (pre-judge) |
|---|---|---|---|
| 1 | Convert this mathematical notation to LaTeX code. | \begin{align*}-\div (y^{1-2m}\nabla w) = 0 \mbox{ in } \mathbb R^n \times \mathbb R_+; w\big\|_{y=0} = \|u\|\end{align*} | \begin{align*}-\div (y^{1-2m}\nabla w)=0\mbox{in}\mathbb R^n\times\mathbb R_+;w\big\|_{y=0}=\|u\|\end{align*} |
| 2 | What are the colors of the text and the background in the image? | The text is black and the background is white. | _(unchanged)_ |


### Example 2 — 2 turns on one image

![case2](samples/case2.png)

| # | question | answer |
|---|---|---|
| 1 | What is the LaTeX representation of this formula? | \begin{align*}k\left( \theta \right) =-\log \left[K\left( \theta \right) K\left( -\theta\right)\right] \quad ,\quad K\left( \theta \right) =R^{(1)}\left( i\frac{\pi}{2}-\theta \right)\ .\end{align*} |
| 2 | What punctuation marks are visible in the formula? | A comma separates the two equations, and a period appears at the very end. |


### Example 3 — 3 turns on one image

![case3](samples/case3.png)

| # | question | answer |
|---|---|---|
| 1 | Provide the LaTeX markup for this mathematical expression. | \begin{align*}S \sim I^{1/2}= \sqrt{({1\over 2} Z_{AB}\bar Z^{AB} -Z_I Z_I)Z }\end{align*} |
| 2 | What is the background color of the image? | White. |
| 3 | How is the equation positioned within the image frame? | Centered. |


### Example 4 — 4 turns on one image

![case4](samples/case4.png)

| # | question | answer |
|---|---|---|
| 1 | Convert this mathematical notation to LaTeX code. | \begin{align*}\rho^a \equiv q^a + \eta^a / \lambda ~,\end{align*} |
| 2 | Which Greek letters appear in the equation? | rho, eta, and lambda |
| 3 | What is the superscript character on the variables? | a |
| 4 | What punctuation mark is at the end of the equation? | A comma |


### Example 5 — 2 turns on one image

![case5](samples/case5.png)

| # | question | answer |
|---|---|---|
| 1 | What LaTeX code would generate this formula? | \begin{align*} &b = z\sqrt{L/2} \\ \iff & z/b = \sqrt{2/L} \\ \iff & (b-z)/b = 1-\sqrt{2/L} \end{align*} |
| 2 | How are the lines of the mathematical derivation aligned in the image? | The lines are aligned vertically at the equals signs, and the 'if and only if' symbols ($\iff$) are aligned in a column to the left. |


### Example 6

![case6](samples/case6.png)

| # | question | answer |
|---|---|---|
| 1 | Transcribe this mathematical equation to LaTeX. | \begin{align*} \sum_{d\leqslant \varepsilon_{1}^\frac{1}{2} \Xi(\alpha )^{-\frac{1}{2}}B^{1-\frac{1}{2r}}}\mu(d)\frac{\varepsilon_1-\varepsilon_2}{2(\alpha^\prime)^2 d^2}B^{2-\frac{1}{r}} &=\frac{6(\varepsilon_1-\varepsilon_2)}{\pi^2 (\alpha^\prime)^2}B^{2-\frac{1}{r}}+O_{\varepsilon_i}(\Xi(\alpha)^\frac{1}{2}B^{1-\frac{1}{2r}}), \end{align*} |


### Example 7

![case7](samples/case7.png)

| # | question | answer |
|---|---|---|
| 1 | Convert this mathematical notation to LaTeX code. | \begin{align*}\left\{\begin{array}{ll}\lambda_i=\sum_{s\in S}\psi_{i}(s),& \mbox{$i=1,\ldots,m$;}\\\mu_{h1}+\mu_{h2}=\sum_{s\in S}\chi_{_h}(s),& h=1,2,\ldots,[\frac{n-1}{2}];\\\mu_{h1}^2+\mu_{h2}^2=\sum_{s_1,s_2\in S}\chi_{_h}(s_1s_2),& h=1,2,\ldots,[\frac{n-1}{2}].\end{array}\right.\end{align*} |


### Example 8 — 4 turns on one image

![case8](samples/case8.png)

| # | question | answer |
|---|---|---|
| 1 | Convert this mathematical notation to LaTeX code. | \begin{align*}A \to_{\nabla} B= \bigcup \{C \| \; \nabla C \wedge A \vdash B\}. \;\;\;\; (*)\end{align*} |
| 2 | What is the color of the mathematical text? | Black |
| 3 | What is the background color of the image? | White |
| 4 | What font style is used for the equation? | Serif |
### Example 9
![case9](samples/case9.png)
| # | question | answer |
|---|---|---|
| 1 | What is the mathematical equation shown in the image? | \sum_{i \in T, \|i\| = n(k)} s_i = \prod_{j=1}^k \left( \sum_{\|i\| = n(j) - n(j-1)} s_i^{(j-1)} \right) |
### Example 10
![case10](samples/case10.png)
| # | question | answer (cleaned) | org_answer (pre-judge) |
|---|---|---|---|
| 1 | Transcribe the mathematical notation in this image to LaTeX. | \begin{align*}\mathrm{Mant}_{M_b, b', \mu_b}(\rho_1 \boxtimes ... \boxtimes \rho_k)= \boxtimes^k_{i=1} \mathrm{Mant}_{G_i, b'_i, \mu_{b,i}}(\rho_i),\end{align*} | \begin{align*}\mathrm{Mant}_{M_b, b' , \mu_b}(\rho_1 \boxtimes ... \boxtimes \rho_k)= \boxtimes^k_{i=1} \mathrm{Mant}_{G_i, b'_i, \mu_{b,i}}(\rho_i),\end{align*} |

	---
	license: other
	task_categories:
	- visual-question-answering
	language:
	- en
	---

	# latexformulas_cleaned

	The latexformulas__x family of the ElliotVL supervised-fine-tuning pool, after VLM cleaning.

	\| \| \|
	\|---\|---\|
	\| images \| 532,565 \|
	\| QA turns \| 987,821 \|
	\| answers rewritten by the cleaning pass \| 63,612 \|
	\| QA created by the cleaning pass (`new_qa`) \| 467,660 (47.3%) \|
	\| shards \| 12 \|

	## How this was cleaned

	A vision-language model read each image together with its QA and judged the item. The pass is
	not a filter that only removes rows — it rewrites answers it finds wrong but salvageable,
	drops what it cannot salvage, and adds QA where the image supports more than the source provided.
	Each row carries the judge's own record in `clean_meta`, including the cleaner identity, the
	policy it applied, and its per-item scores for legibility, richness and coverage.

	A large share of the QA here was written by the cleaning pass, not by the original dataset.
	Across the pool that share runs from roughly half to over 80% of a family's turns, and it is
	reported in the table above. Those rows have an empty `org_answer` because no pre-clean original
	exists. Treat them as model-generated supervision: they were judged against the image, but they
	are not human annotation, and model-written QA is where formatting defects are most likely.

	The effect on the answers that were carried over is substantive rather than cosmetic. In this pool the pass corrects values, not just
	wording — a curve's critical point restated from `4.00` to `2.00`, a computed ratio from `1` to
	`Approximately 1.33` — and for some families it removed the content entirely, which is why those
	families are absent here rather than published empty.

	## `answer` vs `org_answer`

	- `answer` — the cleaned answer. Train on this.
	- `org_answer` — the pre-cleaning answer from the same `(image, question)` in the uncleaned pool.
	It is empty for QA the cleaning pass added, which have no original.

	Where the two differ, the difference is the correction. Keeping both makes every edit auditable
	instead of asking you to take the cleaning on trust.



	## Schema

	- `image` — HF `Image()`, renders directly in the dataset viewer
	- `image_sha256` — content hash of the image
	- `n_qa` — number of turns attached to this image
	- `qa` — list of {`question`, `answer`, `org_answer`}, in source order
	- `family` / `clean_meta` — provenance and the judge's per-row record

	A row with more than one entry in `qa` is a conversation over a single image, not a set of
	independent questions — the turns depend on each other and the image belongs to all of them.
	Keep them together and in order when training.

	Parquet row groups are written at ~32 MB so the dataset viewer pages without stalling.

	## What is NOT claimed

	No rejection sampling was run against this family: there is no accept/reject verdict per row, and
	`answer` is the cleaned reference rather than a model generation that a string verifier confirmed.
	For that, use the `_RS_think` / `_rejected` datasets in [elliot-mllm](https://huggingface.co/elliot-mllm).


	## Examples
	10 rows taken straight from this dataset. Images are the original files as stored here - no downscaling, no recompression - and every turn is shown in full.

	### Example 1 — 2 turns on one image

	![case1](samples/case1.png)

	\| # \| question \| answer (cleaned) \| org_answer (pre-judge) \|
	\|---\|---\|---\|---\|
	\| 1 \| Convert this mathematical notation to LaTeX code. \| \begin{align}-\div (y^{1-2m}\nabla w) = 0 \mbox{ in } \mathbb R^n \times \mathbb R_+; w\big\\|_{y=0} = \\|u\\|\end{align} \| \begin{align}-\div (y^{1-2m}\nabla w)=0\mbox{in}\mathbb R^n\times\mathbb R_+;w\big\\|_{y=0}=\\|u\\|\end{align} \|
	\| 2 \| What are the colors of the text and the background in the image? \| The text is black and the background is white. \| _(unchanged)_ \|


	### Example 2 — 2 turns on one image

	![case2](samples/case2.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| What is the LaTeX representation of this formula? \| \begin{align}k\left( \theta \right) =-\log \left[K\left( \theta \right) K\left( -\theta\right)\right] \quad ,\quad K\left( \theta \right) =R^{(1)}\left( i\frac{\pi}{2}-\theta \right)\ .\end{align} \|
	\| 2 \| What punctuation marks are visible in the formula? \| A comma separates the two equations, and a period appears at the very end. \|


	### Example 3 — 3 turns on one image

	![case3](samples/case3.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| Provide the LaTeX markup for this mathematical expression. \| \begin{align}S \sim I^{1/2}= \sqrt{({1\over 2} Z_{AB}\bar Z^{AB} -Z_I Z_I)Z }\end{align} \|
	\| 2 \| What is the background color of the image? \| White. \|
	\| 3 \| How is the equation positioned within the image frame? \| Centered. \|


	### Example 4 — 4 turns on one image

	![case4](samples/case4.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| Convert this mathematical notation to LaTeX code. \| \begin{align}\rho^a \equiv q^a + \eta^a / \lambda ~,\end{align} \|
	\| 2 \| Which Greek letters appear in the equation? \| rho, eta, and lambda \|
	\| 3 \| What is the superscript character on the variables? \| a \|
	\| 4 \| What punctuation mark is at the end of the equation? \| A comma \|


	### Example 5 — 2 turns on one image

	![case5](samples/case5.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| What LaTeX code would generate this formula? \| \begin{align} &b = z\sqrt{L/2} \\ \iff & z/b = \sqrt{2/L} \\ \iff & (b-z)/b = 1-\sqrt{2/L} \end{align} \|
	\| 2 \| How are the lines of the mathematical derivation aligned in the image? \| The lines are aligned vertically at the equals signs, and the 'if and only if' symbols ($\iff$) are aligned in a column to the left. \|


	### Example 6

	![case6](samples/case6.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| Transcribe this mathematical equation to LaTeX. \| \begin{align} \sum_{d\leqslant \varepsilon_{1}^\frac{1}{2} \Xi(\alpha )^{-\frac{1}{2}}B^{1-\frac{1}{2r}}}\mu(d)\frac{\varepsilon_1-\varepsilon_2}{2(\alpha^\prime)^2 d^2}B^{2-\frac{1}{r}} &=\frac{6(\varepsilon_1-\varepsilon_2)}{\pi^2 (\alpha^\prime)^2}B^{2-\frac{1}{r}}+O_{\varepsilon_i}(\Xi(\alpha)^\frac{1}{2}B^{1-\frac{1}{2r}}), \end{align} \|


	### Example 7

	![case7](samples/case7.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| Convert this mathematical notation to LaTeX code. \| \begin{align}\left\{\begin{array}{ll}\lambda_i=\sum_{s\in S}\psi_{i}(s),& \mbox{$i=1,\ldots,m$;}\\\mu_{h1}+\mu_{h2}=\sum_{s\in S}\chi_{_h}(s),& h=1,2,\ldots,[\frac{n-1}{2}];\\\mu_{h1}^2+\mu_{h2}^2=\sum_{s_1,s_2\in S}\chi_{_h}(s_1s_2),& h=1,2,\ldots,[\frac{n-1}{2}].\end{array}\right.\end{align} \|


	### Example 8 — 4 turns on one image

	![case8](samples/case8.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| Convert this mathematical notation to LaTeX code. \| \begin{align}A \to_{\nabla} B= \bigcup \{C \\| \; \nabla C \wedge A \vdash B\}. \;\;\;\; ()\end{align*} \|
	\| 2 \| What is the color of the mathematical text? \| Black \|
	\| 3 \| What is the background color of the image? \| White \|
	\| 4 \| What font style is used for the equation? \| Serif \|


	### Example 9

	![case9](samples/case9.png)

	\| # \| question \| answer \|
	\|---\|---\|---\|
	\| 1 \| What is the mathematical equation shown in the image? \| \sum_{i \in T, \\|i\\| = n(k)} s_i = \prod_{j=1}^k \left( \sum_{\\|i\\| = n(j) - n(j-1)} s_i^{(j-1)} \right) \|


	### Example 10

	![case10](samples/case10.png)

	\| # \| question \| answer (cleaned) \| org_answer (pre-judge) \|
	\|---\|---\|---\|---\|
	\| 1 \| Transcribe the mathematical notation in this image to LaTeX. \| \begin{align}\mathrm{Mant}_{M_b, b', \mu_b}(\rho_1 \boxtimes ... \boxtimes \rho_k)= \boxtimes^k_{i=1} \mathrm{Mant}_{G_i, b'_i, \mu_{b,i}}(\rho_i),\end{align} \| \begin{align}\mathrm{Mant}_{M_b, b' , \mu_b}(\rho_1 \boxtimes ... \boxtimes \rho_k)= \boxtimes^k_{i=1} \mathrm{Mant}_{G_i, b'_i, \mu_{b,i}}(\rho_i),\end{align} \|