8

I know you’ll be after open source, but Abby fine reader is great in our experience for a variety of tough OCR extraction problems and easy to integrate into your workflows

9

https://pdf.abbyy.com/

Took a look at the Abby fine reader site. While it can convert a PDF to text with the reader, I did not see that it could convert images with technical expression(s) into a format that an AI can understand.

Example of a technical expression, in this specific case typing rules

image
image877×267 14.8 KB

Did I miss something on the site?

1 Like
10

I’m sorry but we have no experience extracting typing rules with Abby, but I would suggest to contact them to confirm. Very good at extracting from image pdfs

11

Here’s another link for the inf-project, seems like it’s also paid tho.

12

Yes typing rules are used by an exclusive group.

Here is another example of a technical expression more familiar to many.

image

(ref)

While that is an image of a fraction, the representation is in MathML

   <mfrac>
	<mrow>
	  <mn>3</mn>
	  <mi>x</mi>
	  <mo>−<!-- − --></mo>
	  <mn>2</mn>
	  <mi>x</mi>
	  <mi>y</mi>
	  <mo>+</mo>
	  <mi>c</mi>
	</mrow>
	<mrow>
	  <mi>y</mi>
	  <mo>−<!-- − --></mo>
	  <mn>1</mn>
	</mrow>
  </mfrac>

which has enough metadata such that an AI should be able to understand that it is a fraction.

Passing the MathML fraction above to ChatGPT alone shows that ChatGPT May 24 Version understands it

Prompt


   <mfrac>
	<mrow>
	  <mn>3</mn>
	  <mi>x</mi>
	  <mo>−<!-- − --></mo>
	  <mn>2</mn>
	  <mi>x</mi>
	  <mi>y</mi>
	  <mo>+</mo>
	  <mi>c</mi>
	</mrow>
	<mrow>
	  <mi>y</mi>
	  <mo>−<!-- − --></mo>
	  <mn>1</mn>
	</mrow>
  </mfrac>

Completion

The expression you provided is a fraction. Let’s break it down and simplify it step by step.

The numerator of the fraction is: 3x - 2xy + c
The denominator of the fraction is: y - 1

So the fraction can be written as:

(3x - 2xy + c) / (y - 1)

Since there is no specific instruction regarding what you would like to do with this expression, I assume you want to simplify it or perform some operations. Please let me know what specific operation or simplification you would like me to assist you with.

2 Likes
13

Eric’s example in latex:

\frac{3x-2xy+c}{y-1}

1 Like
14

Found this fairly interesting bit of OpenCV code

I’m not convinced it will be able to cope with complex notation, but throwing it in here as a starting point for someone else

16

It was interesting waking up to this.

I’ve been looking at this very issue over the past few months, and I’ve tried nearly all of the solutions listed here.

My conclusion is that we’re just not there yet. It’s pretty close in many ways, but there is no single solution that is a one-stop-shop for reading technical PDFs.

Mathpix is the best for extracting information from equation and inline environments, but it can be extremely costly to process a large number of pages and it doesn’t handle other environments (algorithm) particularly well.

Even then, you still need to review the work that comes out of Mathpix because it’s only about 90% correct (depending on complexity of course).

I suspect we will see a big push in the open-source space over the next year or two as more people want to feed technical papers into LLMs.

17

I emailed sciaccess a few months ago to see if they offered an academic discount, and never got a reply.

Didn’t inspire confidence.

18

Good point and one should seriously consider when understanding technical papers.

Also for others that did not notice the jobs posting on Arxiv, seems they are expanding quite a bit.

19

Here is an example of a PDF with typing rules available on Arxiv.

“GPC: A Pattern Calculus for Property Graphs” by Nadime Francis, Amélie Gheerbrant, Paolo Guagliardo, Leonid Libkin, Victor Marsault, Wim Martens, Filip Murlak, Liat Peterfreund, Alexandra Rogova, Domagoj Vrgoč

It is available in a few different formats.

The typing rules being demonstrated are in Figure 2.

image

Text source of typing rules (Click triangle to expand)

This is from file 2210.16580 which is downloaded by clicking Download source on the Format selector page

\begin{figure*}\centering

\newcommand{\custominference}[2]{$\displaystyle\inference{#1}{#2}$}

%\custominference{}{\nodelit{x\,[:\ell]} \vdash x:\tnode} 
\custominference{}{\nodelit{x} \vdash x:\tnode}
\hfil
\custominference{}{\nodelit{x:\ell} \vdash x:\tnode}
\hfil
%\custominference {}{\arclit{x\, [:\ell]}\  \vdash x:\tedge} 
\custominference {}{\arclit{x}\  \vdash x:\tedge} 
\hfil
\custominference {}{\arclit{x :\ell}\  \vdash x:\tedge} 
\hfil
\custominference{ x \notin \var(\pat)}{x=\restrictor\ \pat \vdash x:\tpath}
%\custominference{\pat \vdash x:\tau \quad p \notin \var(\pat)}{p=\pat \vdash p:\tpath,\ x:\tau}


\bigskip

\custominference {\pat\vdash z:\tau}{\pat\quantlit{n..m} \vdash z:\tlist(\tau)} 
\hfil
\custominference {\pat\vdash z:\tau}{\restrictor \pat \vdash z:\tau}
%\hfil
%\custominference{\pat \vdash z:\tau \quad z\neq x}{x=\pat \vdash  z:\tau}
\hfil
\custominference{\pat \vdash z:\tau \quad z\neq x }{ x= \restrictor \pat \vdash  z:\tau}

\bigskip

\custominference {\pat\vdash x:\tau \quad \tau\in\set{\tnode,\tedge}}{\pat \vdash x.a=c:\tbool} \hfil
\custominference {\pat\vdash x:\tau\quad \pat\vdash y:\tau'\quad\tau,\tau'\in\set{\tnode,\tedge}}{\pat \vdash x.a=y.b:\tbool} 

\bigskip

\custominference {\pat\vdash \theta:\tbool \quad \pat\vdash\theta':\tbool}{\pat \vdash \theta\wedge\theta':\tbool} 
\hfil
\custominference {\pat\vdash \theta:\tbool \quad \pat\vdash\theta':\tbool}{\pat \vdash \theta\vee\theta':\tbool} 
\hfil
\custominference {\pat\vdash \theta:\tbool}{\pat \vdash \neg\theta:\tbool} 
\hfil
\custominference {\pat\vdash \theta:\tbool \quad \pat\vdash z:\tau}{\pat\condlit{\theta} \vdash z:\tau} 

\bigskip

\custominference {\pat_1\vdash z:\tau \quad \pat_2\vdash z:\tau}{\pat_1 + \pat_2 \vdash z:\tau}
\hfil
\custominference {\pat_1\vdash z:\tau \quad \pat_2\vdash z:\tmaybe(\tau)}{\pat_1 + \pat_2 \vdash z:\tmaybe(\tau)}
\hfil
\custominference {\pat_1\vdash z:\tmaybe(\tau) \quad \pat_2\vdash z:\tau}{\pat_1 + \pat_2 \vdash z:\tmaybe(\tau)}

\bigskip

\custominference {\pat_1\vdash z:\tau \quad  z \notin \var(\pat_2) }{\pat_1 + \pat_2 \vdash 
z: \tau?} 
\hfil
\custominference {\pat_2\vdash z:\tau \quad z \notin \var(\pat_1) }{\pat_1 + \pat_2 \vdash z: \tau?}

\bigskip

\custominference {\pat_1\vdash z:\tau \quad \pat_2\vdash z:\tau \quad \tau\in\set{\tnode,\tedge}}{\pat_1 \, \pat_2 \vdash z:\tau} 
\hfil
\custominference {\pat_1\vdash z:\tau \quad z \not\in\var(\pat_2)}{\pat_1 \, \pat_2 \vdash z:\tau}
\hfil
\custominference {\pat_2\vdash z:\tau \quad z \not\in\var(\pat_1)}{\pat_1 \, \pat_2 \vdash z:\tau} 

\bigskip

\custominference {Q_1\vdash z:\tau \quad Q_2\vdash z:\tau \quad \tau\in\set{\tnode,\tedge}}{Q_1 , Q_2 \vdash z:\tau}
\hfil
\custominference{Q_1\vdash z:\tau \quad z\not\in\var(Q_2) }{Q_1, Q_2 \vdash z:\tau}
\hfil
\custominference{Q_2\vdash z:\tau \quad z\not\in \var(Q_1) }{Q_1, Q_2 \vdash z:\tau}

\caption{Typing rules for the \gpml type system.}
\label{fig:type-system}
\end{figure*}
Does ChatGPT understand the TeX? (Click triangle to expand)

ChatGPT May 24 Version

Prompt

\begin{figure*}\centering

\newcommand{\custominference}[2]{$\displaystyle\inference{#1}{#2}$}

%\custominference{}{\nodelit{x,[:\ell]} \vdash x:\tnode}
\custominference{}{\nodelit{x} \vdash x:\tnode}
\hfil
\custominference{}{\nodelit{x:\ell} \vdash x:\tnode}
\hfil
%\custominference {}{\arclit{x, [:\ell]}\ \vdash x:\tedge}
\custominference {}{\arclit{x}\ \vdash x:\tedge}
\hfil
\custominference {}{\arclit{x :\ell}\ \vdash x:\tedge}
\hfil
\custominference{ x \notin \var(\pat)}{x=\restrictor\ \pat \vdash x:\tpath}
%\custominference{\pat \vdash x:\tau \quad p \notin \var(\pat)}{p=\pat \vdash p:\tpath,\ x:\tau}

\bigskip

\custominference {\pat\vdash z:\tau}{\pat\quantlit{n…m} \vdash z:\tlist(\tau)}
\hfil
\custominference {\pat\vdash z:\tau}{\restrictor \pat \vdash z:\tau}
%\hfil
%\custominference{\pat \vdash z:\tau \quad z\neq x}{x=\pat \vdash z:\tau}
\hfil
\custominference{\pat \vdash z:\tau \quad z\neq x }{ x= \restrictor \pat \vdash z:\tau}

\bigskip

\custominference {\pat\vdash x:\tau \quad \tau\in\set{\tnode,\tedge}}{\pat \vdash x.a=c:\tbool} \hfil
\custominference {\pat\vdash x:\tau\quad \pat\vdash y:\tau’\quad\tau,\tau’\in\set{\tnode,\tedge}}{\pat \vdash x.a=y.b:\tbool}

\bigskip

\custominference {\pat\vdash \theta:\tbool \quad \pat\vdash\theta’:\tbool}{\pat \vdash \theta\wedge\theta’:\tbool}
\hfil
\custominference {\pat\vdash \theta:\tbool \quad \pat\vdash\theta’:\tbool}{\pat \vdash \theta\vee\theta’:\tbool}
\hfil
\custominference {\pat\vdash \theta:\tbool}{\pat \vdash \neg\theta:\tbool}
\hfil
\custominference {\pat\vdash \theta:\tbool \quad \pat\vdash z:\tau}{\pat\condlit{\theta} \vdash z:\tau}

\bigskip

\custominference {\pat_1\vdash z:\tau \quad \pat_2\vdash z:\tau}{\pat_1 + \pat_2 \vdash z:\tau}
\hfil
\custominference {\pat_1\vdash z:\tau \quad \pat_2\vdash z:\tmaybe(\tau)}{\pat_1 + \pat_2 \vdash z:\tmaybe(\tau)}
\hfil
\custominference {\pat_1\vdash z:\tmaybe(\tau) \quad \pat_2\vdash z:\tau}{\pat_1 + \pat_2 \vdash z:\tmaybe(\tau)}

\bigskip

\custominference {\pat_1\vdash z:\tau \quad z \notin \var(\pat_2) }{\pat_1 + \pat_2 \vdash
z: \tau?}
\hfil
\custominference {\pat_2\vdash z:\tau \quad z \notin \var(\pat_1) }{\pat_1 + \pat_2 \vdash z: \tau?}

\bigskip

\custominference {\pat_1\vdash z:\tau \quad \pat_2\vdash z:\tau \quad \tau\in\set{\tnode,\tedge}}{\pat_1 , \pat_2 \vdash z:\tau}
\hfil
\custominference {\pat_1\vdash z:\tau \quad z \not\in\var(\pat_2)}{\pat_1 , \pat_2 \vdash z:\tau}
\hfil
\custominference {\pat_2\vdash z:\tau \quad z \not\in\var(\pat_1)}{\pat_1 , \pat_2 \vdash z:\tau}

\bigskip

\custominference {Q_1\vdash z:\tau \quad Q_2\vdash z:\tau \quad \tau\in\set{\tnode,\tedge}}{Q_1 , Q_2 \vdash z:\tau}
\hfil
\custominference{Q_1\vdash z:\tau \quad z\not\in\var(Q_2) }{Q_1, Q_2 \vdash z:\tau}
\hfil
\custominference{Q_2\vdash z:\tau \quad z\not\in \var(Q_1) }{Q_1, Q_2 \vdash z:\tau}

\caption{Typing rules for the \gpml type system.}
\label{fig:type-system}
\end{figure*}

Completion

The figure you provided presents a set of typing rules for the \gpml type system. These rules define how different patterns and expressions are typed in the system. Let’s go through each rule:

  1. The first two rules state that a node or an arc literal with or without a label is typed as a node or an edge, respectively.

  2. The third rule states that if a variable x is not bound in the pattern (\pat), then x can be restricted to a path and typed as a path (\tpath).

  3. The fourth rule states that if a pattern \pat is typed as z of type \tau, then the pattern \pat\quantlit{n..m} is typed as z of type List(\tau).

  4. The fifth and sixth rules deal with restricting patterns. If a pattern \pat is typed as z of type \tau, then the pattern \restrictor\ \pat is also typed as z of type \tau.

  5. The seventh rule states that if a pattern \pat is typed as x of type \tau, where \tau is either a node or an edge, then the expression x.a=c is typed as a Boolean (\tbool).

  6. The eighth rule states that if a pattern \pat is typed as x of type \tau and another pattern y is typed as y of type \tau', where both \tau and \tau' are either nodes or edges, then the expression x.a=y.b is typed as a Boolean (\tbool).

  7. The ninth, tenth, eleventh, and twelfth rules deal with Boolean operations. They state that if patterns or expressions \pat and \theta are typed as Boolean values, then the conjunction (\wedge), disjunction (\vee), negation (\neg), and conditional (\condlit{\theta}) expressions are also typed as Booleans.

  8. The thirteenth rule states that if patterns \pat_1 and \pat_2 are both typed as z of type \tau, then the pattern \pat_1 + \pat_2 is also typed as z of type \tau.

  9. The fourteenth, fifteenth, and sixteenth rules deal with patterns that include optional values. They specify how patterns with optional values are typed based on the presence or absence of the value.

  10. The seventeenth, eighteenth, and nineteenth rules deal with concatenating patterns and expressions. They specify the typing for the concatenation operator (,). If patterns or expressions \pat_1 and \pat_2 are typed as z of type \tau, then \pat_1 \, \pat_2 is also typed as z of type \tau. Additionally, if the variable z is not bound in either \pat_1 or \pat_2, then the typing remains the same.

  11. The twentieth, twenty-first, and twenty-second rules deal with concatenating queries (Q_1 and Q_2). They specify the typing for the concatenation operator (,). If queries Q_1 and Q_2 are both typed as z of type \tau, then Q_1 , Q_2 is also typed as z of type \tau. Additionally, if the variable z is not bound in either Q_1 or Q_2, then the typing remains the same.

These rules define the typing behavior of various patterns and expressions in the \gpml type system.

Personal note:

In the completion it notes The first two rules state but it really should be The first four rules state. The first rule is for a Node without a type, the second is for a Node with a type, the third is for an edge without a type and the fourth is for an edge with a type. Thus the number for the remainder of the rules is off but if you have a bit of understanding of how to read typing rules it is easy to match up the description with the typing rule.

PostScript version of second typing rule (Click triangle to expand)

This is from file 2210.16580v1.ps.gz which is downloaded by clicking Download PostScript on the Format selector page

727 190 654 5 v 290 w FN(\271)q FH(G)27 b FF(:)21 b FH(\022)6
b FN(\272)25 b(`)18 b FH(G)28 b FF(:)21 b Fw(No)r(de)p
Does ChatGPT understand PostScript (Click triangle to expand)

Note: Only the PostScript for the second type rule is used as giving ChatGPT all of the PostScript for the typing rules would exceed the token limit.

Prompt

The following is a portion of PostScript, explain what you can.

 727 190 654 5 v 290 w FN(\271)q FH(G)27 b FF(:)21 b FH(\022)6
b FN(\272)25 b(`)18 b FH(G)28 b FF(:)21 b Fw(No)r(de)p

Completion

The portion of code you provided appears to be written in the PostScript programming language. PostScript is a page description language commonly used for printing and graphics.

Let’s analyze the code line by line:

727 190 654 5 v 290 w FN(\271)q FH(G)27 b FF(:)21 b FH(\022)6 b FN(\272)25 b(`)18 b FH(G)28 b FF(:)21 b Fw(No)r(de)p

  1. 727 190 654 5 v: This line consists of four numeric values (727, 190, 654, and 5) followed by the operator v. These values are likely coordinates or parameters related to positioning or transformations. Without more context, it’s difficult to determine their exact purpose.

  2. 290 w: This line contains a numeric value (290) followed by the operator w. Again, without more context, it’s unclear what this line represents.

  3. FN(\271)q FH(G)27 b FF(:)21 b FH(\022)6 b FN(\272)25 b()18 b FH(G)28 b FF(:)21 b Fw(No)r(de)p`: This is a series of instructions involving various operators and string literals. Here’s a breakdown of the individual components:

    • FN(\271): This is likely a font-related instruction, specifying a particular font with a parameter \271.
    • q: This operator saves the current graphics state.
    • FH(G)27 b: This could be another font-related instruction specifying a different font (G) with a parameter 27. The b operator might be related to setting the font weight or style.
    • FF(:)21 b: This is likely a command to print or display a colon (:) using the current font. The 21 b might be related to font size or position.
    • FH(\022)6 b: This could be another font-related instruction, specifying a different font with a non-printable character \022. The 6 b might be related to font size or position.
    • FN(\272)25 b: This could be another font-related instruction specifying a different font with a parameter \272. The 25 b might be related to font size or position.
    • ()18 b: This is likely a command to print or display an opening parenthesis (() using the current font. The 18 b` might be related to font size or position.
    • FH(G)28 b: This could be another font-related instruction specifying a different font (G) with a parameter 28. The b operator might be related to setting the font weight or style.
    • FF(:)21 b: Similar to the previous occurrence, this is likely a command to print or display a colon (:) using the current font. The 21 b might be related to font size or position.
    • Fw(No)r(de)p: This appears to be a command to print or display the string “No” using a specific font (w). The subsequent characters r(de)p are not immediately clear without additional context.

Overall, without further context or knowledge of the surrounding PostScript code, it’s challenging to provide a definitive interpretation or explanation of the code.

Personal note.

Having parsed PostScript by hand know that Fw(No)r(de) is actually the word Node in the second typing rule. While I did not expect ChatGPT to understand everything about the PostScript snippet, was surprised that it did not recognize that as the word Node.

2 Likes
20

For those of us without experience with typing systems, can you tell us how well it understood the TeX code?

21

As with most responses by ChatGPT it depends upon your level of knowledge. For a beginner they do very good but for a expert they would probably find more wrong than correct. But as we know sometimes just getting over the initial hump for learning when there is nothing and having some info as demonstrated in the example will get someone interested enough to keep going.

A much better example to answer your question would be to use the typing rules for a functional programming language like F# or Haskell where the typing rules can be demonstrated also with code and the types included in the function signature.

If I find such I will give it a try and if it works will post as a reply. :slightly_smiling_face:

Update on the search.

I spent about an hour after posting that looking and the language with the best typing rules published was for ML but they were to complex for the beginner.

However typing rules for Lambda Calculus are very easy to understand (ref) but the problem is that many do not understand Lambda Calculus. Typed Lambda Calculus might be better but then the typing rules are a bit more complex.

2 Likes
22

I agree with Eric’s assesment,

Although I do have some reservations about the tex source, in the example used there’s a single \newcommand defined, but the code itself contains several different custom commands, stuff like \pat and tbool

These commands are most likely defined elsewhere in the document source, this issue might be solved with an extended context window.

But we’re out of luck, if theses commands are defined in non-standard latex packages.

1 Like
24

Yes this is a valid point that must be addressed to pass a subset of the TeX or LaTeX to ChatGPT.

Follow up (Click triangle to expand)

In order to work with a larger body of TeX switching to

image
image360×576 11 KB

The book

  • is open source on GitHub
  • is free
  • needs little to no prior knowledge to understand
  • has various representations of technical expressions in TeX that can been viewed in human form in the PDF format.

For this truth table

image

the TeX is

https://github.com/rzach/forallx-yyc/blob/dd26ca3043c9288fc548836e136f2416ed70d93d/forallx-yyc-truthtables.tex#L21-L26

Giving that to ChatGPT as a new conversation

Prompt

\begin{tabular}{c|c}
\metav{A} & \enot\metav{A}\\
\hline
T & F\\
F & T 
\end{tabular}

Completion

The table you provided represents the truth values of a formula and its negation. Let’s break it down:

  • \metav{A}: This is a placeholder representing a statement or proposition. It can take on the truth values True (T) or False (F).

  • \enot\metav{A}: This is the negation of \metav{A}. It represents the opposite truth value of \metav{A}. If \metav{A} is True, then \enot\metav{A} is False, and vice versa.

The table shows the possible truth values for \metav{A} and \enot\metav{A}. When \metav{A} is True, \enot\metav{A} is False. When \metav{A} is False, \enot\metav{A} is True. This is consistent with the logical operation of negation.

So, the table reflects the basic principles of negation in classical logic.

Personal note:
Obviously ChatGPT can understand the TeX but some of the TeX needs to be pretty printed.

Here is a refined prompt in a new conversation that addresses the evident problems in the first completion.

Prompt

LaTeX commands and meaning
\enot - `not` symbol
\metav - meta variable

```LaTeX
\begin{tabular}{c|c}
\metav{A} & \enot\metav{A}\\
\hline
T & F\\
F & T 
\end{tabular}
```

* format for readability by a human
* convert LaTeX  commands to symbols
* do not explain LaTeX 
* do not explain Markdown or other formatting
* explain expression for a beginner

Completion

A | ¬A
------
T | F
F | T

Explanation for a beginner:
This table represents the truth values of a statement A and its negation (¬A). The variable A can take on two truth values: True (T) or False (F). The table shows all possible combinations of truth values for A and its negation ¬A. When A is True, ¬A is False, and vice versa.

Since TeX is actually code with macros, variables and state, such information needs to be passed to ChatGPT to correctly process and/or pretty print the TeX.

While smaller examples of TeX can be passed in a single prompt, there will be TeX that is larger than the token limit and so can not be passed in. Possible solutions would be to use existing code that parses TeX and maybe even runs part of the TeX to establish the state at the time, or to train an LLM so that it can infer reasonable values without seeing all of the TeX.

25

@elmstedt have you tried the InftyReader that @N2U posted above? What can you tell us about it?

26

I believe it was @Foxabilo who brought infreader to our attention, any thoughts on this?

As mentioned by Eric, optical character recognition of complex equations seems to be an issue many have struggled with.

1 Like
27

With regards to PDFs as an image of the documents they are only good for passing to OCR.

As for trying to extract technical expressions from PDFs that use PostScript, that too is not a good solution as the PostScript is more about giving positions of where to place graphics, all of the metadata from a source such as LaTeX is lost which makes the task much harder. I will note that I did try InftyProject and for a PDF that uses PostScript it is the best I have seen of the few things mentioned.

Years ago I was dissuaded by the fact that everywhere one looked at the problem, everything noted and all apps for sale were based on PDFs that used PostScript. After working with that for a while realized while possible there has to be something with much higher accuracy. Now that many PDFs can be downloaded with the original LaTeX, as noted in the example earlier this is much more productive as not only is the technical expression there in a linear format but the metadata helps the LLMs expand on the result and is much quicker. There are still some dots that need connecting but nothing that appears as a show stopper.

28

It’s been a bit quiet here for the past few weeks, but I thought I would share an update on my progress.

Eric’s statement here is indeed correct:

So our first problem is finding a proper dataset to work with, I did some digging and I found this collection of 100k images of formulas with their associated latex source

Next we’ll need a functional ORC system and I found this paper describing such a thing:

https://dl.acm.org/doi/10.1145/3395027.3419580

This research introduces PDF2LaTeX, a unique OCR system designed to extract mathematical content and text from PDFs and convert them into LaTeX markup. They use a Conditional Random Field (CRF) to distinguish between regular text and mathematical expressions, they then use two separate models based on a combination of CNN and LSTM (Long Short-Term Memory) neural network architectures, To translate image blocks of both math expressions and plain text into LaTeX.

While their OCR system outperformed InftyReader, it still has some issues with math as shown in the table below

IMG_20230806_145424
IMG_20230806_1454241080×620 107 KB

1 Like
29

Thanks! :tada:

Going after PDFs as images was not high on my list, PDFs based on PostScript was much higher (think low hanging fruit), but still is a case that is needed.

Took the first item from the list im2latex_formulas.lst to see how well the LaTeX could be understood by ChatGPT (Model: GPT 3.5) and used to help a person.

ChatGPT August 3 Version
Model: GPT-3.5
Prompt

For the following LaTeX for a math expression

  • display as a math expression
  • explain to a university student
  • if it is has a specific use include internet references such as wikipedia
\int_{-\epsilon}^\infty dl\: {\rm e}^{-l\zeta}	\int_{-\epsilon}^\infty dl' {\rm e}^{-l'\zeta}	ll'{l'-l \over l+l'} \{3\,\delta''(l) - {3 \over 4}t\,\delta(l) \} =0.		\label{eq21}

Completion

Display as a math expression:

The given LaTeX expression is:

[
\int_{-\epsilon}^\infty dl : e^{-l\zeta} \int_{-\epsilon}^\infty dl’ : e^{-l’\zeta} \frac{ll’(l’-l)}{l+l’} \left{3\delta’'(l) - \frac{3}{4}t\delta(l)\right} = 0 \quad \text{Eq. (21)}
]

image

Explain to a university student:

In this math expression, we have an equation represented in LaTeX notation. Let’s break down the components step by step:

  1. The expression starts with two integrals:

    (\int_{-\epsilon}^\infty dl) represents the integration over the variable (l) from (-\epsilon) to positive infinity.

    (\int_{-\epsilon}^\infty dl’) represents the integration over the variable (l’) from (-\epsilon) to positive infinity.

  2. Inside the integrals, we have (e^{-l\zeta}) and (e^{-l’\zeta}), which are exponential functions with (l) and (l’) as variables, respectively. The Greek letter (\zeta) seems to be a constant.

  3. Next, we have (ll’(l’-l)), which is a product of three terms involving the variables (l) and (l’).

  4. After that, we have a fraction (\frac{{l’l(l’-l)}}{{l+l’}}), where (l+l’) appears in the denominator.

  5. Then, we have the curly braces ({ }), which contain two terms: (3\delta’‘(l)) and (\frac{3}{4}t\delta(l)). These are delta functions (\delta(l)) and (\delta’'(l)) with coefficients (3) and (\frac{3}{4}t), respectively. The variable (t) seems to be some constant.

  6. Finally, the whole expression is equated to zero, indicating that this entire mathematical expression equals zero.

Please note that without further context or additional information about the variables and constants used in this expression, it is challenging to provide a specific interpretation of the equation’s meaning or its applications. It appears to be a mathematical equation involving integrals and delta functions, but the precise significance depends on the specific field or context it is used in.

Specific Use and Internet References:

Without specific context or information about the origin of the equation, it’s challenging to provide a direct internet reference or source. However, some components of the expression, such as the use of integrals and delta functions, are common in various mathematical fields, including calculus, differential equations, and theoretical physics. If you can provide more context or the field of study where this equation is relevant, I might be able to provide more specific references or explanations.

What would be interesting to know is for the images that generated LaTeX that were not accurate how correct is the expression? What is the confidence level that the expression is correct? In other words it is at times easier for a human to check simple facts that are a hallucination than it is to check an expression that is a hallucination or partial hallucination.

The page did not seem to include the results that were invalid but returned LaTeX, would have been nice to see that list included. If I missed those please point them out.

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