Please spellcheck this subtitle and keep the timecodes unchanged:

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Okay, so we're diving into
the world of AI and math.

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You know, there've been all
those headlines lately about AI

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becoming these
like math geniuses.

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And well, we were definitely intrigued.
But we also wanted to look a little deeper,

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which is why we're doing
this deep dive into

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two brand new research papers that really
kind of throw some shade on that whole

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AI is math genius thing.
Yeah, it seems like almost

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every day now there's like
a new headline about AI.

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Conquering some new frontier,
right? Right. But what these papers really

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highlight is that maybe we need
to like tap the brakes a little bit.

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Yeah. On all those pronouncements,
at least when it comes to

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like truly understanding math.
Exactly. So we're looking at these

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two papers and they both
really try to unpack how well

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large language models those
LLMs you've probably heard of

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can actually handle math.
The first one is called functional

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benchmarks for robust evaluation of
reasoning performance and the reasoning gap.

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Okay. And this
one, this one really,

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really made us think twice about
whether LLMs really deserve

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that math whiz title.
What do you think?

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Yeah, you know, it's
fascinating because what

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they basically do
is they point out that all

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those like amazing scores that LLMs
get on these math tests,

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they might actually
be super misleading.

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It's like, you know, that friend
we all have who can like ace a

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history test just by memorizing all
the dates and names.

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They couldn't tell you why any
of it actually matters.

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They're just playing the game. Exactly.
They don't actually understand the rules.

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Right. So how did
these research papers?

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Researchers like expose this possible
flaw in how

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we're thinking about LLMs in math.
So they came up with

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this really clever car
set that they call the reasoning gap.

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Okay. And the idea is this.
Imagine you present an LLM

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with a math problem,
right? Right. And then you give

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it the exact same problem,
but you just change the numbers in

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the context a bit. So like,
if Sarah has three apples and

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John gives her two more, we change it
to Maria and David swapping oranges.

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Precisely. The core problem,
the math, it's identical.

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It's just dressed up differently.
And so their thinking is if a

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model truly has reasoning skills,
it should be able to solve both

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of those problems super easily.
Like it shouldn't be phased by

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those little like superficial changes.
But if it like stumbles on

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that slightly altered version,
then that kind of suggests

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that it's relying more on like memorized
patterns and not actual understanding.

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Okay. That's actually really clever. So
they put these elements to the test, right?

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Using this whole
reasoning gap concept.

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What did they find? Like
did the LLMs, you know, pass

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with flying colors or
did they totally fall flat?

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Well, they basically created
this like much

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tougher version of this really
popular math benchmark called math.

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They called it naturally math.

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Why, of course. And the results, well,
they were a little concerning

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to say the least. They
tested out a bunch

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of different state
-of-the-art LLMs on this.

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Okay. And the reasoning gaps
they observed get this.

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They ranged from a pretty startling 58% all
the way up to a kind of jaw-dropping 80%.

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Yeah. Whoa, those are some serious gaps.
So even the LLMs that are supposed

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to be like the top performers,
the ones that are wowing us with,

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you know,
their ability to do

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these complex problems,
they might actually be relying

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more on like memorization
than true understanding.

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Yeah, it definitely throws like a
wrench into that whole LLMs

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or math geniuses narrative that's been
going around. But sure.

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And here's where it gets even more
interesting. They found that

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generally speaking,
the more difficult the problems became,

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the wider that reasoning gap grew.

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Okay. So that kind of makes sense though,
right? Right. Like it's easier to rely on,

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you know, memorized formulas
or just simple calculations

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when the problems are
pretty straightforward.

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But when you start like crank
it up the complexity,

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those shortcuts just aren't going
to cut it. Exactly.

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It's like those students who can,
you know, recite the textbook perfectly.

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Yeah. But then like you give them
a real world problem and

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they just freeze. Because their knowledge
is like super superficial.

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Okay. So we've got LLMs potentially like
flunking out of advanced math.

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What about our second source?
This one is called GSM Symbolic.

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Understanding the limitations of
mathematical reasoning

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in large language models.
Yeah. Did this paper kind

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of echo those concerns
about how good LLMs really are at math?

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So this paper actually dug even
deeper into this whole dilemma.

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And they definitely expressed reservations
about those static benchmarks.

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You know, the ones that basically
just test a fixed

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set of problems over and
over. Right. Right.

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They argue that if we really
want to understand what LLMs

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are capable of, we need like a
much more dynamic approach.

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So it sounds like they're calling for less
of a multiple choice and more

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of a show-your-work kind of
test for these LLMs. Exactly.

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And to do that,
they actually introduced something

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called GSM Symbolic.
Okay. GSM Symbolic sounds intriguing.

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So tell us more. Tell us more about
this new benchmark and how it's trying

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to give us like a clearer picture of
this whole LLMs in math situation.

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Okay. So think of it this way.
Instead of just testing the

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same problem repeatedly,
they're creating variations on a theme.

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So they make sure that
like the underlying mathematical

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logic of the problem stays the same,
but the specifics of it, they change.

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And to do that,
they use what they call

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Symbolic Templates to
generate like a whole bunch

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of different versions of
existing math problems.

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Okay. They took these from a popular
data set called GSM 8K.

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So they're really shaking things up a bit.
This is cool because it lets researchers

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see how well LLMs can adapt and
apply their knowledge to new situations.

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Which is a much better test
of genuine reasoning. Exactly.

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So what about the results?
What did they find?

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Did GSM Symbolic like vindicate
our LM friends here?

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Or did it kind of solidify
that whole? They're just

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really good at a very
convincing game of pretend thing.

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Well, you're gonna have to
like fasten your seatbelts

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here because we're
about to uncover some,

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well, some pretty
surprising vulnerabilities.

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So their evaluations using this
GSM Symbolic Benchmark,

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they showed that LLMs, well, they can be
surprisingly fragile when it comes to math.

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Exactly.

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When they just tweaked the
numbers within a problem

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but kept everything else exactly the same,
the LLMs performance totally tanked.

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Wait, so they struggle just
because the numbers change.

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You'd think that would be like
the easiest part for them.

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It's almost like they're
so focused on the

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pattern of the problem,
you know what I mean?

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Right.

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That they kind of
forget that numbers can

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change without changing
the underlying math.

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It's like getting hung up on what font
a test question is in or something.

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It's totally a fascinating
paradox though, isn't it? Because

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we assume that numerical
manipulation would be their forte.

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Right.

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But this research really
suggests that they

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might be clinging to those
superficial patterns instead of

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actually applying
true adaptable mathematical reasoning.

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So they're more like master
calculators than actual mathematicians.

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Right.

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Like they excel at crunching numbers
when the pattern is familiar.

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But their ability to reason flexibly
and adapt to new situations,

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it's, well, let's just say
there's room for improvement.

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I think that's a really
good analogy actually.

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And if that wasn't enough to make
us question their reasoning skills,

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the researchers actually took things
a step further.

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So remember how we were talking
about the reasoning gap earlier?

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Yeah, yeah.

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They found this really curious
disconnect between how LLMs

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handle numbers versus how
they handle words.

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A disconnect. Okay,
now I'm really intrigued. Tell me more.

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So they discovered that LLMs
were much more robust

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to changes in proper names
within the problems.

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Like swapping out, say,
Sarah for John or apples for oranges,

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that didn't really phase them.

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But as we discussed, even
tiny, tiny tweaks to the numerical

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values sent their
performance into a total tailspin.

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That is so wild. You'd
think numbers, like the

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literal foundation of math
would be their strong suit.

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It's almost as if they're treating
numbers more like arbitrary

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symbols rather than quantities that
have meaning in relationships.

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Like, they can read the letters,
but they don't know what the words mean.

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That's a great way to put it.
It suggests that they might

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be leaning super
heavily on like the linguistic patterns,

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the structure of the sentences to
guide their problem solving,

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and almost like ignoring the
numerical aspect altogether.

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So they're better at understanding
the story than the mass behind the story.

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Yeah. It's like they can read a
recipe and recognize all the ingredients,

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but they have no clue how
to actually combine them.

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Exactly. And this actually brings
us to a really

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crucial question that both of
these papers raise.

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Which is, if LLMs struggle with
even like basic mathematical reasoning,

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then what does that mean for their
applications in the real world?

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Right. Because we hear so much hype about
AI revolutionizing everything.

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From healthcare to finance.

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Are we getting ahead of ourselves?
Should we be putting like

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the breaks on all those
AI-powered financial models?

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I don't necessarily think it's about saying
that AI will never be able to grasp math.

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Or that we should be hitting
the pause button on everything.

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But it's more about recalibrating our
expectations a little bit.

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And really understanding that while
LLMs have shown incredible

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promise in certain areas like
natural language processing

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and creative writing and things like that,
tasks that require heavy

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logical reasoning,
things like medical diagnoses

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or as you said financial
modeling, those might

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require a bit of a more
cautious approach.

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So maybe not handing over the keys
to the stock market yet.

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It's crucial to remember that these
models are still essentially in

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their infancy when it comes to
this kind of reasoning.

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And while they can be
incredibly valuable tools,

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they shouldn't be replacing human
expertise and judgment just yet.

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Especially not when the stakes are high.

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Yeah, it's so tempting to get caught up
in the excitement of it all.

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But we can't forget that these
are tools. They're not oracles.

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They can enhance our abilities but
not replace them entirely.

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Especially when we're
talking about things

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like complex reasoning
and decision making.

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Absolutely. And to bring things back to
those research papers for a second,

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I think it would be helpful to
look at some specific examples.

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Okay.

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Because I think that'll really highlight
some of these limitations in action.

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Yes, I'm all ears.
I always find that real world

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examples really help make these
complex concepts click.

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Totally. Remember that
problem from the functional

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benchmarks paper about
the letters in the words 16?

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Uh-huh.

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And calculating the probability of the E's
not being next to each other.

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Yeah, yeah.

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The one that they use to kind of illustrate
the whole functionalization process.

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It's coming back to me. Yeah,
it involves some clever

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counting and probability,
not just like your basic arithmetic.

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Exactly. And GPT-4 aced the original
static version of that problem.

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But when the researchers hit it
with those functional variants,

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you know, using different words,
but with that same underlying logic.

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Yeah.

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It could only solve one out of three.

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Interesting. So even though the
reasoning was identical,

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just changing the specifics of the
problem tripped it up.

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Yeah. It's like,
it learned the answer to that

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specific problem with 16, but it didn't
actually understand the underlying concept.

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Right. Great.

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And then there's another example.
This one involves like spinners and

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calculating the probability of getting an
even two-digit number.

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Okay. Yeah. Yeah. I vaguely
remember that one.

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Something about like multiplying
the numbers on two different spinners.

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Right. You got... and again, GPT-4,
no problem solving the static version.

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Right.

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But when they threw those
functional versions at it,

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it just kept saying no solution
for every single one.

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No solution.

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Right. That's a pretty definitive
answer for a model

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that supposedly excels at these
kinds of problems.

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Yeah.

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There's like, it hit a wall.
Like, it couldn't even attempt

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to apply its knowledge to
a slightly different context.

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Exactly. And it suggests that, again,
that initial success that it had,

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it might have been more about
recognizing a familiar pattern than

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it was about genuinely understanding
the problem at hand.

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So it's not just about
getting the right answer.

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It's about understanding how
and why that answer is correct.

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It's about the journey, not
just the destination, as they say.

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Yes. That is a beautiful way to put it.
And I think that really is the

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crux of this entire debate,
right? Like, we can't

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just rely on surface-level
performance anymore.

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We have to dig deeper.
We have to understand how these LLMs

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are arriving at their answers and
determine if they're actually exhibiting,

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like, genuine reasoning or
if they're simply

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mimicking patterns that they've
seen before.

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Okay. So we've talked about some
pretty significant limitations here.

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But, I mean, where
do we go from here?

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Is there hope for LLMs in math?

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I don't think these papers are
meant to be like

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a final exam for LLMs. It's more like,
they're a wake-up call.

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They highlight a really,
really critical area that needs a lot

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more exploration and development.
We need new training methods,

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new evaluation techniques that really push
LLMs beyond just surface-level

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pattern matching and move them
towards genuine adaptable reasoning.

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So how do we actually
bridge this reasoning gap?

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How do we help LLMs move beyond
just mimicry and into true understanding?

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That is the million-dollar question,
right? But some researchers are

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exploring some really,
really promising avenues.

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One of them is incorporating
more what we call

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symbolic reasoning
into the training process.

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So essentially teaching them to
manipulate abstract representations of

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mathematical concepts rather than
just crunching numbers.

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So it's about teaching them
the why behind the how, right?

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Helping them actually
grasp those underlying

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principles that govern
mathematical relationships.

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It's going to like moving
beyond rote memorization,

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to understanding the elegance and,
dare I say,

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the beauty of these mathematical concepts.

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Yes, exactly. Another approach
is developing new

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benchmarks that go beyond those
static problem sets and actually test

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their ability to generalize,
you know, to adapt.

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We need challenges that force them
to think critically and creatively,

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not just regurgitate patterns
that they've memorized.

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It sounds like we're really
on the verge of

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a whole new era in AI research.
One that focuses on

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developing machines that
can truly reason and understand,

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especially in that really complex
realm of mathematics.

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It's a fascinating and potentially
incredibly transformative journey.

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But before we get too
far ahead of ourselves,

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let's take a moment to reflect
on what we've learned today.

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What are your final thoughts
on all of this?

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Yeah, it really has been like a wild ride,
hasn't it? We started off all excited

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about AI's potential and math and then
those papers kind of threw us for a loop.

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I know,
right? It's like realizing that friend

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who's like amazing at
trivia night. They might

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not actually be a
mathematical genius after.

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Like they're great at playing
the game show,

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but then you ask them
to solve a real -world

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problem and they're like
completely lost. Exactly.

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But I do appreciate how these papers,
they don't just like point

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out the problems. They also like
really push us to think about solutions.

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Oh, absolutely. And I think one of the
most exciting takeaways for me is

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this whole idea that we need more
like dynamic and creative benchmarks.

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Like it's about designing tests that
actually challenge LLMs to

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think outside the box.
You know what I mean?

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So less about can you solve for X and more
like can you explain the

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concept of infinity? Or like can you
come up with a new mathematical theory?

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And now you're talking.
We need to be challenging

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these models to not
just process information,

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but to actually understand it and apply it
in like totally new and creative ways.

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That is such a good point.
It's not just about

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teaching LLMs to be like
better calculators or something.

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It's about like really nurturing
a deeper understanding

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of those underlying
mathematical principles.

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Which makes you wonder like
down the line could

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AI actually contribute to like
new mathematical discoveries?

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It's a mind blowing thought,
isn't it? Like imagine an AI actually

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collaborating with like
real mathematicians,

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you know,
pushing the boundaries of human knowledge.

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Yeah. I mean, that's
the kind of potential

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that makes this field
so incredible exciting.

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It really does. And it makes you
think about like the future

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of AI in general and its
role in our world.

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And I think it's pretty clear
that we need to

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approach AI development
with like a balance of

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optimism, but also like a
healthy dose of caution.

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Totally. I mean, as we've seen today,
these models are undeniably powerful,

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but they still have some
pretty significant limitations.

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And I think it's our responsibility to,
you know,

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to really understand those
limitations and to

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make sure that we're
guiding AI development in a

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direction that ultimately
benefits all of humanity.

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AI's mastery of math might be a
little over-height right now.

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At least the potential is
definitely still there.

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It's just going to take some time,
a lot more research and maybe like a whole

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new way of thinking
about intelligence itself.

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00:17:10,950 --> 00:17:14,230
Well said, as always,
I'm really excited to see what, you know,

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what kind of amazing
discoveries await us as we

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continue to explore this
ever evolving world of AI.

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Us too. Thanks so much for joining us
for this deep dive. Until next time,

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everyone, keep asking
questions, stay curious

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and never be afraid to
challenge those headlines.

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Especially when it comes to AI and math.