All right, get ready, because today we're diving into a paper about AI intelligence,
but it's not just about like getting a computer pass a math test or something.
It's way more interesting than that.
Yeah.
This paper says we need to go deeper.
Yeah.
Like understand how AI solves problems,
especially those that require like abstract thinking, you know.
It is fascinating.
They use this framework called Algebraic Circuit Complexity
to analyze how AI thinks.
OK, so you're saying it's like we're trying to make a blueprint of AI's thought process.
Exactly.
Break it down.
Into like individual steps and connections.
So imagine AI's thinking process.
Like a circuit board with all these different paths and connections.
Exactly. Those circuits represent how AI tackles these problems, especially ones
that involve abstract concepts like we see in algebra.
So like algebra.
Yeah. And the complexity of those circuits.
Things like how many connections they have are like the longest path from input to output.
Those tell us how hard a problem is.
For the AI to solve.
Yeah, for the AI to solve.
So we're not just seeing if the AI gets the right answer.
Yeah.
We're like, wait a minute.
Exactly.
How did you get there?
It's the how.
Here were the steps.
Not just what, but how.
Yeah.
And it's about going beyond simply testing if AI can handle bigger numbers or longer
equations.
Right. Like you were saying.
Yeah.
Just because it can do a simple thing.
Exactly.
Doesn't mean it's actually thinking.
It doesn't mean it understands the concepts behind it.
Right.
This paper argues that true symbolic reasoning is about understanding
OK.
The relationships between different pieces of information.
So like we do in algebra when we solve for X.
Exactly like when we solve for X in algebra.
Got it.
It's about understanding those relationships.
Not just crunching numbers.
Right.
It's got to understand the concept.
It's about understanding the concepts behind them.
Yeah. Behind them.
Yeah. OK.
And the paper highlights this idea of composable functions.
OK.
Which is AI's ability to break down a complex problem into smaller parts.
OK.
Figure out the rules for each part.
Right.
And then put it all back together.
To solve something new.
To solve something new and more challenging.
I'm thinking like learning to bake.
Yes.
You need to like master every little step.
Perfect analogy.
Before you can make like a crazy cake.
Exactly.
Here's something.
One way researchers test this ability in AI.
OK.
Is through something called polynomial identity testing.
Polynomial identity testing.
Imagine showing AI two recipes that look totally different.
OK.
And asking do these actually make the same cake.
Interesting.
That's essentially what they're doing.
They're seeing.
Challenging AI to see through different forms of an equation.
If it can.
Like cut through the noise.
That they are actually equivalent.
OK.
They might look different.
Got it.
But they're actually the same.
You're like are they actually getting it.
It is.
They just like.
You know.
Parrot.
Regurgitating.
Just repeating what they've seen before.
Yeah.
OK.
So it's like we're testing if it can see.
Right.
The underlying structure.
The essence of the problem.
Beyond just the superficial differences.
Got it.
And to really push AI's limits.
The paper proposes a few specific benchmark.
Exit like tests.
Yeah.
Tests.
Right.
One they call systematic compositional generalization.
Systematic compositional generalization.
It's like testing if AI after learning to combine basic ingredients can now create
variations of a recipe at the same complexity level.
So like once you've learned how to make cookies.
Yes.
Can you make different flavors of cookies.
You got it.
But it's still cookies.
It's still cookies.
OK.
Then there's productive compositional generalization.
Productive compositional generalization.
Which is about taking things up a notch.
This benchmark tests if AI can generalize to entirely new levels of complexity.
So now we're talking like.
Now we're talking instead of cookies.
Yeah.
It's a wedding cake.
A multi tiered wedding cake.
Oh OK.
We're talking about AI tackling problems that are significantly more complex.
OK.
And these benchmarks involve changing the structure.
OK.
Those algebraic circuits we talked about.
OK.
Making them larger and deeper to represent more complex calculations.
So we're really trying to push AI.
We're really pushing those limits.
So what's limits here.
To see how far it can go.
See what it can do.
With its symbolic reasoning muscles.
Yeah.
And it's not just about like I said before.
It's not just about can it get the right answer.
Yeah.
But like how is it.
It's about understanding the process.
Getting there.
Yeah.
You're absolutely right.
It's one of the biggest challenges in AI.
Right.
It is.
Figuring out.
What's.
Keeking inside the black box.
Trying to understand why AI makes the decisions it does.
Like trying to see the gears turning.
Exactly.
Trying to see those gears turning.
In the AI's brain.
And the paper suggests that this framework.
Uh huh.
Of algebraic circuits could be a powerful tool for doing just that.
OK.
So researchers can compare what's happening inside AI.
Yeah.
For example where a language model focuses its attention.
OK.
To the actual circuit diagram that represents the problem.
So we can see if it's thinking.
Yeah.
Like we would.
Is it thinking like we do.
Yeah.
If it's solving the problem.
Is it aligning with our understanding of math.
In a way that makes sense to us.
Exactly.
OK.
And this brings us to a really exciting point.
OK.
You know those impressive large language models like chat GPT.
Yeah.
Everybody's talking about those.
Everyone's talking about them.
Yeah.
Well even these language models.
OK.
Can be evaluated using this framework.
Wait so even though they're about language.
Yeah.
They could be thinking mathematically.
Potentially.
By designing problems that require abstract reasoning on variables.
Uh huh.
We can challenge them to go beyond just spitting out text.
OK.
And see if they can truly grasp.
Wow.
These complex concepts.
This is blowing my mind.
It's exciting stuff.
So we're really.
We're pushing those boundaries.
Pushing the boundaries here.
Of what we understand about AI.
Yeah.
And by understanding how AI tackles symbolic reasoning.
OK.
Through this lens of algebraic circuits.
We can get a much clearer picture.
Of its capability.
Of what it's capable of and develop more reliable.
OK.
Interpretable.
Yeah.
And ultimately more trustworthy AI systems.
This is fascinating.
It is.
So we've covered a lot of ground here.
We have.
I want to hear more about this whole circuit divergence idea.
Absolutely.
Because it sounds like that's.
It's a key part of this research.
Really important.
It's all about how researchers are tweaking these circuits.
OK.
To create these different levels of challenge for AI.
All right.
So like.
Like setting up an obstacle course.
Yeah.
An obstacle course.
For its reasoning abilities.
I love that.
Yeah.
OK.
I'm ready.
Let's unpack it.
To unpack it.
Let's dive deeper into the specifics.
Right.
Of how these circuits are designed.
All right.
And how they're being used to test AI's limits.
Do it.
Let's go.
So this whole idea of circuit divergence.
It's about creating these different versions.
Of algebraic circuits.
Each with its own level of complexity.
Like different levels of difficulty.
Yeah.
It's like setting up an obstacle course with different challenges.
To test how far.
I like that.
AI can jump.
So to speak.
Yeah.
But before we get into like the obstacles themselves.
Yeah.
Can we just like back up for a sec.
Sure.
And remind me how these circuits actually work.
Of course.
I think I still wrap in my head around it.
So think of it like this.
An algebraic circuit is like a visual representation.
Oh yeah.
Of a mathematical formula.
Each part of the circuit.
Yeah.
It's called a gate.
And it performs a specific operation.
So it's kind of like those old calculators.
Yeah.
Where you'd input the numbers and then you'd press the plus sign or the minus sign.
Like a plus or minus or multiply.
Yeah.
Anything like that.
Yeah.
Dealing with variables.
OK.
But this is all happening visually.
OK.
Like a flow chart for math.
I like that flow chart.
Yeah.
So for a simple equation like I don't know.
Yeah.
Five plus seven.
OK.
So in a circuit you'd have two input gates.
One for the number five one for the number seven.
Those would feed into a sum gate which does the addition.
OK.
And the output of that sum gate would be 12.
OK.
So it's like five goes into one gate.
One gate.
Seven goes into the other.
The other gate.
And then they come together in the sum gate.
In the sum gate.
And it spits out 12.
It spits out 12 exactly.
OK.
Got it.
So for more complex equations you'd just have more gates and different types of gates.
OK.
Representing different operations all connected in a specific way.
Like a more complex flow chart.
Exactly a more complex flow chart.
Right.
And the beauty of this is we can visualize how AI tackles a problem.
Step by step by following that flow through the circuit.
OK.
Now when researchers talk about circuit divergence.
OK.
They're essentially changing different aspects.
OK.
Of these circuits.
Yeah.
To create more challenging problems for the AI.
OK.
So like they're changing the obstacle course.
They're like changing the hurdles.
Exactly.
Making them higher or lower.
Making them higher or lower wider.
You know.
Different things like that.
So what kind of changes are they making.
So one way is by changing the depth of the circuit.
The depth.
Think of depth as the number of steps.
OK.
Involved in solving the problem.
OK.
A deeper circuit means a more complex calculation.
So more steps.
It requires more steps to reach that final answer.
So it's like adding more layers to the cake.
Perfect analogy.
Adding more layers to that cake.
Making it harder to bake.
Making it more intricate.
More time consuming to bake.
Got it.
And then there's the size of the circuit.
OK.
Which refers to the number of gates and connections involved.
OK.
A larger circuit generally means more complex calculations.
OK.
And more information for the AI to process.
It's a bigger circuit.
Bigger circuit.
More ingredients.
More steps.
Harder to keep track of.
More challenging for AI to keep track of everything.
Yeah.
And get that right outcome.
Yeah.
And by systematically varying these properties.
OK.
The depth, the size and even the types of gates used.
OK.
Researchers create this whole range of problems.
To really test it.
To test AI's symbolic reasoning abilities.
To see what it can do.
Yeah.
Throwing everything they can at it to see how well it can adapt and generalize its knowledge.
OK.
So just to be clear.
Yeah.
We're not just talking about numbers here.
We're not just talking about the numbers themselves.
It's about concepts.
It's about abstract concepts represented by variables.
Like the X.
Like X.
Exactly.
In algebra.
The real test is whether AI can understand the relationships between those variables.
Manipulate them according to the rules.
OK.
And come up with a solution that applies in different contexts.
So it's not just memorizing.
It's not about memorization.
An equation.
It's about understanding the underlying principles.
OK.
Those abstract ideas that govern these mathematical relationships.
Got it.
And that's where those benchmarks we talked about earlier come in.
Right.
Remember polynomial identity testing.
Yeah.
With the cakes.
Remember the cake analogy.
Yeah.
Polynomial identity testing is about presenting AI with two different looking
equations and asking are these actually the same just written in different ways.
Got it.
It's challenging AI to see through the superficial differences.
Uh huh.
And recognize that underlying mathematical equivalence.
So it's like can you simplify this fraction.
Exactly.
And get to the same answer.
Like recognizing that two fourths is the same as one half.
Yeah.
Even though it looks different.
Even though they look different on the surface.
Yeah.
It's about understanding that core mathematical concept.
It's about understanding it.
Not just memorizing specific forms of an equation.
OK.
I've started to see how these tests can reveal.
Yeah.
A lot about how AI is actually thinking.
They do.
They really do.
Yeah.
And then there's the polynomial expansion and factorization benchmark.
OK.
So more polynomial.
More polynomials.
There's got to be a reason why we keep talking about this.
There is polynomials are just a powerful way to represent.
Oh, I complex mathematical relationships.
OK.
Think of polynomial expansion like translating a concise set of instructions.
OK.
Into a more elaborate program with all the details spelled out.
OK.
And then factorization is the reverse.
OK.
Taking that complex program and simplifying it back to those core instructions.
So it can go back and forth.
It's like going back and forth between different levels of complexity.
Got it.
And this ability is crucial for all sorts of tasks like understanding how AI might translate.
Yeah.
Between different programming languages or decipher complex scientific formulas.
So it's not just about the math.
It's not just about the math.
It's about the thinking.
It's about the underlying thinking and reasoning.
OK.
It's about those fundamental skills that are necessary.
Yeah.
For really any kind of complex problem solving.
So these benchmarks.
Yeah.
They're really putting AI through its paces.
They are.
They're really challenging it to see what it can do.
And one of the things that you said that they're looking for.
Yes.
Is this circuit divergence.
It could diverge.
I feel like we keep dancing around this idea.
We do.
So can you break it down for me?
Absolutely.
What is it?
So remember how we talked about researchers creating these different
versions.
Yeah.
Different difficulty levels.
Of circuits with varying levels of complexity.
Uh-huh.
Circuit divergence is a way to measure.
OK.
How much AI is problem solving strategy changes.
OK.
When it's faced with these different challenges.
But they give it an easy one.
Yeah.
And then a hard one.
Yeah.
Does circuit divergence tell us.
It tells us how much its approach has to adapt.
To solve the harder one.
To solve that harder problem.
Got it.
It's like observing how a chef's techniques might change.
When they go from baking a simple cookie.
OK.
To creating a complex multi-layered cake.
I like where this is going.
Do they use completely different tools and methods.
Yeah.
Or are there some fundamental skills that carry over.
OK.
You know it's about understanding that adaptation process.
So there's high circuit divergence.
Yeah.
It means that the AI had to really change things up.
Yeah.
It suggests that AI is maybe struggling to generalize its knowledge.
That it's relying on very specific strategies that don't transfer well to more
complex problems.
OK.
And a low degree of circuit divergence.
So not a lot of change.
Not a lot of change might indicate that AI has learned more fundamental principles.
OK.
That can be applied across different levels of complexity.
So it's about understanding how well those core skills transfer.
Yeah.
To those more challenging tasks.
So we can actually use these circuits.
You can use these circuits.
Not just to test if the AI can do it.
Not just to test the abilities.
But like see how it's learning.
But to gain insights into its learning process and its problem solving strategies.
That's really cool.
It is.
And this whole framework of algebraic circuit complexity is still relatively new.
OK.
So there's a lot more research to be done to be done in this area.
But it's giving us new ways.
It's opening up exciting new avenues of looking at AI for understanding how AI
thinks and learns.
So I'm following all this.
Yeah.
But I got to ask.
Yeah.
Like how much of this is actually applicable.
That's a great question.
To you know.
Yeah.
The AI we see in the real world.
It's a very valid question.
Because it seems very focused on these abstract math problems.
And you're right.
This research is very much focused on the foundations of symbolic reasoning.
But the insights we gain from studying AI's ability to handle these abstract
problems can have far reaching implications.
OK.
Tell me more.
I'd be happy to.
OK.
So how does all this abstract math stuff.
Yeah.
Help us build better AI.
So think of it like this symbolic reasoning the kind we're exploring with these circuits.
OK.
It's about understanding relationships.
OK.
Rules and logic.
And those are fundamental skills for any kind of intelligent system.
OK.
Whether it's solving equations or navigating a busy city street.
So even though we're testing it with math.
Yeah.
The skills are more general.
Exactly.
If we can understand how AI learns to manipulate these abstract concepts.
OK.
And solve complex problems in a structured domain like math.
We can apply those insights to other areas.
Like what kind of areas.
Like natural language processing.
OK.
Image recognition.
Even robotics.
So it's like teaching the basics.
It's like teaching AI the fundamental grammar of intelligence.
I like that.
So to speak.
The grammar of intelligence.
And this research also raises some fascinating questions.
OK.
About the nature of AI's learning process.
Like what.
For instance one of the things researchers are exploring is something called algebraic
representation learning.
Algebraic representation learning.
Yeah.
What is that.
So traditionally we train AI by feeding it tons of data.
Like showing it equations and answers.
Showing it examples of equations and their solutions.
OK.
But algebraic representation learning is about going a step further.
OK.
And investigating how AI actually represents and manipulates.
But we want to know how it's thinking.
These algebraic concepts internally.
Not just that it gets the right answer.
It's not enough to know if AI gets the right answer.
But how it gets there.
We want to understand the thought process.
Yeah.
The internal language it's using.
Yeah.
To solve the problem.
OK.
And how do we do that.
And this is where those algebraic circuits become really valuable tools.
Right.
Because they're like a visual representation.
Exactly.
The steps.
They provide that visual representation of the problem solving steps.
So researchers can compare AI's internal representation.
To the circuits.
To these circuits and see if they align.
See if it's thinking.
See if it's thinking the way we expect it to.
The way that makes sense.
Yeah.
And one of the fascinating things.
Yeah.
Is that AI might develop its own internal algorithms.
Whoa.
Different from the ones that we explicitly program into it.
So it's like it's like coming up with its own way.
Figuring out their own unique way to solve a math problem.
Of solving the problem.
Even though they were taught a specific method.
That's kind of scary.
It's exciting.
It's exciting but also like.
But it also raises some questions.
Yeah.
Like what if we don't understand.
Exactly.
How do we ensure.
Oh it's getting there.
That these internal algorithms are reliable.
Right.
How do we debug them.
If they lead to errors.
Because it's not just a black box anymore.
It's not just a black box.
Right.
We want to understand.
We want to understand the reasoning so we can trust the decisions.
OK.
So what do we do.
Well the paper highlights a few approaches.
OK.
For tackling this challenge.
Right.
One is using techniques called mechanistic interpretability.
Mechanistic interpretability.
It's all about analyzing AI's internal workings.
Kind of like taking it apart and figuring out how each component functions.
So we're like reverse engineering it.
In a way.
Yes.
Remember how we talked about comparing the attention weights in a language model
to the actual circuit diagram.
Uh-huh.
That's one example of mechanistic interpretability.
OK.
By looking at where AI focuses its attention.
OK.
We can get clues about how it's breaking down the problem.
What aspects it considers most important.
We'll kind of see how it's thinking.
Exactly.
We can see those gears turning.
Yeah.
Another promising approach is the development of neurosymbolic AI system.
Norsymbolic.
These systems combine elements of both symbolic AI,
which is all about rules and logic.
Right.
And neural networks.
OK.
Which are inspired by the human brain.
So it's like the best of both worlds.
Exactly.
Blending the best of both worlds.
The logic.
The precision of symbolic reasoning.
And the flexibility.
And the adaptability of neural networks.
Club of brain.
And the idea is that these hybrid systems might be more transparent.
OK.
And interpretable.
So we can understand them.
Then purely neural network based approaches.
OK.
So it's not just about.
That's just an academic exercise.
Making AI that can do stuff.
It's about building AI that we can understand, trust and collaborate with.
Wow.
This has been really interesting.
It has.
We've learned a lot.
We've gone from the nuts and bolts of algebraic circuits.
Yeah.
All the way to like.
To the grand vision of trustworthy and collaborative AI.
Yeah.
The future.
It's clear that there's still so much to discover.
Yeah.
But this research is pushing the boundaries.
It really is.
Of what we know about AI's capability.
Wow.
And paving the way for a future where humans and machines.
Yeah.
Can work together in truly meaningful ways.
I completely agree.
I couldn't agree more.
It's a really exciting time.
It is an exciting time to be at the forefront of AI research.
You'd be working in AI.
Unraveling the complexity.
Of how these things think.
Of how these systems think and learn.
Thank you so much for.
It was my pleasure.
Talking to us about this.
I'm always thrilled to share my passion for AI.
Yeah.
And explore these thought provoking ideas.
And to all of our listeners out there.
Thank you so much for joining us on this deep dive.
And we hope this is.
You know.
Sparked your curiosity.
About the future of AI.
About AI.
And the quest to understand its remarkable potential.
Yeah.
And keep exploring.
Keep asking questions.
Keep pushing the boundaries of what's possible.
Exactly.
Until next time.