Episode #122

Deep Learning Decoded: The Math Behind the Machine

Herman and Corn pull back the curtain on AI to explain the mathematical "plumbing" of neural networks and the future of machine learning.

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Episode Overview

In this episode of My Weird Prompts, Corn and Herman Poppleberry take a deep dive into the fundamental technology powering today’s AI revolution: deep neural networks. While we often focus on what AI can do—from writing poetry to driving cars—we rarely discuss the underlying "plumbing." Herman breaks down the crucial differences between classical symbolic AI and modern deep learning, debunking the common misconception that artificial neurons are perfect replicas of the human brain. Instead, they explore the reality of matrix multiplication, backpropagation, and the iterative process of training through epochs. The duo also looks toward 2026, discussing why Recurrent Neural Networks (RNNs) are making a surprising comeback through liquid neural networks and state-space models. Whether you're curious about how a car recognizes a pedestrian or why transformers are so memory-hungry, this episode provides a clear, jargon-free roadmap to the mathematical structures defining our future.

The Plumbing of the Future: Understanding Deep Neural Networks

On the December 29, 2025, episode of My Weird Prompts, hosts Corn and Herman Poppleberry stepped away from the flashy headlines of generative AI to examine the "plumbing" of the industry. Prompted by their housemate Daniel, the brothers spent the hour deconstructing the fundamental technology that makes modern artificial intelligence possible: the deep neural network. As Herman noted, while the world is obsessed with what AI can produce, few understand the mathematical structures that allow these machines to learn.

AI vs. Deep Learning: A Neighborhood in a City

One of the most significant points Herman addressed was the common misconception that all AI is built on neural networks. He used a clever analogy, describing AI as a massive city where deep learning is merely one—albeit currently the most popular—neighborhood.

Before the "deep learning revolution" of 2012, AI was dominated by classical or symbolic systems. These are "expert systems" built on rigid if-then rules. For example, a GPS routing algorithm or a chess program doesn't necessarily "learn" in the modern sense; it follows a human-defined search algorithm like A-star to find the most efficient path. The shift to deep learning occurred when researchers moved from giving the machine rules to giving it raw data. In classical AI, a human tells a computer that an apple is red and round. In deep learning, the computer looks at 10,000 images of apples and identifies the patterns of "red" and "round" for itself.

The Biological Myth

The conversation took a turn toward the biological, specifically the "artificial brain" analogy. While the term "neuron" suggests a direct mimicry of human biology, Herman was quick to point out that this is largely a mathematical approximation.

In the 1940s, researchers like Warren McCulloch and Walter Pitts were inspired by how biological neurons fire based on electrical thresholds. However, modern artificial neural networks are essentially massive, multi-layered calculators. They function through matrix multiplication: nodes receive numerical inputs, multiply them by "weights" (the strength of the connection), and pass them through an activation function.

Herman emphasized that the human brain does not use "backpropagation"—the process by which a network calculates its errors and adjusts its weights. Humans can learn from a single example, whereas a deep neural network requires millions of data points and immense electrical power to achieve the same result. The "artificial brain" is less a biological simulation and more a sophisticated form of statistical regression.

The Birth of a Network: Training and Epochs

To explain how a network actually "learns," the hosts walked through the lifecycle of a model. At the start, a neural network is essentially a "newborn" with randomized weights, capable of seeing only digital static.

The training process involves showing the network data—such as the MNIST dataset of handwritten digits—and letting it guess what it sees. When it guesses incorrectly, a "loss function" measures the error, and an "optimizer" moves backward through the layers to nudge the weights closer to the correct answer.

Herman explained the concept of "epochs," which are full passes through a training dataset. Just as a student might read a textbook multiple times to prepare for an exam, a network requires dozens or hundreds of epochs to refine its understanding. Over time, the network stops seeing random pixels and begins to recognize edges, then shapes, and finally, the abstract concept of a number.

A Diversified Architecture

The episode also touched on the fact that not all neural networks are created equal. Different tasks require different "plumbing" layouts:

  • Convolutional Neural Networks (CNNs): These are the workhorses of computer vision, used in autonomous vehicles to distinguish pedestrians from lampposts by sliding "filters" across images to detect spatial patterns.
  • Graph Neural Networks (GNNs): These are used in drug discovery to model the connections between atoms in a molecule.
  • Transformers: The architecture behind GPT, which uses "attention mechanisms" to look at all parts of a data sequence simultaneously.

The Return of the RNN

Perhaps the most forward-looking part of the discussion involved the evolution of Recurrent Neural Networks (RNNs). For years, RNNs were considered "legacy tech," replaced by the more powerful Transformer models. RNNs process data sequentially (word by word), which often led to a "vanishing gradient problem" where the model would forget the beginning of a long sentence.

However, as we head into 2026, RNNs are making a comeback in the form of "state-space models" and "liquid neural networks." Herman explained that Transformers are incredibly memory-intensive, with compute requirements that grow quadratically as the input gets longer. New architectures like "Mamba" allow for the processing of nearly infinite sequences with much lower overhead. These "liquid" networks are becoming essential for long-term video analysis and real-time robotics, where a continuous "stream of thought" is more efficient than the heavy processing of a Transformer.

Conclusion

The episode concluded with a reminder that while the terminology of AI often sounds like science fiction, the reality is grounded in iterative mathematical refinement. By understanding the "plumbing"—the weights, the layers, and the shifting architectures—we can better appreciate the staggering pace of innovation as we move into 2026. As Herman put it, it’s not about building a brain; it’s about building a better way to process the world’s data.

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Episode #122: Deep Learning Decoded: The Math Behind the Machine

Corn
Hey everyone, welcome back to My Weird Prompts! I am Corn, and I am joined as always by my brother.
Herman
Herman Poppleberry, reporting for duty. It is great to be here.
Corn
We have got a big one today. Our housemate Daniel sent over an audio prompt that really gets back to the basics, but in a way that is actually quite complex once you start pulling the thread. He wants to talk about the fundamental technology of deep learning and deep neural networks.
Herman
I love that he brought this up. We talk so much about what AI can do, you know, writing poems or diagnosing diseases, but we rarely stop to talk about the actual plumbing. And Daniel is right, there is this common misconception that large language models are the only show in town, but the underlying tech, the neural network, is everywhere.
Corn
Exactly. And since it is December twenty-ninth, twenty-twenty-five, we have seen these networks evolve at a breakneck pace over the last year. But before we get to the future, Herman, let us tackle the fundamental question Daniel asked. Do all forms of artificial intelligence use deep neural networks?
Herman
That is a great starting point for some misconception busting. The short answer is a definitive no. AI is a massive umbrella. Think of it like a big city. Deep learning is just one very popular, very powerful neighborhood in that city. Before the deep learning revolution really took off around twenty-twelve, most AI was what we call classical AI or symbolic AI.
Corn
Right, like the stuff that plays chess or handles your GPS routing. Those are algorithms, but they are not necessarily neural networks.
Herman
Precisely. You have got things like expert systems, which are basically just huge sets of if-then rules. If the engine is making a knocking sound and the oil light is on, then check the pressure. That is AI, but it is not a neural network. Then you have things like decision trees or support vector machines. Even the pathfinding in a video game, like when a character finds its way around a wall, that is AI. But it is usually just a search algorithm like A-star. Deep neural networks only come into play when we want the machine to learn features on its own from raw data.
Corn
So, if I am understanding you correctly, the difference is between giving a machine the rules versus giving it the data and letting it find the rules?
Herman
That is exactly it. In classical AI, humans define the features. We tell the computer, look for a round shape and a red color to find an apple. In a deep neural network, we just show it ten thousand pictures of apples and it figures out what an apple looks like through layers of processing.
Corn
Okay, so let us talk about those layers. Daniel mentioned the artificial brain analogy. We call them neurons, we call it a neural network. But Daniel pointed out that our understanding of the actual human brain is still pretty primitive. So, how close is this analogy, really? Is it just a marketing term, or is there some biological truth to it?
Herman
It is a bit of both, but honestly, mostly it is a mathematical approximation. The original inspiration back in the nineteen-forties and fifties was definitely biological. Scientists like Warren McCulloch and Walter Pitts wanted to create a mathematical model of a biological neuron. In your brain, a neuron receives electrical signals through its dendrites. If those signals are strong enough, the neuron fires an impulse down its axon to other neurons.
Corn
And the artificial version tries to mimic that firing threshold?
Herman
Right. In an artificial neural network, we have these nodes. Each node receives numerical inputs. Each input has a weight attached to it, which represents the strength of that connection. The node multiplies the inputs by their weights, adds them all up, and then passes that sum through an activation function. If the sum is high enough, the node passes information to the next layer.
Corn
But this is where the analogy starts to break down, right? Because my brain is not actually doing matrix multiplication every time I decide to eat a sandwich.
Herman
Exactly! And this is a point I am really passionate about. The way these networks learn is through something called backpropagation. When the network makes a mistake during training, we calculate exactly how much each weight contributed to that error and we tweak them. There is no evidence that the human brain does backpropagation. Our brains are much more efficient. We can learn from a single example, whereas a deep neural network might need millions of examples and a small power plant worth of electricity to learn the same thing.
Corn
That is fascinating. So, when we say artificial brain, we are really just talking about a massive, multi-layered calculator that is loosely inspired by the idea of interconnected nodes. It is not a simulation of a brain; it is a mathematical structure that happens to be very good at recognizing patterns.
Herman
Precisely. It is more like a very sophisticated statistical regression than a biological entity. But because it has millions or billions of these connections, it can capture nuances that a simple equation never could.
Corn
You mentioned the history a bit earlier. Daniel wanted to know about the process of pattern recognition, specifically using things like training, epochs, and weights. Can we walk through what actually happens when one of these networks is being born?
Herman
Oh, I would love to. Think of a neural network at the very beginning of its life. All its weights, those connection strengths we talked about, are randomized. It knows absolutely nothing. It is like a newborn that can only see static.
Corn
So, it is essentially guessing.
Herman
It is completely guessing. Let us say we are training it to recognize handwritten digits, the classic MNIST dataset. We show it a picture of a five. The network passes that image through its layers, doing all that math with its random weights, and at the end, it says, I think this is a two.
Corn
And then we tell it, no, you are wrong, that was a five.
Herman
Right. That is the training part. We use a loss function to measure the distance between its guess and the truth. Then we use an optimizer to go backward through the network, layer by layer, adjusting those weights just a tiny bit so that the next time it sees that image, its guess will be a little closer to five.
Corn
And what about the epochs? I always hear people talking about how many epochs they ran their model for.
Herman
An epoch is just one full pass through the entire training dataset. So, if you have sixty thousand images of digits, one epoch means the network has seen all sixty thousand once. Usually, you need many epochs, dozens or hundreds, because the weight adjustments are very small. You do not want to change them too much at once or you will ruin what the network learned from previous images. It is a slow, iterative process of refinement.
Corn
It sounds like a student studying for an exam. They go through the textbook once, that is one epoch. Then they go through it again to catch what they missed.
Herman
That is a great analogy. And the weights are the student's memory. Over time, the network stops seeing random pixels and starts recognizing edges. Then it recognizes loops and lines. By the final layers, it is recognizing the concept of a five.
Corn
This seems like a good spot to take a quick break for our sponsors.

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Herman
...Alright, thanks Larry. I am not even sure how one would hammer something into floorboards without causing a leak, but anyway.
Corn
Yeah, let us stick to the digital neurons for now. So, Herman, we have talked about the basics. But Daniel mentioned that these networks are used for things other than just large language models. Can you give us some examples of deep neural networks in other fields?
Herman
Absolutely. One of the biggest areas is computer vision. If you have a car with autonomous driving features, it is using convolutional neural networks, or CNNs. These are specialized for processing grids of data, like pixels in a camera feed. They are incredibly good at finding the difference between a pedestrian and a lamppost in real-time.
Corn
And those are different from the transformers used in something like GPT?
Herman
They are. While transformers look at the relationships between all parts of a sequence, CNNs use these things called filters that slide across the image to detect local patterns. It is very efficient for spatial data. Then you have things like Graph Neural Networks, which are used in drug discovery. They can model the way atoms are connected in a molecule to predict if a new compound will be effective against a virus.
Corn
That is incredible. So it is the same basic principle of weights and layers, but the architecture is tweaked for the specific type of data it is looking at.
Herman
Exactly. And that brings us to another thing Daniel asked about: Recurrent Neural Networks, or RNNs.
Corn
Right, he asked how they are evolving as we look toward twenty-twenty-six. I remember a few years ago, RNNs were the big thing for anything involving sequences, like translation or speech recognition. But then transformers kind of took over, didn't they?
Herman
They did. Transformers are the reason we have the massive AI boom we are in right now. The problem with traditional RNNs is that they process data one step at a time. If you are reading a sentence, the RNN reads the first word, then the second, then the third. It has a hidden state that acts like a short-term memory, carrying information forward.
Corn
But it has a hard time remembering the beginning of a long sentence by the time it gets to the end, right?
Herman
Precisely. We call that the vanishing gradient problem. The memory just fades away. Transformers solved this with attention mechanisms, allowing the model to look at every word in a sentence simultaneously. But, here is where it gets interesting for twenty-twenty-five and twenty-twenty-six. RNNs are making a comeback in a new form.
Corn
Really? I thought they were basically legacy tech at this point.
Herman
Not quite! There is a new wave of research into things called state space models and liquid neural networks. These are essentially the next generation of RNNs. One major issue with transformers is that they are incredibly memory-intensive. As the input gets longer, the amount of compute you need grows quadratically.
Corn
So, if you want a model to read an entire library, a transformer might just choke on the sheer volume of data.
Herman
Exactly. But these new recurrent architectures, like Mamba or various liquid networks, can process sequences of almost infinite length with much lower memory requirements. They are much more like a continuous stream of thought. In twenty-twenty-five, we have started seeing these being used for long-term video analysis and real-time robotics, where you cannot afford the heavy overhead of a massive transformer.
Corn
That is a classic tech cycle, isn't it? An old idea gets refined with new math and suddenly it is the cutting edge again.
Herman
It really is. And the liquid neural networks are particularly cool because their parameters can change over time even after training. They can adapt to new environments on the fly. We are seeing a lot of excitement about how these will be integrated into the next generation of autonomous systems in twenty-twenty-six.
Corn
So, looking at the big picture Daniel painted, we have gone from simple rules to these massive, multi-layered patterns. We are using them for vision, for medicine, for language. But I want to go back to Daniel's point about human cognition. He mentioned that when he walks down the street, his brain isn't just saying, this reminds me of walking.
Herman
Right. He is talking about the difference between pattern recognition and actual understanding or reasoning.
Corn
Exactly. If a deep neural network is just a glorified pattern recognizer, are we ever going to reach a point where it actually thinks? Or are we just building bigger and bigger mirrors of our own data?
Herman
This is the billion-dollar question. Some researchers argue that if you recognize enough patterns and the relationships between them, reasoning emerges naturally. It is called the emergent properties hypothesis. If a model understands the pattern of how logic works, is it actually being logical?
Corn
But others would say it is just a stochastic parrot, just repeating what it has seen in a very complex way.
Herman
Right. And I think the truth is somewhere in the middle, especially as of late twenty-twenty-five. We are seeing models that can perform complex multi-step reasoning, but they still fail at basic common sense in ways a human never would. A human brain has things these networks don't, like a world model, a sense of physics, and most importantly, an internal drive or agency.
Corn
We don't have to train a human with ten million pictures of a hot stove for them to know not to touch it.
Herman
Exactly! We have this innate ability to generalize from very few examples because we have a context of what it means to be an entity in a physical world. Deep neural networks, even the most advanced ones we are seeing heading into twenty-twenty-six, are still essentially trapped in a box of data. They don't have a body, they don't have feelings, and they don't have a biological survival instinct.
Corn
So, the analogy of the artificial brain is useful for understanding the structure, but it is a dangerous one if we use it to assume the AI has a human-like mind.
Herman
I think that is a perfect way to put it. It is a tool that mimics some functions of the brain, but it is not a brain. It is like an airplane. An airplane is inspired by a bird, it has wings and it flies, but an airplane does not flap its wings, it does not build a nest, and it does not have feathers. It is a different way of achieving the same goal: flight.
Corn
That is a great analogy. So, what are the practical takeaways for someone like Daniel or our listeners who are trying to keep up with this?
Herman
First, realize that when you hear deep learning, it just means a neural network with a lot of layers. The deep part isn't mystical; it just means there is more math between the input and the output. Second, know that while LLMs are the stars right now, the underlying tech is what is running your face ID, your Netflix recommendations, and the medical imaging that might save your life.
Corn
And third, keep an eye on those new recurrent models. The transformer might not be the king forever, especially as we try to make AI more efficient and capable of handling longer and longer streams of information.
Herman
Definitely. Twenty-twenty-six is likely going to be the year of efficiency. We have proven we can make models big; now we have to make them smart and lean.
Corn
Well, this has been a deep dive, no pun intended. I feel like I have a much better handle on the actual mechanics of these things now. It is not just magic; it is millions of tiny adjustments to millions of tiny numbers.
Herman
It is the most complex construction project in human history, and we are building it out of math instead of bricks.
Corn
I love that. Thanks to Daniel for the prompt. It is always good to get back to the basics, especially when the basics are this fascinating.
Herman
Absolutely. It was a pleasure.
Corn
If you want to get in touch with us or send in your own prompt, you can find the contact form at myweirdprompts.com. We are also on Spotify, so make sure to follow us there for all the latest episodes.
Herman
And don't forget to check under your floorboards for any loose static. Larry's grounding rod might be calling your name.
Corn
Please do not hammer copper pipes into your floorboards. This has been My Weird Prompts. We will see you next time!
Herman
Goodbye everyone!

This episode was generated with AI assistance. Hosts Herman and Corn are AI personalities.

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