How AI Finds the Right Answer: The Magical Universality of 'Gradient Descent'

Imagine you are trying to find treasure on a mountain peak in pitch-black darkness. You don’t know where the summit is, but by the slope you feel with your feet, you can at least tell whether you are standing on an uphill or downhill slope. So, you examine the terrain under your feet every step of the way, avoiding downhill and walking along the uphill. Eventually, you will reach the summit. The process by which artificial intelligence learns data is surprisingly similar to this.

The artificial intelligence we use today, like ChatGPT, shows incredible performance by learning from vast amounts of data. So, what magic does this smart AI use to efficiently find the answers to complex problems? One of the key secrets is a mathematical optimization method called “Gradient Descent.”

Why It Matters

Gradient descent is not just an academic concept. It is used as the core engine for learning in almost all modern artificial intelligence application fields, including image recognition, reinforcement learning, and machine translation Ref 2, Ref 3.

For general readers, it is important to “understand how AI learns.” Knowing that the process by which AI finds answers is built on a solid mathematical foundation allows us to have more confidence in the results produced by AI. Furthermore, as this technology develops more efficiently, we will be able to experience changes such as lower operating costs for AI services, or AI becoming faster and more deeply integrated into our daily lives.

The Explainer

Let’s use an analogy. Suppose AI is a “student learning something.” This student doesn’t memorize answer keys; instead, they revise their knowledge bit by bit every time they solve a problem, reflecting on why they got it wrong.

1. Backpropagation: When a student gets a question wrong, this is the process of tracing back to check where the mistake occurred.
2. Gradient Descent: Once the mistake is identified, they modify their thinking (parameters) little by little in a direction that reduces the mistake Ref 16.

In simple terms, gradient descent is an optimization process of taking steps in a direction that reduces error Ref 2. As learning continues, the AI gets closer to the correct answer (the minimum value of the loss function).

There is a truly surprising research result here: “Universality.” Researchers have discovered that “if any algorithm can find a good answer (weights) through data, an appropriately expanded form of an artificial intelligence model can find the exact same answer using only gradient descent” Ref 2, Ref 8.

In other words, in AI learning, gradient descent is like a “universal tool” that can do almost anything. The fact that no matter how complex or sophisticated the method used to find an answer, gradient descent can eventually reach the same result, means that the versatility of AI learning is much more powerful than we thought.

Where We Stand

Most AI systems around us currently use this gradient descent as a base Ref 10. However, when training AI in reality, not only is basic gradient descent used, but advanced optimization techniques adapted to the situation are also used together to increase efficiency Ref 10, Ref 14.

Although gradient descent is very powerful, there are still challenges to solve. The functions that serve as the targets for AI learning are often very tangled (non-convex), and in the worst case, learning itself can be extremely difficult Ref 3. Nevertheless, by processing vast amounts of real-world data, we are proving that this method is practically very successful.

What’s Next

Future AI learning will move in the direction of utilizing gradient descent even smarter. As the size of models increases, the number of parameters to be calculated also grows to the trillions Ref 16. Researchers are studying faster and smarter optimization algorithms to drastically reduce the time and resources generated in this process.

Before long, we will encounter much more efficient artificial intelligence models that learn vast amounts of knowledge with less power. It will be very interesting to watch how the deep-rooted tree called gradient descent sprouts even more lush leaves (performance).

MindTickleBytes AI Reporter’s View

Research on the universality of gradient descent provides a mathematical answer to “why AI is bound to work well,” going beyond the simple fact that “AI works well.” This is an important milestone showing that technology has firmly established itself in the realm of science, moving beyond empirical magic. The fact that the AI services we use are undergoing meticulous and sophisticated mathematical optimization processes internally, as much as they appear flamboyant on the outside, gives those of us living in the age of artificial intelligence another form of reassurance.

References

1. Universality of gradient descent neural network training https://arxiv.org/abs/2007.13664
2. Universality of Gradient Descent Neural Network Training (PDF) https://arxiv.org/pdf/2007.13664v1
3. Universality of Gradient Descent Neural Network Training (Bytez) https://bytez.com/docs/arxiv/2007.13664/paper
4. Universality of Gradient Descent Neural Network Training (Arxiv.gg) https://arxiv.gg/abs/2007.13664
5. Unified convergence analysis for gradient descent https://arxiv.org/pdf/2607.04233
6. Stochastic Gradient Descent: Mini-Batches, LR Schedules https://mbrenndoerfer.com/writing/stochastic-gradient-descent-neural-network-optimization
7. How Neural Networks Power AI Systems in 2025 https://hiperform.eu/uncategorized/what-is-a-neural-network-and-why-it-matters-in-ai/