Artificial Intelligence Theory and Application

Comparison of latent space in transformers versus noise in diffusion models: Latent Space in Transformers Nature : Learned, structured representations that encode meaningful semantic and syntactic information. Each position in the latent space corresponds to specific features, relationships, or concepts extracted from the input data. Purpose : Serves as an information-rich intermediate representation that captures context, relationships, and patterns. It's where the model performs its core reasoning and computation through attention mechanisms. Characteristics : Deterministic given the same input Preserves and transforms information from the input High-dimensional vectors contain interpretable features Built through learned weights during training Maintains semantic continuity (similar inputs → similar representations) Noise in Diffusion Models Nature : Random Gaussian noise that progressively corrupts or generates data. It represents the starting point (pure randomnes...

  Quiz: Can mathematics solve complex, high-dimensional problems (those involving hundreds or thousands of parameters)? A) Yes, mathematics can easily handle all such problems B) No, not without significant computational time and resources, and some problems may not have solutions C) Only problems with three or fewer dimensions When a perfect solution with zero error is unattainable, what approach should be taken? A) Abandon the problem B) Seek an approximate solution that minimizes error C) Keep trying until zero error is achieved What is the conventional method for measuring the difference between actual and calculated values? A) Simple subtraction B) Mean Squared Error (MSE) or Sum of Squared Errors C) Just guessing the difference If an error function is visualized as a 3D landscape with mountains and valleys, which region represents the optimal solution? A) The highest peak B) The lowest valley (global minimum) C) The flattest area How can we ...

  Gradient Descent: The Algorithm Behind Machine Learning Gradient descent is an optimization algorithm that finds the minimum of a function by iteratively moving in the direction of steepest descent. Think of it as a hiker trying to reach the bottom of a valley in thick fog—they can't see the entire landscape, but they can feel the slope beneath their feet and consistently step downhill. Keep this two images [specifically Neural Networks - but applies to non NN models also] in mind, so we know what we are up to. (Source: https://www.geeksforgeeks.org/deep-learning/the-role-of-weights-and-bias-in-neural-networks/) IGNORE https://github.com/lilipads/gradient_descent_viz   (visualizations)  Differential Calculus 1. d/dx or derivative of a function is what? [SLOPE] 2. Integration or Integral of a function is what? [Area Under that part of the Curve] How Differentials Find the Slope Differentials (derivatives) are mathematical tools that tell us the instantaneous...