ML
Machine learning notes across foundations, computer vision, transformers, optimization, and more.
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QC
Quantum computing notes across qubits, gates, algorithms, and practical intuition.
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00 Complex Numbers
Complex numbers, and more generally higher-dimensional numbers like quaternions and octonions, are fascinating mathematical constructs that help us describe and understand multidimensional spaces and phenomena.
Open note →01 Cloud Deploy
Fine-tuning Flan-T5-XXL on AWS SageMaker can be quite expensive due to the model’s size and computational requirements. The cost depends on several factors, including: Instance Type: You’ll likely need a...
Open note →01 Observables
In quantum mechanics, an observable is a physical quantity that can be measured—such as position, momentum, or energy. Mathematically, an observable is represented by a Hermitian (self-adjoint) operator acting on...
Open note →02 Eigenstate
An eigenstate is a state that satisfies the equation
Open note →03 Hilbert Space
A Hilbert space is a complete vector space equipped with an inner product. It provides the mathematical setting for quantum mechanics, where states, observables, and dynamics are all formulated. Let’s...
Open note →04 Born Rule
The Born rule is a foundational principle in quantum mechanics that connects the abstract mathematical description of a quantum state with the probabilities of observable outcomes. Here’s a detailed explanation:...
Open note →05 Superposition
In quantum mechanics, a qubit is not simply a bit that is either 0 or 1. Instead, it exists in a superposition of both states. Its state is typically written...
Open note →06 Euler Formula
1. The Role of Euler’s Formula in Representing Complex Numbers
Open note →07 Angles and Phases
Let’s break it down:
Open note →08 Bloch Sphere
The state of a qubit is much more than a simple bit—it’s a quantum state that can exist as a superposition of two basis states. Geometrically, we represent a pure...
Open note →09 Unitary
In quantum computing, unitary transformations are indispensable because they ensure that the fundamental postulates of quantum mechanics—especially the preservation of probability—remain valid during the evolution of quantum states. Let’s explore...
Open note →10 Interference
Let’s break down quantum interference in a way that connects the math to physical intuition. In quantum mechanics, rather than directly adding probabilities (as in classical systems), we add complex...
Open note →Attention
prompt - can you please explain below excerpt in details in the context of attention, encoder-decoder architechture, "To understand the flow in more details,let us consider the French translation example...
Open note →Encoder-Decoder Architecture
Encoder: The encoder processes the input sequence (e.g., a sentence) one timestep at a time. At each timestep, it produces a hidden state (hidden variable) that captures information about the...
Open note →Grover's Algorithm Overview
Grover’s algorithm gives a quadratic speedup for unstructured search.
Open note →NeRF
Let’s take a detailed journey into Neural Radiance Fields (NeRF)—both at the conceptual and mathematical level. NeRF was introduced as a way to represent a 3D scene continuously using a...
Open note →Residual Blocks
Residual blocks
Open note →Score Distillation Sampling
Let’s dive deep into Score Distillation Sampling (SDS), a key technique introduced (for example, in DreamFusion) to distill the rich, text-conditioned knowledge of a pre-trained diffusion model into another model—in...
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