Compute

/ˈprɪn.sə.pəl kəˈpoʊ.nənt əˈnæl.ə.sɪs/

noun … “a way to rotate data until its most important structure faces you.”

Principal Component Analysis is a statistical technique used to reduce the dimensionality of data while preserving as much meaningful variation as possible. It transforms a dataset with many correlated variables into a smaller set of new variables, called components, that are uncorrelated and ordered by how much variance they explain. The goal is not compression for its own sake, but clarity: fewer dimensions, less noise, and a structure that is easier to analyze, visualize, and model.

The key idea behind Principal Component Analysis is variance. In most real-world datasets, not all dimensions contribute equally to the underlying structure. Some directions in the data space carry strong signals, while others mostly encode redundancy or noise. PCA identifies the directions along which the data varies the most and re-expresses the data in terms of those directions. These directions are orthogonal, meaning they are mathematically independent, and each successive component explains less variance than the one before it.

Mathematically, Principal Component Analysis is grounded in linear algebra. It relies on concepts such as eigenvectors and eigenvalues of a covariance matrix. The covariance matrix captures how variables change together, and its eigenvectors define the axes of maximal variance. Eigenvalues quantify how much variance each axis explains. This is why PCA is often introduced alongside Linear Algebra, Covariance Matrix, Eigenvector, Eigenvalue, and Dimensionality Reduction, all of which form its conceptual backbone.

In practical workflows, Principal Component Analysis is commonly applied as a preprocessing step. High-dimensional data can overwhelm models, slow computation, and obscure patterns. By projecting data onto the first few principal components, analysts can often retain most of the informative structure while discarding minor variations. This is especially useful before applying methods such as clustering or classification, where distance and geometry matter.

Visualization is one of the most intuitive uses of Principal Component Analysis. Data with dozens or hundreds of variables can be projected into two or three components and plotted, revealing clusters, gradients, or outliers that were invisible in the original space. These plots do not show the full data, but they often show the most important relationships, which makes PCA a powerful exploratory tool.

It is important to understand what Principal Component Analysis does not do. It does not discover causal relationships, and it does not know which variables are meaningful in a domain-specific sense. PCA is purely statistical and unsupervised. It optimizes for variance, not relevance. A component that explains a large amount of variance may still be unimportant for a specific task, while a low-variance direction could contain critical information. This limitation is why PCA is often paired with domain knowledge or downstream evaluation.

Example conceptual workflow of Principal Component Analysis:

start with a dataset containing many variables
center the data by subtracting the mean
compute the covariance matrix
find eigenvectors and eigenvalues
sort components by explained variance
project data onto the top components

Principal Component Analysis also plays a supporting role in broader analytical and modeling contexts. It is frequently used alongside Machine Learning to stabilize training, reduce overfitting, and improve computational efficiency. In signal processing, it helps separate structure from noise. In scientific research, it offers a way to summarize complex measurements without discarding their essential shape.

Conceptually, Principal Component Analysis is best thought of as a change in perspective. Instead of describing data in terms of the variables you happened to measure, it describes the data in terms of how it actually varies. Like rotating an object under a light, the structure was always there, but PCA finds the angle where the shape becomes obvious.

/məˈʃiːn ˌlɜːrnɪŋ/

noun … “teaching machines to improve by experience instead of explicit instruction.”

Machine Learning is a branch of computer science focused on building systems that can learn patterns from data and improve their performance over time without being explicitly programmed for every rule or scenario. Rather than encoding fixed logic, a machine learning system adjusts internal parameters based on observed examples, feedback, or outcomes, allowing it to generalize beyond the data it has already seen.

The defining idea behind Machine Learning is adaptation. A model is exposed to data, evaluates how well its predictions match reality, and then updates itself to reduce error. This process is typically framed as optimization, where the system searches for parameter values that minimize some measurable loss. Over many iterations, the model converges toward behavior that is useful, predictive, or discriminative, depending on the task.

Several learning paradigms dominate practical use. In supervised learning, models learn from labeled examples, such as images tagged with categories or records paired with known outcomes. Unsupervised learning focuses on discovering structure in unlabeled data, identifying clusters, correlations, or latent representations. Reinforcement learning introduces feedback in the form of rewards and penalties, enabling agents to learn strategies through interaction with an environment rather than static datasets.

Modern Machine Learning relies heavily on mathematical foundations such as linear algebra, probability theory, and optimization. Concepts like gradients, vectors, and distributions are not implementation details but core building blocks. This is why the field naturally intersects with Neural Network design, Linear Regression, Gradient Descent, Decision Tree models, and Support Vector Machine techniques, each offering different tradeoffs between interpretability, expressiveness, and computational cost.

Data representation plays a critical role. Raw inputs are often transformed into features that expose meaningful structure to the learning algorithm. In image analysis, this might involve pixel intensities or learned embeddings. In language tasks, text is converted into numerical representations that capture semantic relationships. The quality of these representations often matters as much as the learning algorithm itself.

Evaluation is another essential component. A model that performs perfectly on its training data may still fail catastrophically on new inputs, a phenomenon known as overfitting. To guard against this, datasets are typically split into training, validation, and test sets, ensuring that performance metrics reflect genuine generalization rather than memorization. Accuracy, precision, recall, and loss values are used to quantify success, each highlighting different aspects of model behavior.

While Machine Learning is frequently associated with automation and prediction, its broader value lies in pattern discovery. Models can surface relationships that are difficult or impossible to specify manually, revealing structure hidden in large, complex datasets. This makes the field central to applications such as recommendation systems, anomaly detection, speech recognition, medical diagnosis, and scientific modeling.

Example workflow of a basic machine learning process:

collect data
clean and normalize inputs
split data into training and test sets
train a model by minimizing error
evaluate performance on unseen data
deploy and monitor the model

Despite its power, Machine Learning is not magic. Models inherit biases from their data, assumptions from their design, and limitations from their training regime. They do not understand context or meaning in a human sense; they optimize mathematical objectives. Responsible use requires careful validation, transparency, and an awareness of where statistical inference ends and human judgment must begin.

A useful way to think about Machine Learning is as a mirror held up to data. What it reflects depends entirely on what it is shown, how it is allowed to learn, and how its results are interpreted. When used well, it amplifies insight. When used carelessly, it amplifies noise.

/əˈweɪt/

verb … “to pause execution until an asynchronous operation produces a result.”

await is a language-level operator used in asynchronous programming to suspend the execution of a function until a related asynchronous operation completes. It works by waiting for a Promise to settle, then resuming execution with either the resolved value or a thrown error. The defining feature of await is that it allows asynchronous code to be written in a linear, readable style without blocking the underlying event loop or execution environment.

Technically, await can only be used inside a function declared as async. When execution reaches an await expression, the current function is paused and control is returned to the runtime. Other tasks, events, or asynchronous operations continue running normally. Once the awaited Promise resolves or rejects, the function resumes execution from the same point, either yielding the resolved value or propagating the error as an exception.

This behavior is crucial for non-blocking systems. Unlike traditional blocking waits, await does not freeze the process or thread. In environments such as browsers and Node.js, this means the event loop remains free to handle user input, timers, network events, or other callbacks. As a result, await delivers the illusion of synchronous execution while preserving the performance and responsiveness of asynchronous systems.

await is deeply integrated with common communication and I/O patterns. Network requests performed through Fetch-API are typically awaited so that response data can be processed only after it arrives. Message-based workflows often await the completion of send operations or the arrival of data from receive operations. In reliable systems, an awaited operation may implicitly depend on an acknowledgment that confirms successful delivery or processing.

One of the major advantages of await is structured error handling. If the awaited Promise rejects, the error is thrown at the point of the await expression. This allows developers to use familiar try–catch logic instead of scattering error callbacks throughout the codebase. Asynchronous control flow becomes easier to reason about, debug, and maintain, especially in complex workflows involving multiple dependent steps.

await also supports composability. Multiple awaited operations can be performed sequentially when order matters, or grouped together when parallel execution is acceptable. This flexibility makes await suitable for everything from simple API calls to large-scale orchestration of distributed systems and services.

In practical use, await appears throughout modern application code: loading data before rendering a user interface, waiting for file operations to complete, coordinating background jobs, or synchronizing client–server interactions. It has become a standard tool for writing clear, maintainable asynchronous logic without sacrificing performance.

Example usage of await:

async function loadData() {
  const response = await fetch('/api/data');
  const result = await response.json();
  return result;
}

loadData().then(data => {
  console.log(data);
});

The intuition anchor is that await behaves like placing a bookmark in your work. You step away while something else happens, and when the result is ready, you return to exactly the same spot and continue as if no interruption occurred.

/ˈprɒmɪs/

noun … “a construct that represents the eventual completion or failure of an asynchronous operation.”

Promise is a foundational abstraction in modern programming that models a value which may not be available yet but will be resolved at some point in the future. Instead of blocking execution while waiting for an operation to complete, a Promise allows a program to continue running while registering explicit logic for what should happen once the result is ready. This approach is central to asynchronous systems, where latency from input/output, networking, or timers must be handled without freezing the main execution flow.

Conceptually, a Promise exists in one of three well-defined states. It begins in a pending state, meaning the operation has started but has not yet completed. It then transitions to either a fulfilled state, where a resulting value is available, or a rejected state, where an error or failure reason is produced. Once a Promise leaves the pending state, it becomes immutable: its outcome is fixed and cannot change. This immutability is critical for reasoning about correctness in concurrent and asynchronous systems.

From a technical perspective, a Promise provides a standardized way to attach continuation logic. Instead of nesting callbacks, developers attach handlers that describe what should occur after fulfillment or rejection. This structure eliminates deeply nested control flow and makes error propagation explicit and predictable. In environments such as browsers and Node.js, Promise is a first-class primitive used by core APIs, including timers, file systems, and networking layers.

Promise integrates tightly with the async programming model. The async and await syntax is effectively syntactic sugar built on top of Promise, allowing asynchronous code to be written in a style that resembles synchronous execution while preserving non-blocking behavior. Under the surface, await pauses execution of the current function until the associated Promise settles, without blocking the event loop or other tasks.

In real systems, Promise frequently appears alongside communication primitives. Network operations performed through Fetch-API return promises that resolve to response objects. Message-based workflows often coordinate send and receive steps using promises to represent delivery or processing completion. Reliable systems may also combine promises with acknowledgment signals to ensure that asynchronous work has completed successfully before moving forward.

One of the most important properties of a Promise is composability. Multiple promises can be chained so that the output of one becomes the input of the next, forming a deterministic sequence of asynchronous steps. Promises can also be grouped, allowing a program to wait for several independent operations to complete before continuing. This capability is essential in data pipelines, API aggregation, parallel computation, and user interface rendering where multiple resources must be coordinated.

Error handling is another defining feature of Promise. Rejections propagate through chains until they are explicitly handled, preventing silent failures. This behavior mirrors exception handling in synchronous code, but in a form that works across asynchronous boundaries. As a result, programs built around Promise tend to be more robust and easier to reason about than those using ad-hoc callbacks.

In practical use, Promise underpins web applications, backend services, command-line tools, and distributed systems. It enables efficient concurrency without threads, supports responsive user interfaces, and allows complex workflows to be expressed declaratively. Its semantics are consistent across platforms, making it a unifying abstraction for asynchronous logic.

Example usage of a Promise:

function delayedValue() {
  return new Promise((resolve, reject) => {
    setTimeout(() => {
      resolve(42);
    }, 1000);
  });
}

delayedValue().then(value => {
  console.log(value);
});

The intuition anchor is that a Promise is like a claim ticket at a repair shop. You do not wait at the counter while the work is done. You receive a ticket that guarantees you can come back later, either to collect the finished item or to be told clearly that something went wrong.

/ˈeɪ.sɪŋk/

adjective … “executing operations independently of the main program flow, allowing non-blocking behavior.”

async, short for asynchronous, refers to a programming paradigm where tasks are executed independently of the main execution thread, enabling programs to handle operations like I/O, network requests, or timers without pausing overall execution. This approach allows applications to remain responsive, efficiently manage resources, and perform multiple operations concurrently, even if some tasks take longer to complete.

In practice, async is implemented using constructs such as callbacks, promises, futures, or the async/await syntax in modern languages like JavaScript, Python, or C#. Asynchronous tasks are typically executed in the background, and their results are handled when available, allowing the main thread to continue processing other operations without waiting. This contrasts with synchronous execution, where each task must complete before the next begins.

async integrates naturally with other programming concepts and systems. It is often paired with send and receive operations in networking to perform non-blocking communication, works with Promise-based workflows for chaining dependent tasks, and complements event-driven architectures such as those in Node.js or browser environments.

In practical workflows, async is widely used for web applications fetching data from APIs, real-time messaging systems using WebSocket, file system operations in high-performance scripts, and distributed systems where tasks must be coordinated without blocking resources. It improves efficiency, reduces idle CPU cycles, and enhances user experience in interactive applications.

An example of an async function in Python:

import asyncio

async def fetch_data():
print("Start fetching")
await asyncio.sleep(2)  # simulate network delay
print("Data fetched")
return {"data": 123}

async def main():
result = await fetch_data()
print(result)

asyncio.run(main()) 

The intuition anchor is that async acts like a “background assistant”: it allows tasks to proceed independently while the main program keeps moving, ensuring efficient use of time and resources without unnecessary waiting.

/ˌoʊ.ɛnˈɛks ˈrʌnˌtaɪm/

noun … “a high-performance engine for executing machine learning models in the ONNX format.”

ONNX-Runtime is a cross-platform, open-source inference engine designed to execute models serialized in the ONNX format efficiently across diverse hardware, including CPUs, GPUs, and specialized accelerators. By decoupling model training frameworks from deployment, ONNX-Runtime enables developers to optimize inference workflows for speed, memory efficiency, and compatibility without modifying the original trained model.

The engine operates by interpreting the ONNX computation graph, which contains nodes (operations), edges (tensors), and metadata specifying data types and shapes. ONNX-Runtime applies graph optimizations such as operator fusion, constant folding, and layout transformations to reduce execution time. Its modular architecture supports execution providers for hardware acceleration, including NVIDIA CUDA, AMD ROCm, Intel MKL-DNN, and OpenVINO, allowing seamless scaling from desktops to cloud or edge devices.

ONNX-Runtime integrates naturally with AI ecosystems. For instance, a Transformer model trained in PyTorch can be exported to ONNX and executed on ONNX-Runtime for high-throughput inference. Similarly, CNN-based vision models, GPT text generators, and VAE generative networks benefit from accelerated execution without framework-specific dependencies.

Key features of ONNX-Runtime include support for multiple programming languages (Python, C++, C#, Java), dynamic shape inference, graph optimization passes, and model version compatibility. These capabilities make it suitable for deployment in cloud services, mobile devices, and embedded systems, ensuring deterministic and reproducible results across heterogeneous environments.

An example of using ONNX-Runtime in Python:

import onnxruntime as ort
import numpy as np

session = ort.InferenceSession("resnet18.onnx")
input_name = session.get_inputs()[0].name
dummy_input = np.random.randn(1, 3, 224, 224).astype(np.float32)
outputs = session.run(None, {input_name: dummy_input})
print(outputs[0].shape)  # outputs predicted tensor 

The intuition anchor is that ONNX-Runtime acts like a universal “engine room” for AI models: it reads the standardized instructions in ONNX, optimizes computation, and executes efficiently on any compatible hardware, letting models perform at scale without worrying about framework lock-in or platform-specific constraints.

/ˌoʊ.ɛnˈɛks/

noun … “an open format for representing and interoperating machine learning models.”

ONNX, short for Open Neural Network Exchange, is a standardized, open-source format designed to facilitate the exchange of machine learning models across different frameworks and platforms. Instead of tying a model to a specific ecosystem, ONNX provides a common representation that allows models trained in one framework, such as PyTorch or TensorFlow, to be exported and deployed in another, like Caffe2, MXNet, or Julia’s Flux ecosystem, without requiring complete retraining or manual conversion.

The ONNX format encodes models as a computation graph, detailing nodes (operations), edges (tensors), data types, and shapes. It supports operators for a wide range of machine learning tasks, including linear algebra, convolution, activation functions, and attention mechanisms. Models serialized in ONNX can be optimized and executed efficiently across CPUs, GPUs, and other accelerators, leveraging frameworks’ backend runtimes while maintaining accuracy and consistency.

ONNX enhances interoperability and production deployment. For example, a Transformer model trained in PyTorch can be exported to ONNX and then deployed on a high-performance inference engine like ONNX Runtime, which optimizes execution for various hardware targets. This reduces friction in moving models from research to production, supporting tasks like natural language processing, computer vision with CNN-based architectures, and generative modeling with GPT or VAE networks.

ONNX is closely associated with related technologies like ONNX Runtime, a high-performance engine for model execution, and converter tools that translate between framework-specific model formats and the ONNX standard. This ecosystem enables flexible workflows, such as fine-tuning a model in one framework, exporting it to ONNX for deployment on different hardware, and integrating it with other AI pipelines.

An example of exporting a model to ONNX in Python:

import torch
import torchvision.models as models

model = models.resnet18(pretrained=True)
dummy_input = torch.randn(1, 3, 224, 224)
torch.onnx.export(model, dummy_input, "resnet18.onnx") 

The intuition anchor is that ONNX acts as a universal “model passport”: it lets machine learning models travel seamlessly between frameworks, hardware, and platforms while retaining their learned knowledge and computational integrity, making AI development more flexible and interoperable.

/ˌviː.eɪˈiː/

noun … “a probabilistic neural network that learns latent representations for generative modeling.”

VAE, or Variational Autoencoder, is a type of generative neural network that extends the concept of Autoencoder by introducing probabilistic latent variables. Instead of encoding an input into a fixed deterministic vector, a VAE maps inputs to a distribution in a latent space, typically Gaussian, allowing the model to generate new data points by sampling from this distribution. This probabilistic approach enables both reconstruction of existing data and generation of novel, realistic samples, making VAE a powerful tool in unsupervised learning and generative modeling.

The architecture of a VAE consists of an encoder, a latent space parameterization, and a decoder. The encoder predicts the mean and variance of the latent distribution, the latent vector is sampled using the reparameterization trick to maintain differentiability, and the decoder reconstructs the input from the sampled latent point. Training minimizes a combination of reconstruction loss and a regularization term (the Kullback-Leibler divergence) that ensures the latent space approximates the prior distribution, typically a standard normal distribution.

VAE is widely used in image generation, anomaly detection, data compression, and semi-supervised learning. For images, convolutional layers from CNN are often incorporated to extract hierarchical spatial features, while in sequential data tasks, recurrent layers like RNN can process temporal dependencies. The probabilistic nature allows smooth interpolation between data points, latent space arithmetic, and controlled generation of new samples.

Conceptually, VAE is closely related to Autoencoder, Transformer-based generative models, and probabilistic graphical models. Its innovation lies in combining representation learning with a generative probabilistic framework, allowing latent embeddings to encode both structural and statistical characteristics of the data.

An example of a VAE in Julia using Flux:

using Flux

encoder = Chain(Dense(784, 400, relu), Dense(400, 20*2))  # outputs mean and log-variance
decoder = Chain(Dense(10, 400, relu), Dense(400, 784, sigmoid))
vae = Chain(encoder, decoder)

x = rand(Float32, 784, 1)
z_mean, z_logvar = encoder(x)
epsilon = randn(Float32, size(z_mean))
z = z_mean .+ exp.(0.5 .* z_logvar) .* epsilon  # reparameterization
x_recon = decoder(z) 

The intuition anchor is that a VAE is a “creative autoencoder”: it not only compresses data into a meaningful latent space but also treats this space probabilistically, enabling it to imagine, generate, and interpolate new data points in a coherent way, bridging the gap between data compression and generative modeling.

/ˌdʒiːˌpiːˈtiː/

noun … “a generative language model that predicts and produces coherent text.”

GPT, short for Generative Pre-trained Transformer, is a deep learning model designed to understand and generate human-like text by leveraging the Transformer architecture. Unlike traditional rule-based systems, GPT learns statistical patterns and contextual relationships from massive corpora of text during a pretraining phase. It uses self-attention mechanisms to capture dependencies across words, sentences, or even longer passages, enabling the generation of coherent, contextually appropriate responses in natural language.

The architecture of GPT is based on stacked Transformer decoder blocks. Each block consists of masked self-attention layers and feed-forward networks, allowing the model to predict the next token in a sequence autoregressively. Pretraining involves unsupervised learning over billions of tokens, followed by optional fine-tuning on specific tasks, such as summarization, translation, or question answering. This two-phase approach ensures that GPT develops both a broad understanding of language and specialized capabilities when needed.

GPT is closely related to other Transformer-based models such as BERT for bidirectional contextual understanding, Transformer for sequence modeling, and CNN-augmented architectures for multimodal data. Its design emphasizes scalability, with larger models achieving better fluency, coherence, and reasoning capabilities, while relying on high-performance hardware like GPUs or TPUs to perform massive matrix multiplications efficiently.

Practical applications of GPT include chatbots, content generation, code completion, educational tools, and knowledge retrieval. It can perform zero-shot, few-shot, or fine-tuned tasks, making it flexible across domains. Its generative capability allows it to create human-like prose, compose emails, draft technical documentation, or answer queries by predicting the most likely sequence of words based on context.

An example of GPT usage in practice with a simplified API call might look like this:

using OpenAI

prompt = "Explain quantum computing in simple terms."
response = GPT.generate(prompt)
println(response)  # outputs coherent, human-readable explanation 

The intuition anchor is that GPT acts as a “predictive language engine”: it observes patterns in text and produces the next word, sentence, or paragraph in a way that mimics human writing. Like an infinitely patient and context-aware apprentice, it transforms input prompts into fluent, meaningful outputs while maintaining the statistical essence of language learned from massive datasets.

/ˈɔːtoʊˌɛnˌkoʊdər/

noun … “a neural network that learns efficient data representations by reconstruction.”

Autoencoder is a type of unsupervised neural network designed to compress input data into a lower-dimensional latent representation and then reconstruct the original input from this compressed encoding. The network consists of two primary components: an encoder, which maps the input to a latent space, and a decoder, which maps the latent representation back to the input space. The goal is to minimize the difference between the original input and its reconstruction, forcing the network to capture the most salient features of the data.

This architecture is widely used for dimensionality reduction, feature extraction, denoising, anomaly detection, and generative modeling. By learning compact representations, Autoencoder can reduce storage requirements or computational complexity for downstream tasks such as classification, clustering, or visualization. Its effectiveness relies on the network’s capacity and the structure of the latent space to encode meaningful patterns while discarding redundant or noisy information.

Autoencoder interacts naturally with other neural network concepts. For example, convolutional layers from CNN can be integrated into the encoder and decoder to process image data efficiently, while recurrent structures like RNN can handle sequential inputs such as time series or text. Variants such as Variational Autoencoders (VAEs) introduce probabilistic latent variables, enabling generative modeling of complex distributions, while denoising autoencoders explicitly learn to remove noise from corrupted inputs.

Training an Autoencoder involves optimizing a reconstruction loss function, such as mean squared error for continuous data or cross-entropy for categorical data, typically using gradient-based methods on GPUs or other parallel hardware. Its latent space representations can then be used for downstream supervised or unsupervised tasks, enabling models to learn from unlabelled data efficiently.

In practice, Autoencoder is employed in image compression, where high-dimensional images are encoded into compact vectors; anomaly detection, where reconstruction error signals deviations from normal patterns; and pretraining for complex deep networks, where latent representations initialize subsequent supervised models. Integration with attention-based models like Transformers and probabilistic frameworks further expands their applicability to modern AI pipelines.

An example of an Autoencoder in Julia using Flux:

using Flux

encoder = Chain(Dense(784, 128, relu), Dense(128, 64, relu))
decoder = Chain(Dense(64, 128, relu), Dense(128, 784, sigmoid))
autoencoder = Chain(encoder, decoder)

x = rand(Float32, 784, 1)
y_pred = autoencoder(x)  # reconstruction of input 

The intuition anchor is that an Autoencoder acts like a “smart compressor and decompressor”: it learns to capture the essence of data in a condensed form and then reconstruct the original, revealing hidden patterns and removing redundancy. It provides a bridge between raw high-dimensional data and efficient, meaningful representations for analysis and modeling.