InterviewsVector

Build AI systems from first principles.

A capability-driven Academy for engineers who want to derive the mechanism, ship the smallest tested version, break it on purpose, and defend the production trade-off.

Start the first live labChoose a role path

Choose the capability you need next

These are suggested sequences, not promises of instant seniority. Time ranges estimate the complete mapped curriculum at five focused hours per week; live flagship labs are marked separately.

Applied AI Engineer

Build retrieval and agent features with measurable behavior.

Baseline → math → foundation models → retrieval → evaluation

≈16–20 weeks at 5h/week

Open the mathematical path

Model & Inference Engineer

Reason from computation graphs to serving capacity.

Math → neural systems → model internals → adaptation → AI infra

≈20–24 weeks at 5h/week

Open the neural systems path

Staff AI Engineer / Architect

Own boundaries, failure budgets, economics, and governance.

Retrieval → agents → reliability → infrastructure → architecture

≈18–22 weeks at 5h/week

Open the architecture path

The Vector Loop

Every published lesson moves from a mental model to evidence you can operate and defend. A framework call never substitutes for the mechanism.

  1. 01

    Model

    Name the problem, boundary, assumptions, and mental model.

  2. 02

    Derive

    Work only the mathematics needed to predict behavior.

  3. 03

    Build

    Implement the smallest tested version that exposes the mechanism.

  4. 04

    Stress

    Break it with adversarial inputs, scale, and incorrect assumptions.

  5. 05

    Operate

    Add observability, cost, security, rollback, and realistic constraints.

  6. 06

    Defend

    Explain the trade-off in an interview, design review, or incident.

The capability spine

Eleven dependency-aware arcs move from reproducible experiments to production architecture. “Planned” means mapped and unpublished—not hidden content; withdrawn publications remain available only at their retained URLs.

38 live / 76 mapped

  1. 01

    Software Engineer

    Engineering Baseline for AI Work

    Turn a software project into a reproducible experiment, with explicit data, environment, cost, and verification boundaries.

    Capability: Run an AI experiment another engineer can reproduce and audit.

    Mapped units
    6
    Arc estimate
    ≈8h
    Inspect the complete arc

  2. 02

    Software Engineer

    Mathematical Machinery for AI Systems

    Learn the math as executable engineering machinery: representations, transformations, optimization, uncertainty, and numerical failure.

    Capability: Reason about model behavior without hiding behind library calls.

    Mapped units
    7
    Arc estimate
    ≈13h
    Inspect the complete arc

  3. 03

    AI Engineer

    Learning Systems and Classical ML

    Build the discipline that still governs foundation-model products: splits, baselines, leakage control, calibration, drift, and causal humility.

    Capability: Ship and defend a supervised learning system with trustworthy evaluation.

    Mapped units
    7
    Arc estimate
    ≈15h
    Inspect the complete arc

  4. 04

    AI Engineer

    Neural Systems from Computation Graphs

    Build neural networks as computation graphs with local derivative contracts, then diagnose optimization and representation failures.

    Capability: Implement, test, and debug a neural training loop from first principles.

    Mapped units
    7
    Arc estimate
    ≈16h
    Inspect the complete arc

  5. 05

    Senior AI Engineer

    Transformers and Foundation-Model Internals

    Trace the complete path from bytes to tokens, attention, transformer blocks, training objectives, decoding, and inference state.

    Capability: Explain and capacity-plan the machinery behind modern language models.

    Mapped units
    8
    Arc estimate
    ≈19h
    Inspect the complete arc

  6. 06

    Senior AI Engineer

    Model Adaptation and Multimodal Systems

    Choose between prompting, retrieval, fine-tuning, preference optimization, and multimodal fusion using evidence rather than fashion.

    Capability: Adapt a foundation model while preserving evaluation, safety, and rollback paths.

    Mapped units
    6
    Arc estimate
    ≈15h

    Editorial sequence published here as each full lab clears the quality gate.

    Inspect the complete arc

  7. 07

    Senior AI Engineer

    Retrieval and Knowledge Systems

    Build retrieval as a measurable information system: representations, indexing, chunking, filtering, ranking, grounding, and freshness.

    Capability: Diagnose a RAG system by stage and improve the right component.

    Mapped units
    7
    Arc estimate
    ≈17h
    Inspect the complete arc

  8. 08

    Staff AI Engineer

    Agentic Systems, Tools, and Protocols

    Treat agents as bounded distributed workflows with typed tools, explicit state, permissions, recovery, and human authority.

    Capability: Ship a tool-using workflow whose actions are bounded, observable, and recoverable.

    Mapped units
    7
    Arc estimate
    ≈18h
    Inspect the complete arc

  9. 09

    Staff AI Engineer

    Evaluation, Safety, and Reliability

    Make quality a release system: task-specific datasets, calibrated judges, human review, security tests, telemetry, and incident learning.

    Capability: Define a release bar that catches quality, safety, and reliability regressions.

    Mapped units
    7
    Arc estimate
    ≈17h

    Editorial sequence published here as each full lab clears the quality gate.

    Inspect the complete arc

  10. 10

    Staff AI Engineer

    Inference, Training, and AI Infrastructure

    Connect model execution to hardware reality: memory movement, precision, batching, parallelism, schedulers, storage, and failure recovery.

    Capability: Capacity-plan and operate training and inference systems under real constraints.

    Mapped units
    7
    Arc estimate
    ≈19h

    Editorial sequence published here as each full lab clears the quality gate.

    Inspect the complete arc

  11. 11

    AI Architect

    Production AI Architecture and Technical Leadership

    Integrate models, data, retrieval, tools, safety, reliability, economics, governance, and organizational ownership into durable platforms.

    Capability: Lead an AI architecture decision from requirements through operations and governance.

    Mapped units
    7
    Arc estimate
    ≈20h
    Inspect the complete arc

38 labs. 38 defensible artifacts.

These are complete vertical slices: original explanation, runnable code, failure cases, production constraints, checks, primary references, and an artifact to keep.

The publication contract requires source control, passing artifacts, visible authorship, real dates, and an indexability gate.

Lab 0155 min

Draw the AI System Boundary

Separate deterministic software, probabilistic model behavior, data, and human judgment before choosing tools.

AI system boundary mapEnter lab Lab 0280 min

Reproducible Experiments, Not Reproducible Notebooks

Make code, data, seeds, dependencies, and hardware assumptions inspectable.

Experiment manifestEnter lab Lab 0370 min

Data Contracts for Models

Specify schema, meaning, time, lineage, and allowed use before training or retrieval.

Versioned model data contractEnter lab Lab 0465 min

Define the Measurement Before the Model

Translate a product claim into offline, online, safety, latency, and cost measures.

Measurement contractEnter lab Lab 0575 min

A First AI Workload Cost Model

Estimate tokens, accelerator time, storage, and network movement before committing architecture.

AI workload cost modelEnter lab Lab 0675 min

From Experiment to Service Boundary

Extract a tested model contract from exploratory code without copying notebook state into production.

Inference contractEnter lab Lab 0780 min

Vectors as Representations

Connect coordinates, basis, scale, and information loss to learned representations.

Representation invariance auditEnter lab Lab 0895 min

Similarity Is a Retrieval Policy

Derive dot product and cosine similarity, then show why normalization changes what a retrieval system rewards.

Tested similarity auditEnter lab Lab 0990 min

Matrices as Small Programs

Read a matrix as a composition of projection, scaling, rotation, and mixing operations.

Tested linear-map pipelineEnter lab Lab 1095 min

Probability for Decisions, Not Decoration

Use conditional probability, calibration, and expected cost to make model outputs actionable.

Cost-sensitive decision policyEnter lab Lab 11100 min

Optimization Under Noise

Derive stochastic gradients and distinguish noisy progress from broken learning.

Noisy optimizer diagnosticEnter lab Lab 12100 min

Numerical Stability Is Part of the Algorithm

Break softmax, log likelihood, and low-precision reductions, then repair them.

Numerical stability harnessEnter lab Lab 1385 min

Complexity for Tensor Programs

Estimate FLOPs, memory traffic, activation storage, and asymptotic traps from tensor shapes.

Tensor cost estimatorEnter lab Lab 1490 min

The Generalization Contract

Define the population, decision, loss, and evidence under which performance is expected to transfer.

Generalization contract auditEnter lab Lab 15105 min

Split Data by Causality, Not Convenience

Use information availability, time, entity, group, and provenance to construct honest evaluation partitions.

Causal split validatorEnter lab Lab 16110 min

Linear Models as Debugging Instruments

Use transparent linear baselines to expose target, feature, split, scale, and slice failures before adding complexity.

Linear baseline diagnosticEnter lab Lab 17110 min

Trees, Boosting, and the Shape of Residual Error

Understand how tree ensembles partition mistakes and when their inductive bias wins.

Residual partition auditEnter lab Lab 18100 min

Calibration, Thresholds, and Decision Cost

Turn scores into actions using reliability curves and asymmetric error costs.

Calibrated threshold policyEnter lab Lab 1990 min

When the Product Needs Ranking, Not Classification

Choose ranking losses and metrics when ordering quality matters more than labels.

Ranking evaluation contractEnter lab Lab 20110 min

Drift, Feedback Loops, and Delayed Labels

Design monitoring when the system changes the data it later learns from.

Drift feedback monitorEnter lab Lab 2180 min

A Neuron Is a Parameterized Decision Surface

Connect affine maps and nonlinearities to representation capacity.

Neuron representation auditEnter lab Lab 2290 min

Computation Graphs Make Learning Inspectable

Represent forward values, dependencies, and local derivatives explicitly.

Computation graph trace validatorEnter lab Lab 23120 min

Backpropagation as Local Contracts

Derive reverse-mode autodiff as small, testable vector-Jacobian products rather than one mysterious global formula.

Tiny autodiff engine and testsEnter lab Lab 24105 min

Read Optimization Dynamics

Use loss curves, gradient statistics, and parameter updates to separate data, optimization, and capacity failures.

Optimization dynamics diagnosticEnter lab Lab 25105 min

Normalization and Residual Paths

Understand why signal and gradient paths shape trainability in deep networks.

Signal path contractEnter lab Lab 26105 min

Convolutions and Locality as an Inductive Bias

Build a convolution and connect weight sharing to images, audio, and structured grids.

Convolution equivariance auditEnter lab Lab 27110 min

Neural Training Incident: Loss Becomes NaN

Trace a realistic failure through inputs, precision, activations, gradients, and optimizer state.

Neural training incident runbookEnter lab Lab 28105 min

Tokenization as a Compression Contract

Study how vocabulary construction changes sequence length, multilingual behavior, cost, and failure modes.

Tokenizer compression auditEnter lab Lab 29120 min

Derive Attention from Content-Based Routing

Build scaled dot-product attention from the need to route information between positions.

Attention routing auditEnter lab Lab 3095 min

Multi-Head Attention Is Parallel Representation Routing

Explain head dimension, projections, and what head diversity does and does not guarantee.

Multi-head routing auditEnter lab Lab 31105 min

Position, Context, and Extrapolation

Compare positional mechanisms by the invariants they encode and how they fail outside training lengths.

Position extrapolation auditEnter lab Lab 32140 min

Assemble and Test a Transformer Block

Compose attention, MLP, normalization, masking, and residual paths with shape tests.

Minimal transformer blockEnter lab Lab 33105 min

Pretraining Objectives Shape Model Behavior

Connect next-token prediction, masking, data mixtures, and preference objectives to observable capabilities.

Training objective auditEnter lab Lab 3490 min

Decoding Is a Product Policy

Treat temperature, top-p, constraints, and stopping as explicit quality and risk decisions.

Decoding policy auditEnter lab Lab 35120 min

The KV Cache Capacity Plan

Derive per-token cache memory, then connect context length, concurrency, precision, batching, and paging to serving capacity.

Tested KV-cache estimatorEnter lab Lab 36125 min

Diagnose RAG by Stage

Measure corpus, retrieval, reranking, context, generation, citation, latency, and cost separately so failures remain attributable.

Stage-isolated RAG evaluation harnessEnter lab Lab 37135 min

A Tool-Using Agent Is a Bounded State Machine

Implement budgets, typed transitions, approval gates, idempotency, and terminal states around a probabilistic planner.

Tested bounded agent runtimeEnter lab Lab 38145 min

Design a Multi-Tenant AI Gateway

Create one policy and observability boundary for provider routing, tenant isolation, budgets, fallback, and release evidence.

Gateway architecture and capacity modelEnter lab
Legacy open-source reading archive20 imported phases · noindex

The prior roadmap is preserved for learners with saved links. Its metadata, glossary, artifacts, and lesson text come from Rohit Ghumare’s ai-engineering-from-scratch project under the MIT License. Archive pages are attributed and excluded from indexing; they are not claimed as InterviewsVector curriculum.

Open attributed glossary archive