Transformers from Scratch — Intuition, Math & Code

A deep, hands-on exploration of the transformer architecture: the math, the implementation choices, the engineering tradeoffs, and how to take models from prototype to production.

1. How attention works (intuitively)

At its core, attention answers a simple question: given a query, which parts of the input should I focus on? Unlike RNNs that process items sequentially, attention computes pairwise affinities between elements and produces a weighted sum. This expressivity is what lets transformers model long-range dependencies without recursion.

Scaled dot-product attention uses the dot product between query and key vectors to score importance. The scores are scaled by the square root of the key dimension (to avoid large gradients), and a softmax turns those scores into a distribution. Multiply those weights with values and you have context-aware representations.

2. Exact math (concise)

Attention(Q,K,V) = softmax((Q K^T) / sqrt(d_k)) V

Multi-head attention computes that operation in several subspaces: project inputs into multiple smaller heads, compute attention in each, then concatenate. This gives the model parallel ways to capture different relationships (syntax, semantics, locality, long-range patterns).

3. Positional information

Since attention is permutation-invariant, we must provide position information. There are three mainstream approaches: sinusoidal fixed encodings, learned embeddings per position, and relative position encodings (which bias attention based on distance between tokens). For long sequences, relative encodings often yield better generalization.

4. Depth, normalization and stability

Core blocks: multi-head attention, residual connections, layer normalization, and feed-forward layers (usually MLPs with GeLU or ReLU). Residuals let gradients flow through deep stacks, while careful initialization and normalization keep training stable at scale.

5. Training recipes

Good training isn't magic — it's engineering. Key ingredients:

• Large, curated datasets and careful deduplication.
• Tokenization strategy: byte-level vs subword (BPE/SentencePiece) — choose based on languages and scripts.
• LR schedules: linear warmup for a few thousand steps, then cosine or polynomial decay.
• Optimizer: AdamW with decoupled weight decay. For very large-scale training, look at LAMB or Adafactor for memory benefits.
• Regularization: dropout in FFN layers, careful weight decay, and selective layer freezing for fine-tuning.

6. Practical code sketch (pseudo)

// simplified attention (pseudo)
function attention(Q, K, V){
  let scores = matmul(Q, transpose(K));
  scores = scores / Math.sqrt(Q.shape[-1]);
  let weights = softmax(scores, -1);
  return matmul(weights, V);
}

7. Memory & compute optimizations

Vanilla attention is O(n²) in sequence length. Mitigations:

• Sparse attention (Longformer, BigBird): only compute certain blocks.
• Linearized attention (Performer): kernel approximations to reduce complexity.
• Segmented processing with recall mechanisms (Compressive Transformers).
• Offload gradients or activations using rematerialization to fit models onto fewer GPUs.

8. Inference & serving

For autoregressive models, caching key/value tensors across decoding steps (KV cache) is essential to avoid recomputation. For latency-critical services, use quantized models (8-bit, 4-bit) and compilers (XLA, TVM) to squeeze additional throughput. Batch small requests at the edge with request coalescing to improve GPU utilization without increasing tail latency excessively.

9. Responsible deployment

Models can hallucinate, leak sensitive content, or exhibit biases. Deploy with layered mitigations: prompt design, response filters, model-based fact-checking, and human review for high-risk outputs. Keep model lineage and training-data provenance well documented.

10. Recommended hands-on path

1. Re-implement a miniature transformer, train it on a small language modeling task (Wiki small).
2. Grow a model, measure scaling effects, and experiment with batch sizes and LR schedules.
3. Implement a KV cache and deploy a simple inference service to learn serving constraints.

References: Vaswani et al. — Attention Is All You Need; BERT, T5; and modern engineering writeups from major labs. Build small, instrument thoroughly, iterate.

Prompt Engineering & System Design for LLMs

How to turn a powerful model into a predictable, useful application using prompts, orchestration, and evaluation engineering.

1. Where prompts fit in the stack

Prompts are the interface between human intent and model capability. They don’t change weights, but they heavily influence model outputs. Treat prompt design as product engineering: version it, test it, and treat it like code.

2. Prompt patterns that work

• System messages: set persona and constraints.
• Few-shot examples: show desired input-output pairs for structure-sensitive tasks.
• Chain-of-thought: request step-by-step reasoning for complex tasks — but validate since chain-of-thought can reflect spurious correlations.
• Output schema enforcement: demand JSON or CSV and validate strictly client-side.

3. Safety and guardrails

Never rely on prompts alone for safety. Add runtime filters, allowlist/blocklist, and human review for sensitive operations. Implement rejection sampling for highly risky classes of outputs.

4. Evaluation loop & metrics

Automate the evaluation pipeline: unit tests (expected outputs), regression tests, and human evaluation for nuance. Monitor metrics like factuality rate, instruction-following accuracy, and hallucination frequency.

5. Tooling & orchestration

Design systems where models are one component: retrieval (vector DBs) for context, small analyzers for post-processing, and policy engines that decide when to escalate to human agents. This modular approach reduces risk and improves reliability.

6. Practical example: structured extraction

System: You are a strict JSON extractor.
User: Extract name, email, and phone from the text. Return VALID JSON only.

Always validate and run a schema check on returned JSON. Reject and retry when the schema is violated.

7. Observability for LLM-driven features

Instrument inputs and outputs, but keep privacy in mind. Use synthetic tests to detect drift. Track time-to-first-byte and latency percentiles to ensure UX quality.

Practical tip: Keep prompt changes under version control and test small variations — small wording shifts can produce large behavior changes.

Modern Web Performance — Core Web Vitals to Observability

Practical end-to-end strategies to make websites feel fast and resilient, from resource loading to real-user monitoring.

1. User-centric metrics

Core Web Vitals (LCP, INP/FID, CLS) capture perceivable quality. Measure them in the wild with RUM to capture real user conditions and identify geographic or network-specific regressions.

2. Critical rendering path

Optimize what matters for first meaningful paint: compress critical CSS, defer non-critical JS, and avoid large render-blocking resources. For single-page apps, prefer server- or edge-rendering for the first paint and hydrate progressively.

3. Images and media

Serve modern formats (AVIF, WebP), use responsive srcset, and lazy-load below-the-fold assets with the intersection observer. Use low-quality image placeholders (LQIP) or blurred placeholders to reduce perceived layout shifts.

4. Observability

Combine synthetic monitoring (Lighthouse) with RUM and custom tracing to understand both lab and field behavior. Alert on trends rather than single anomalies to avoid alert fatigue.

Performance is continuous — make it part of the CI pipeline and review performance budgets on every release.

Progressive Web Apps — Offline-first Architecture

Design PWAs that gracefully degrade on poor networks, sync efficiently, and keep user data consistent across offline and online states.

1. Service Workers and caching

Service workers intercept network requests; implement a cache-first strategy for static assets and a stale-while-revalidate or network-first approach for dynamic content depending on freshness needs.

2. Data synchronization

Local storage with IndexedDB and sync queues are core. Resolve conflicts with CRDTs or last-writer-wins depending on your data model. Provide UX that surfaces sync status and conflicts to users responsibly.

PWAs provide great user experiences if you design sync and reconciliation explicitly — not as an afterthought.