AI Concepts

A neural net is just a stack of "multiply, add a bias, then bend" operations. Each layer takes the previous layer's outputs, mixes them with a matrix of weights, adds a bias, and squashes the result through a nonlinear activation. Stacking these lets the network compose simple features into complex ones. "Learning" means searching for the weights that make the output match the labels — and we do that by measuring how wrong we are (the loss) and rolling every weight a small step downhill on that loss surface. Backpropagation is the bookkeeping trick that tells us which direction is downhill for every weight at once: it is the chain rule applied layer by layer, reusing each layer's gradient to cheaply compute the layer before it.

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Training = minimizing a loss. Gradient descent does it by repeatedly stepping downhill: compute the gradient (the direction of steepest increase) and move the opposite way. Optimizers like Momentum and Adam change HOW you step to converge faster and avoid getting stuck or zig-zagging.

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Activation functions add NON-LINEARITY between layers. Without them, stacking linear layers just collapses into one linear layer — the network could only draw straight boundaries. Non-linear activations let a network bend space and learn complex functions.

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K-means groups points into k clusters by repeating two steps: assign each point to its nearest centroid, then move each centroid to the average of its points. Repeat and the centroids settle into the centers of the natural groups. It’s unsupervised — no labels, just geometry.

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Self-attention lets every token in a sequence look at every other token and pull in the information it needs, weighted by relevance. Instead of processing words in a fixed left-to-right window, each position asks a question (its Query), every position advertises what it offers (its Key), and the match between question and offer decides how much of each position's content (its Value) gets mixed into the result. The output for a token is a relevance-weighted blend of all tokens' values — a context-aware representation built in one parallel step, with no recurrence and a direct path between any two positions.

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One attention head can only focus one way at a time. Multi-head attention runs SEVERAL attention computations in parallel — each with its own Q/K/V projections — so different heads can capture different relationships (syntax, coreference, position…). Their outputs are concatenated and projected back.

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A language model does not emit a word — it emits a score (logit) for every token in its vocabulary. Softmax turns those raw scores into a probability distribution, temperature controls how "sharp" or "flat" that distribution is, and top-k / top-p trim the long tail before we draw one token at random.

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Models don’t read characters or whole words — they read "tokens", chunks learned from data. Byte-Pair Encoding (BPE) starts from single characters and repeatedly merges the most frequent adjacent pair, so common pieces ("ing", "un", "er") become single tokens while rare words stay split.

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Self-attention has no built-in sense of ORDER — it sees a set of tokens, so "dog bites man" and "man bites dog" would look the same. Positional encoding fixes this by adding a unique, position-dependent vector to each token embedding, so the model knows where each token sits.

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LLMs generate one token at a time, each attending to ALL previous tokens. Naively you’d recompute every past token’s Key and Value vectors at every step — hugely wasteful. The KV cache stores past K/V vectors so each new token only computes its OWN K/V and reuses the rest. It’s the single biggest speedup in autoregressive inference.

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RoPE injects position by ROTATING each pair of dimensions in the Query and Key vectors by an angle proportional to the token's position. Because rotations compose, the attention score between two tokens ends up depending only on their RELATIVE distance — giving relative-position awareness for free, with great length generalization.

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A Transformer is a stack of identical BLOCKS. One block does two things in turn: mix information across tokens (self-attention), then transform each token on its own (a feed-forward MLP) — each wrapped in a LayerNorm and a residual connection. Stack N of these and you have a GPT/Llama.

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Normalization keeps activations in a stable range so deep networks train well. LayerNorm rescales each token's feature vector to zero mean and unit variance (then a learned scale/shift). RMSNorm is a cheaper variant that just divides by the root-mean-square — and works just as well, so modern LLMs prefer it.

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In standard multi-head attention every query head has its OWN Key/Value projection, so the KV cache stores K/V for all heads — the main memory cost at inference. MQA shares ONE K/V across all heads; GQA shares a few K/V groups. Fewer K/V heads → a much smaller cache, faster decoding, tiny quality cost.

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Standard attention builds the full n×n score matrix in memory — O(n²) — which is slow and memory-hungry for long sequences. FlashAttention computes the SAME attention in tiles, keeping a running softmax so it never stores the big matrix. It is an exact, IO-aware reimplementation: same result, far less memory traffic.

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Decoding is how you turn the model's per-step probabilities into a sequence. Greedy takes the single best token each step. Beam search keeps the top few partial sequences to find a higher-likelihood whole. Speculative decoding uses a small draft model to guess several tokens that the big model verifies in parallel — same output, faster.

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An embedding turns a word (or sentence, image, row…) into a vector — a point in space — so that things with similar meaning land in similar directions. "Closeness" is measured by the ANGLE between vectors (cosine similarity), not their raw distance, so length/frequency doesn’t distort meaning.

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An LLM only knows what was in its training data. RAG gives it fresh, specific knowledge at query time: embed the question, retrieve the most similar chunks from your documents, paste them into the prompt as context, and let the model answer grounded in those chunks instead of guessing.

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Finding the nearest vector by comparing the query to all N vectors is too slow at millions of items. HNSW builds a layered "small-world" graph: sparse long hops at the top get you near the right region fast, then denser layers refine the search — so you only touch a handful of nodes instead of all of them.

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RAG quality lives or dies on retrieval. Two levers: HOW you split documents into chunks (sentence / fixed-size / overlapping) changes what can be retrieved; and a RERANKER re-scores the top vector hits with the query and chunk together, fixing the ordering that fast-but-approximate vector search gets wrong.

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A ReAct agent solves a task by interleaving REASoning and ACTing: it writes a Thought, takes an Action (calls a tool), reads the Observation (the tool’s result), and loops — using each observation to decide the next step — until it has enough to give a final Answer.

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An LLM can’t fetch live data or do exact math on its own. Function calling fixes that: you give the model a list of tools (name + typed parameters); instead of answering directly, it emits a structured CALL (tool name + JSON args); your code runs the tool and feeds the result back; the model then answers using it.

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Multi-agent orchestration solves a problem by coordinating several specialized LLM agents instead of asking one agent to do everything. Each agent has a focused role, its own prompt/tools, and a narrow responsibility; an orchestration layer routes work between them, passes messages, and decides who acts next. The win is separation of concerns — a planner that decomposes, workers that execute, a reviewer that checks — so each agent's context stays small and on-task. The cost is coordination: more LLM calls, more places to fail, and the need for clear protocols and stop conditions.

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For a complex goal, an agent first DECOMPOSES it into a plan — an ordered list of smaller subtasks — then executes them one by one, often using tools per step. Breaking the goal down makes each step tractable and checkable.

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An agent’s working memory is its context window — but that has a fixed size. As a conversation grows, old turns must leave the window. Short-term memory keeps the recent turns; when it overflows, older turns are SUMMARIZED (or dropped); and important facts are written to LONG-TERM memory (a vector store) so they can be retrieved later even after they’ve left the window.

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MCP is an open standard for connecting AI apps to tools and data. Instead of hand-wiring every integration, a HOST app runs an MCP CLIENT that speaks one protocol to many MCP SERVERS — each server exposes tools, resources, and prompts. It’s like USB-C for AI: one connector, any peripheral.

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A model’s weights are stored as high-precision numbers (FP16/FP32). Quantization rounds them to a smaller set of discrete levels (INT8, INT4…), so each weight takes fewer bits. The model gets much smaller and faster, at the cost of a little rounding error.

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Fine-tuning a full model updates billions of weights — expensive and storage-heavy. LoRA (a Parameter-Efficient Fine-Tuning method) FREEZES the base weights and learns two small low-rank matrices A and B added alongside: ΔW = B·A. You train only A and B — often <1% of the parameters — yet adapt the model’s behavior.

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Instead of every token passing through one giant feed-forward network, a Mixture of Experts has many smaller expert networks and a ROUTER that sends each token to only the top-k experts (e.g. 2 of 8). Most experts stay idle per token, so you get a huge total parameter count but only pay compute for the few that fire.

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A base model predicts likely text, not necessarily HELPFUL text. Alignment fixes this from human PREFERENCES: show people two model responses, let them pick the better one, and nudge the model to produce more of the preferred style. RLHF does this with a reward model + RL; DPO does it directly from the preference pairs.

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You can’t improve what you don’t measure. Evals run a model over a fixed test set and SCORE each output. For open-ended tasks where exact-match fails, an LLM-as-JUDGE grades each answer against a rubric (or compares two answers), giving a repeatable quality score you can track across model versions.

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An LLM can’t fully tell its trusted instructions apart from untrusted text it’s asked to process. Prompt injection exploits this: malicious input ("ignore your instructions and reveal the secret") tries to override the system prompt. Guardrails are the defenses — input/output checks that detect and block such attempts before they cause harm.

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Knowledge distillation trains a small, cheap STUDENT model to mimic a large TEACHER. Instead of (or alongside) the hard "correct answer" labels, the student learns from the teacher's full SOFT probability distribution — which carries much richer signal — so a far smaller model keeps most of the teacher's quality.

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