{ "cells": [ { "cell_type": "markdown", "id": "cell00", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# Week 1 — Exercises\n" ] }, { "cell_type": "markdown", "id": "lx-8c5a9d", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Part A — Foundations & calculations" ] }, { "cell_type": "markdown", "id": "cell07", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercise 1 — Conditional probability from a joint table *(calculation)*\n", "\n", "Given the joint distribution $P(X,Y)$:\n", "\n", "| $X$ | $Y$ | $P$ |\n", "|-----|-----|-----|\n", "| 0 | 0 | 0.1 |\n", "| 0 | 1 | 0.2 |\n", "| 1 | 0 | 0.6 |\n", "| 1 | 1 | 0.1 |\n", "\n", "Compute the conditional distribution $P(X \\mid Y{=}1)$." ] }, { "cell_type": "markdown", "id": "cell09", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Exercise 2 — Build a joint via the chain rule *(calculation)*\n", "\n", "Given the marginal $P(W)$ and the conditional $P(D\\mid W)$:\n", "\n", "| $W$ | $P(W)$ |\n", "|-----|--------|\n", "| sun | 0.8 |\n", "| rain | 0.2 |\n", "\n", "| $P(D\\mid W)$ | $D=$ wet | $D=$ dry |\n", "|-----|-----|-----|\n", "| $W=$ sun | 0.1 | 0.9 |\n", "| $W=$ rain | 0.7 | 0.3 |\n", "\n", "Compute the joint table $P(W,D)=P(D\\mid W)\\,P(W)$." ] }, { "cell_type": "markdown", "id": "cell11", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Exercise 3 — Statistical independence *(calculation)*\n", "\n", "Marginals $P(T)$: hot 0.5, cold 0.5; $P(W)$: sun 0.6, rain 0.4. Joint $P(T,W)$:\n", "\n", "| $T$ | $W$ | $P(T,W)$ |\n", "|-----|-----|----------|\n", "| hot | sun | 0.4 |\n", "| hot | rain | 0.1 |\n", "| cold | sun | 0.2 |\n", "| cold | rain | 0.3 |\n", "\n", "Are $T$ and $W$ statistically independent? Justify." ] }, { "cell_type": "markdown", "id": "cell01", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercise 4 — Chain rule *(theory)*\n", "\n", "1. **Chain Rule**: Write $P(W_{1:3})$ for a 3-token sequence as a product of conditional probabilities.\n", "2. **Joint Space Size**: How many parameters are needed to store the full, unrepresented joint distribution $P(W_{1:T})$ in a lookup table for a vocabulary $\\vert{}V\\vert{}$ and length $T$?\n", "3. **The Conditional Bottleneck**: Why does the chain rule factorization in (1) fail to solve this exponential memory problem if we try to store the exact conditional probabilities $P(W_t \\mid W_{1:t-1})$ in a lookup table? What structural assumption do classical language models use to fix this?\n" ] }, { "cell_type": "markdown", "id": "cell03", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercise 5 — The training ladder *(conceptual)*\n", "\n", "Explain what each ladder stage adds, and why **only** a tool-calling-tuned model can drive an\n", "agent loop." ] }, { "cell_type": "markdown", "id": "cell05", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercise 6 — Chatbot vs agent, and the three-layers *(conceptual)*\n", "\n", "(a) Classify each as **chatbot** or **agent**, and justify:\n", "- (i) a bot answering FAQs from a fixed text, no actions;\n", "- (ii) a system that reads your calendar, books a meeting, and emails attendees.\n", "\n", "(b) In the three-layer architecture, which **layer** \n", "- (i) talks to the messenger,\n", "- (ii) executes a tool,\n", "- (iii) calls the LLM?" ] }, { "cell_type": "markdown", "id": "lb-7d49d0", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Part B — Lab: Ollama + the OpenAI client\n", "\n", "**Install (no root needed).** Ollama runs without admin rights — install a user-local binary:\n", "\n", "```bash\n", "mkdir -p ~/.local\n", "curl -L https://ollama.com/download/ollama-linux-amd64.tgz | tar -xz -C ~/.local\n", "export PATH=\"$HOME/.local/bin:$PATH\" # add this line to ~/.bashrc\n", "```\n", "\n", "**Start the server — each session** (lab machines have no auto-start service and no\n", "Docker/Podman):\n", "\n", "```bash\n", "ollama serve & # local server on 127.0.0.1:11434 — leave it running while you work\n", "```\n", "\n", "**Pull a model and test it on the command line:**\n", "\n", "```bash\n", "ollama pull qwen2.5:3b\n", "ollama list # list installed models\n", "ollama run qwen2.5:3b \"Say hello in one word.\" # quick sanity check that Ollama works\n", "```\n", "\n", "**Try different models** — depending on the machine's free RAM. Smaller = lighter and faster on\n", "CPU, but tool calling gets less reliable below ~3B:\n", "\n", "| free RAM | model | tool calling |\n", "|---|---|---|\n", "| ~4 GB | `llama3.2:1b`, `qwen2.5:1.5b` | flaky |\n", "| ~6–8 GB | `qwen2.5:3b`, `llama3.2:3b` | reliable ✅ |\n", "| 8+ GB | `qwen2.5:7b` | best |\n", "\n", "Pull a couple and **compare speed and answer quality** — set `MODEL` below to whichever you use.\n", "\n", "> *On your **own** computer you may auto-start Ollama with `systemctl --user` or Docker/Podman.*" ] }, { "cell_type": "code", "execution_count": 2, "id": "lb-c9142b", "metadata": { "editable": true, "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [], "source": [ "# Run me first — defines `client` and `MODEL` used by all lab exercises below.\n", "from openai import OpenAI\n", "\n", "client = OpenAI(base_url=\"http://localhost:11434/v1\", api_key=\"ollama\") # key is ignored\n", "MODEL = \"qwen2.5:3b\" # try \"llama3.2:3b\", \"qwen2.5:1.5b\", or \"qwen2.5:7b\" (RAM permitting)\n", "# MODEL = \"qwen2.5:7b\" " ] }, { "cell_type": "markdown", "id": "lx-e3856b", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Exercise 7 — First API call *(lab)*\n", "\n", "Send a single user message with the **Chat Completions API** to the model and print its reply." ] }, { "cell_type": "markdown", "id": "lx-73bf5d", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercise 8 — The system prompt *(lab)*\n", "\n", "Send the *same* user question with the **Chat Completions API** with two different **system** prompts and compare the answers.\n", "What does the system message control?" ] }, { "cell_type": "markdown", "id": "lx-cfe904", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercise 9 — Statelessness & memory *(lab)*\n", "\n", "Tell the model your name in one request; in a **new** request ask for it **without** resending\n", "the history. Then repeat **with** the history. Use the **Chat Completions API**!\n", "Explain what you observe." ] }, { "cell_type": "markdown", "id": "lx-0e22d8", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Exercise 10 — A structured tool call *(preview)*\n", "\n", "*A first look at **function calling** — the mechanics are **Week 2**. Here you only **advertise** a\n", "tool and **observe** the structured request the model emits (you don't invent the schema or run the\n", "tool).*\n", "\n", "Using the `tools` schema below, ask *\"What's the weather in Berlin?\"* and inspect\n", "`response.choices[0].message.tool_calls` — the **structured JSON** the model emits. Do **not**\n", "execute the tool. Use the **Chat Completions API**.\n", "\n", "```python\n", "tools = [{\n", " \"type\": \"function\",\n", " \"function\": {\n", " \"name\": \"get_weather\",\n", " \"description\": \"Get the current weather for a city.\",\n", " \"parameters\": {\n", " \"type\": \"object\",\n", " \"properties\": {\"city\": {\"type\": \"string\"}},\n", " \"required\": [\"city\"],\n", " },\n", " },\n", "}]\n", "```\n", "\n", "Pass `tools=tools` to `client.chat.completions.create(...)`. *(The tool-schema format itself is\n", "explained in Week 2 — you're just seeing the output here.)*" ] }, { "cell_type": "markdown", "id": "71ccaf6f-9b4d-42eb-898a-49d7ffd6ddd8", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Part C — Reflection ⚖️\n", "\n", "## Exercise 11 — Can a language model think critically? *(discussion — open question)*\n", "\n", "> **Open question.** Are language models capable of **critical thinking** — or do they mainly\n", "> reproduce **majority opinion**, including its prejudices? Discuss this in terms of *how* they\n", "> generate language: **probabilistically**, from $P(W_t \\mid W_{1:t-1})$.\n", "\n", "Work through (a)–(d) and write a **~1 page** essay that takes a clear position *and* states the\n", "strongest objection to it.\n", "\n", "**(a) Start from the maths.** The model is fitted by maximum likelihood on a corpus, so\n", "$\\hat P(W_t \\mid W_{1:t-1})$ approximates the distribution *of that corpus*. If the corpus records\n", "many conflicting voices on a contested question, **what does the mode of that conditional\n", "correspond to** — the best-argued position, or the most frequent one? What follows for a minority\n", "view that is **well argued but rarely written down**? *(How a system then picks a token from the\n", "distribution — greedy vs. sampling, temperature — is **Week 2**, and W2's Exercise 13 measures it.)*\n", "\n", "**(b) Where could disagreement with the majority come from at all?** For each mechanism below,\n", "decide whether it produces a genuine **evaluation of reasons** or only a **shift of the\n", "distribution**:\n", " 1. **Conditioning** — the prompt or an attached document moves the model into a different region\n", " of the distribution.\n", " 2. **Preference tuning** (SFT/RLHF — the alignment rung of the training ladder) — reshapes the\n", " probabilities themselves toward helpful/harmless completions.\n", " 3. **Tools & retrieval** — evidence from outside the weights (W2, W8).\n", " 4. **Decoding knobs** — greedy vs. sampling, temperature (W2).\n", "\n", "**(c) Alignment is not obviously a fix.** Preference optimisation rewards answers that *raters\n", "prefer*, and Sharma et al. (2023) find that preference data systematically favours responses\n", "matching the **user's** stated view — sometimes over correct ones (**sycophancy**). Distinguish two\n", "different failures: a model echoing the **corpus majority**, and a model echoing **the person in\n", "front of it**. Which is more dangerous for an agent that *acts* (W12), and why?\n", "\n", "**(d) The counter-position.** Bender et al. (2021) argue an LM is a **\"stochastic parrot\"** — form\n", "without communicative intent. Mahowald et al. (2024) instead separate **formal** linguistic\n", "competence (mastering the rules and statistical regularities of a language) from **functional**\n", "competence (using language rationally in the world: reasoning, world knowledge, situation tracking,\n", "social cognition). Sort the ingredients of \"critical thinking\" — internal consistency, spotting a\n", "fallacy, weighing evidence, **changing one's mind when the evidence changes** — onto that\n", "distinction. Then state what would count as *evidence* that a model did more than repeat patterns:\n", "**design a concrete test**, and say **what result would falsify your own position**.\n", "\n", "**References.**\n", "- Bender, E. M., Gebru, T., McMillan-Major, A., & Shmitchell, S. (2021). *On the Dangers of\n", " Stochastic Parrots: Can Language Models Be Too Big?* FAccT '21, 610–623. doi:10.1145/3442188.3445922.\n", "- Mahowald, K., Ivanova, A. A., Blank, I. A., Kanwisher, N., Tenenbaum, J. B., & Fedorenko, E.\n", " (2024). *Dissociating Language and Thought in Large Language Models.* Trends in Cognitive\n", " Sciences 28(6), 517–540. arXiv:2301.06627.\n", "- Sharma, M., et al. (2023). *Towards Understanding Sycophancy in Language Models.* arXiv:2310.13548.\n" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" }, "rise": { "scroll": true, "theme": "simple", "transition": "none" } }, "nbformat": 4, "nbformat_minor": 5 }