LLGA · Independent study notes

Large Language Models, Graphs and Applications (LLGA)

Programme of the Master of Science and Technology (MScT) of École Polytechnique

Official description of the master

The LLGA Master’s specialization is a two-year, fully English-taught degree with a strong international outlook. Designed for ambitious students, the specialization equips graduates with both a solid theoretical foundation and hands-on industry expertise in Generative AI. With a special emphasis on Large Language Models (LLMs) and graph-structured data, students gain the skills to harness cutting-edge technologies and apply them across diverse fields—from healthcare and biology to finance, social networks, and beyond.

In recent years, Generative AI has grown explosively, with Large Language Models (LLMs) transforming how society and the economy interact with the digital world. From translation and code generation to creative content and advanced reasoning, these technologies achieve tasks once unimaginable.

The LLGA Master’s specialization prepares students to master this field, combining theory with real-world applications. Graph-based models, such as Graph Neural Networks (GNNs), add another layer by capturing complex structures in networks, molecules, or logistics. Together, LLMs and graph methods enable multimodal generative AI, opening opportunities in healthcare, finance, recommendation systems, and beyond.

The LLGA specialization provides a strong foundation in machine and deep learning, plus hands-on experience with cutting-edge generative techniques. Through projects, case studies, and industry applications, graduates gain rare expertise, equipping them to lead the next generation of AI innovation.

Source: official LLGA programme page (École Polytechnique).

What is this website?

This website is an independent, open-source project. It is not created, maintained or endorsed by École Polytechnique or its professors.

Its purpose is to share with the open community what may be taught during the master, based on the state of the art and on existing published work. The content is organised and completed with the help of AI and LLM tools. For enrolment rules, ECTS and official course lists, always refer to the official documentation.

Curriculum tree

Mandatory / Choose N = official curriculum (choice rules: LLGA wiki; course units offered in 2026–2027: SynapseS catalogue, see the programme table)
TBC = “to be confirmed”
Slot TBC = announced but not yet defined by the programme · A route button dims the electives it does not recommend; mandatory items are never dimmed — a route is guidance, not a rule.

The route buttons preselect inside the official choice groups only — they never override Mandatory items.

Programme 2026–2027: course units and hours

This table lists the course units of the first-year LLGA track in the SynapseS 2026–2027 catalogue (semester lists LLGA 1 – S1 and LLGA 1 – S2) and the second-year modules announced by the programme. For each one, it shows how these notes fit the official volume.

The track page and every course-unit sheet were read in full on 22 October 2026. Volumes come from the sheets. Where a sheet displays none (Computer Animation, Graph ML, Multimodal Generative AI, Optimization for AI), they come from the programme’s curriculum wiki (last modified 9 September 2026), which states:

  • all M1 courses after the refreshers are 36 h and 4.5 ECTS;
  • the Year-2 courses Large Language Models and Geometric Data are 24 h and 2 ECTS each.

How to read “These notes”. Every course page has a Session plan: the official volume split into sessions.

  • 36 h course: 12 sessions of 3 h; 12 h refresher: 4 sessions; 24 h Year-2 course: 8 sessions.
  • Each session has a level — 1 foundations, 2 core methods, 3 advanced — that never goes down from one session to the next.
  • Chapters that do not fit in the official hours (instructors’ research notes, extensions) are listed as self-study with a time estimate. The in-class part of every page holds about as much as its hours can cover.

Across the two years, the difficulty rises with the periods: the refreshers stay at level 1, Period 1 courses assume them, Period 2 courses assume Machine Learning and one Deep Learning course, and Year 2 builds on Period 2.

What changed in the 2026–2027 catalogue

  • New refresher: the track lists a Refresher in Computer Graphics (CSC_51438_EP, Marie-Paule Cani, Pascal Guehl) next to the computer-science and statistics refreshers. These notes do not cover it yet.
  • Period 1 options no longer in the list: Probability Theory for ML (APM_51056_EP), Database Management System (CSC_51053_EP) and Statistical Learning Theory (APM_51059_EP) are still taught at the École in other tracks but are not part of the LLGA 1 – S1 list; their notes stay on this site for reference. The P1 options are now Deep Learning, Signal Processing, Collaborative Learning, Computer Animation, Image Analysis and Computer Vision, Topological Data Analysis and Shapes.
  • Moved course: Optimisation and Responsible AI is now CSC_51076_EP, taught in Period 1; its former code CSC_52073_EP (Period 2) is gone, and the course is not in the LLGA lists.
  • Period 2 list: LLGA 1 – S2 offers nine scientific units — Reinforcement Learning, Graph ML and Text Mining & NLP (mandatory), plus Multimodal Generative AI, Deep Learning (P2 variant), Optimal Transport, Optimization for AI, Advanced Deep Learning and Image Synthesis. Statistics in Action remains in the catalogue but not in this list; Social Media: Probabilistic Models has no 2026–27 sheet.
  • Management, culture and internship units: Period 1 has IME_51456_EP Introduction au marketing et à la stratégie (36 h); Period 2 has two new management units, IME_52441_EP Simulation d’entreprise (a one-day business serious game) and IME_52470_EP Digital Transformation and AI in Organisations and Society, which replace the wiki’s startup/entrepreneurship pair; about thirty humanities and French-culture options (for example HSS_51G16_EP Sociology of AI); and the internship is INT_52402_EP, a 16-week research-oriented internship.
  • Year 2: the catalogue shows empty LLGA 2 – S3 and S4 groups and a gap-year internship (INT_52400_EP, Stage de Césure); the Year-2 volumes below are the programme’s 24 h figure for Large Language Models (CSC_53432_EP), marked “assumed” where a course publishes none.
CourseCodePeriodOfficial volumeThese notesSelf-study2026–27 SynapseS listing
Year 1 · Period 1 — refreshers
Refresher in StatisticsAPM_51438_EPY1 P112 h4 sessions≈ 24 hlisted in LLGA 1 – S1
Refresher in Computer ScienceCSC_51440_EPY1 P112 h4 sessions≈ 18 hlisted in LLGA 1 – S1
Refresher in Computer GraphicsCSC_51438_EPY112 h——listed in LLGA 1 – S1, new (M.-P. Cani, P. Guehl; 6 h lectures + 6 h small classes); not covered by these notes
Refresher Neural Nets—Y1 P1— (self-study)6 steps · 12 h≈ 6 hoff-curriculum support (no course unit)
Year 1 · Period 1 — courses
Machine LearningMDC_51006_EPY1 P136 h12 sessions≈ 3 hlisted in LLGA 1 – S1 (mandatory)
Deep LearningCSC_51054_EPY1 P136 h12 sessions≈ 3 hlisted in LLGA 1 – S1; wiki: Deep Learning once, in P1 or P2
Signal ProcessingAPM_51055_EPY1 P136 h12 sessions≈ 2 hlisted in LLGA 1 – S1
Emerging Subjects in ML and Collaborative LearningAPM_51178_EPY1 P136 h12 sessions≈ 3 hlisted in LLGA 1 – S1
Computer AnimationCSC_51085_EPY1 P136 h12 sessions≈ 2 hlisted in LLGA 1 – S1
Image Analysis and Computer VisionCSC_51073_EPY1 P136 h12 sessions≈ 2 hlisted in LLGA 1 – S1
Topological Data AnalysisCSC_51056_EPY1 P136 h9 sessions≈ 2 hlisted in LLGA 1 – S1
Digital Representation and Analysis of ShapesCSC_51074_EPY1 P136 h12 sessions≈ 1.5 hlisted in LLGA 1 – S1
Year 1 · Period 2 — courses
Reinforcement Learning and Autonomous AgentsCSC_52081_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2 (mandatory)
Graph Machine and Deep Learning for Generative AICSC_52072_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2 (mandatory)
Introduction to Text Mining and NLPCSC_52082_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2 (mandatory)
Multimodal Generative AICSC_52002_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2
Deep LearningAPM_52183_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2
Machine learning with Optimal Transport and Algorithmic FairnessAPM_52188_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2
Optimization for AIAPM_52067_EPY1 P236 h12 sessions≈ 3 hlisted in LLGA 1 – S2
Advanced Deep LearningCSC_52087_EPY1 P238.25 h9 sessionsnonelisted in LLGA 1 – S2
Image Synthesis: Theory and PracticeCSC_52084_EPY1 P236 h12 sessions≈ 2 hlisted in LLGA 1 – S2
Year 1 — management, culture and internship units
Introduction au marketing et à la stratégieIME_51456_EPY136 h——listed in LLGA 1 – S1 (P. Ginier-Gillet) — framed by our page Strategy / Marketing
Simulation d’entrepriseIME_52441_EPY11 day——listed in LLGA 1 – S2: business serious game (C. Steux); not covered
Digital Transformation and AI in Organisations and SocietyIME_52470_EPY1———listed in LLGA 1 – S2 (D. Curto); not covered
Sociology of AIHSS_51G16_EPY1———listed in LLGA 1 – S1 (N. Wanlin, A. Wirth); humanities option — not covered
About thirty humanities and French-culture optionsLEN_51G07_EP · HSS_52G27_EP · …Y120 h typical——listed — see Languages, Humanities
16-week research-oriented internshipINT_52402_EPY116 weeks——listed in LLGA 1 – S2 — see Research-Oriented Internship
Year 1 — notes kept for reference: courses not in the 2026–27 LLGA lists
Probability Theory for ML: Applications to Monte Carlo Methods and Generative ModelsAPM_51056_EPY1 P136 h9 sessions≈ 3 hnot in the LLGA 1 – S1 list; still offered in other 2026–27 tracks
DataBase Management SystemCSC_51053_EPY1 P136 h12 sessions≈ 1.5 hnot in the LLGA 1 – S1 list; still offered in other 2026–27 tracks
Statistical Learning TheoryAPM_51059_EPY1 P136 h12 sessions≈ 3 hnot in the LLGA 1 – S1 list; still offered in other 2026–27 tracks
Optimization and Responsible AI for SustainabilityCSC_51076_EPY1 P136 h (announced)9 sessions≈ 2 hnow CSC_51076_EP in Period 1 (was CSC_52073_EP, P2); not in the LLGA lists
Statistics in ActionAPM_52066_EPY1 P236 h12 sessions≈ 2 h36 h unit of the 2026–27 catalogue, not in the LLGA lists
Social Media and Communication: Probabilistic Models and AlgorithmsAPM_51058_EPY1 P236 h12 sessions≈ 3 habsent from the 2026–27 catalogue (last sheet 2025–26)
Computer Vision: From Fundamentals to Applications—Y1 P236 h12 sessionsnoneannounced slot, no SynapseS code
Real-time AI in Video Games: decisive & collaborative actions—Y1 P236 h12 sessionsnoneannounced slot, no SynapseS code
Year 2 — Periods 1 and 2
Large Language ModelsCSC_53432_EPY2 P124 h8 sessions≈ 3 hmandatory (wiki); LLGA 2 – S3/S4 published empty so far
Analysis and Deep Learning on Geometric DataCSC_53431_EPY2 P124 h8 sessions≈ 3 hmandatory (wiki); LLGA 2 – S3/S4 published empty so far
Advanced Graph Neural Networks—Y2 P124 h (assumed)8 sessions≈ 3 hLLGA 2 – S3/S4 published empty so far
Privacy and Uncertainty Quantification—Y2 P124 h (assumed)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
From Boosting to Foundation Models: learning with Tabular Data—Y2 P124 h (assumed)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
Control in Generative AI—Y2 P124 h (assumed)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
ML Ops and LLM Engineering Principles—Y2 P224 h (announced)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
Fundamentals of Security and Robustness for AI—Y2 P224 h (announced)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
Graph Generative Models and Applications—Y2 P224 h (announced)8 sessions≈ 5.5 hLLGA 2 – S3/S4 published empty so far
Explainability, Security, Privacy of LLMs—Y2 P224 h (announced)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
Speech Technology for Conversational AI—Y2 P224 h (announced)8 sessionsnoneLLGA 2 – S3/S4 published empty so far
Advanced Topics in Large Language Models—Y2 P224 h (announced)8 sessionsnoneLLGA 2 – S3/S4 published empty so far

Grey rows are course units of the listing that these notes do not cover. Table regenerated by tools/programme_table.py from each page’s session plan.

Projects and assessment

Every science page ends with a Projects and assessment section: solo and group project subjects (each with its scale, deliverables, chapters used and success criterion, at least one of them the study of a research paper), a written-exam proposal with sample questions and expected answers, and a grading rubric. These are proposals of these notes; the official assessment of each course is quoted in its fiche.

The end-of-year projects page proposes ten integrative projects that make the courses work together, one repository per team:

  • Year 1, end of Period 2 — combining Machine Learning, a Deep Learning course and the mandatory Reinforcement Learning, Graph ML and NLP courses, graded through the official Period 2 vehicles (Graph ML team project, RL course project, NLP capstone): GraphRAG with a learned retrieval router · fleet dispatch with natural-language bookings · cold-start news recommendation · molecules from words · scene-graph question answering.
  • Year 2, Transverse project (8 ECTS) — combining Large Language Models and Geometric Data with the Period 2 advanced topics: biomedical GraphRAG with calibrated abstention · a text-to-3D-molecule copilot · voice-first 3D product search · a natural-language dispatcher over exact and learned routing · fraud alerts under attack and drift.

The courses share one set of symbols, listed on the notation conventions page, so that a student moving from one course to the next reads the same notation.

Official documentation

These notes are independent; enrolment rules, ECTS and course lists live in the official sources:

After the master

An overview of the roles and problem spaces the track opens onto — inferred from the curriculum and these notes, not an official employability claim.

  • Graph × LLM systems engineer — own the diagnosis: where relational structure and text together change the decision (fraud, recommendation, knowledge graphs), and where a simpler model is enough.
  • Retrieval and knowledge-platform engineer — graph-augmented RAG over document and entity graphs: multi-hop retrieval, hallucination control with neighbourhood constraints, structured citation of graph nodes.
  • ML infrastructure engineer for industrial graphs — neighborhood sampling, over-squashing, depth and GPU budgets on billion-edge graphs; versioning graphs, embeddings and evaluations.
  • Trustworthy-AI engineer — robustness, privacy and explainability inside generation pipelines: attacks on graph retrieval, leakage via sensitive subgraphs, honest explanations of GNN + LLM decisions.
  • Research engineer / PhD track — open problematics at the Graph × LLM frontier: reliable knowledge graphs feeding LLMs, neuro-symbolic reasoning, geometric deep learning beyond flat GNNs.