Feat/project llm validity (#46)

* feat(project): add llm validity project

* fix(propic): update davide beltrame's assets/img/team/ file

* feat(ui): add alternative (full) picture for project cover and support for distinct cover (all projects page) and header img (single project page)

* fixes

---------

Co-authored-by: giacomo-ciro <giacomociro02@gmail.com>

Author: davide-beltrame

_layouts/project.html

@@ -15,7 +15,7 @@
           <article class="article">
 
             <div class="post-img">
-              <img src="{{ page.cover }}" alt="{{ page.title }}">
+              <img src="{{ page.header_image | default: page.cover }}" alt="{{ page.title }}">
             </div>
 
             <h2 id="project-title" class="title text-center">{{ page.title }}</h2>

_projects/llm-validity.md

@@ -0,0 +1,32 @@
+---
+title: "LLM Validity via Enhanced Conformal Prediction: Conditional Guarantees, Score Learning, and Response-Level Calibration Under Dependent Claims"
+type: Article
+status: completed
+date: 2026-02-07
+cover: /assets/img/proj/llm_validity.png
+header_image: /assets/img/proj/llm_validity_cropped.png
+authors:
+  - name: "Davide Beltrame"
+    avatar: "/assets/img/team/davide_beltrame.jpg"
+    link: "https://www.linkedin.com/in/davide-beltrame/"
+    desc: "MSc in Artificial Intelligence"
+---
+
+Finite-sample validity guarantees for large language model (LLM) outputs are attractive because they are post-hoc and model-agnostic, but they are fragile when prompts are heterogeneous and factuality signals are noisy.
+
+Cherian et al. (2024) propose enhanced conformal methods for *factuality filtering* that (i) replace marginal guarantees with function-class conditional guarantees and (ii) improve utility via level-adaptive calibration and conditional boosting that differentiates through conditional conformal cutoffs.
+
+This discussion paper reviews the conformal prediction and LLM factuality context, presents the selected paper and proposes a future direction: *response-level conformalization under dependent claims*.
+The key idea is to treat an entire response as the exchangeable unit, use blocked calibration that keeps all claims from a response together, and calibrate response-level tail losses conditionally on prompt/response features to align guarantees with user-facing risk when claim errors are dependent.
+
+<div class="d-flex align-items-center justify-content-around">
+  <a href="/assets/reports/llm_validity_paper.pdf" class="btn-custom">Full Paper</a>
+  <a href="https://github.com/jjcherian/conformal-safety" class="btn-custom">Code (Conformal Safety)</a>
+  <a href="https://github.com/jjcherian/conditional-conformal" class="btn-custom">Code (Conditional Conformal)</a>
+</div>
+<br>
+
+**Notes:**
+- This work is a discussion paper of Cherian et al. (2024).
+- The authors released a [filtered `MedLFQA` benchmark](https://github.com/jjcherian/conformal-safety) with non-health-related prompts removed, as well as the generated/parsed text and experiment notebooks.
+- Their [conditional conformal inference Python package](https://github.com/jjcherian/conditional-conformal) now supports level-adaptive conformal prediction.