From a1c26909092c8a39a4be1fca15ae90984c90bdfa Mon Sep 17 00:00:00 2001
From: Dane Sabo <dane.sabo@pitt.edu>
Date: Mon, 7 Jul 2025 11:46:39 -0400
Subject: [PATCH] vault backup: 2025-07-07 11:46:38

---
 ...mal Methods applied to Machine Learning.md | 12 ++++++----
 ...mal Methods applied to Machine Learning.md | 23 +++++++++++++++----
 2 files changed, 26 insertions(+), 9 deletions(-)

diff --git a/Literature Notes/A Review of Formal Methods applied to Machine Learning.md b/Literature Notes/A Review of Formal Methods applied to Machine Learning.md
index 9782e66c..02106f84 100644
--- a/Literature Notes/A Review of Formal Methods applied to Machine Learning.md	
+++ b/Literature Notes/A Review of Formal Methods applied to Machine Learning.md	
@@ -7,7 +7,7 @@ authors:
   
 citekey: "urbanReviewFormalMethods2021"
 publish_date: 2021-04-21
-last_import: 2025-06-30
+last_import: 2025-07-07
 ---
 
 # Indexing Information
@@ -18,8 +18,7 @@ Published: 2021-04
 #Computer-Science---Machine-Learning, #Computer-Science---Logic-in-Computer-Science, #Computer-Science---Programming-Languages
 
 
-#InFirstPass
-
+#ToRead
 
 
 >[!Abstract]
@@ -207,7 +206,7 @@ Published: 2021-04
 
 >[!tip] Brilliant
 > hen the training inputs are not linearly separable in the input space, the input space is implicitly projected, using so-called kernel functions, into a much higher-dimensional space in which the training inputs become linearly separable. This allows a support vector machine to also learn non-linear decision boundaries.
-> 2025-06-30 1:59 pm
+> 2025-07-07 11:41 am
 >
 
 >[!done] Important
@@ -239,6 +238,7 @@ Published: 2021-04
 
 
 
+
 ## Follow-Ups
 
 >[!example] 
@@ -277,3 +277,7 @@ Published: 2021-04
   >[107] B. Livshits, M. Sridharan, Y. Smaragdakis, O. Lhot  ́ak, J. Nelson Amaral, B.-Y. E. Chang, S. Z. Guyer, U. P. Khedker, A. Møller, and Dimitrios Vardoulakis. In Defense of Soundiness: A Manifesto. 2015.
   >- [ ]  #Follow-Up
   
+>[!example] 
+  >[131] F. Ranzato, M. Zanella Robustness Verification of Support Vector Machines. In SAS 2019.
+  >- [ ]  #Follow-Up
+  
diff --git a/Notes on Papers/A Review of Formal Methods applied to Machine Learning.md b/Notes on Papers/A Review of Formal Methods applied to Machine Learning.md
index d3784415..aee652e4 100644
--- a/Notes on Papers/A Review of Formal Methods applied to Machine Learning.md	
+++ b/Notes on Papers/A Review of Formal Methods applied to Machine Learning.md	
@@ -23,7 +23,6 @@ Very well written, easy to understand. Except, what is abstractification of a
 network?
 
 # Second Pass
-**What is the main thrust?**
 This review gives an overview of formal methods applied to machine learning.
 Formal methods has been used for ML to test for robustness for various 
 perturbations on inputs. They start by talking about several types of formal 
@@ -47,12 +46,26 @@ That way, if a safety condition is violated, the SMT solver will pick it up as a
 counter example. 
 
 MILP based solvers are Mixed Integer Linear Programming solvers. MILPs use
-linear programming where certain constraints are integers to reduce the solving space.
+linear programming where certain constraints are integers to reduce the
+solving space. Instead of having an explicity satisffiability condition on safety
+or not, MILPs instead can use a minimizing function to generate counter
+examples. For example, a MILP saftey condition might be formalized as:
+$$ \text{min}\space \bf{x}_n$$
+where a negative value of $\bf{x}_n$ is 'a valid counter example'.
 
-**What is the supporting evidence?**
+There are also 'incomplete formal methods'. These incomplete methods are
+sound, meaning they will not produce false negatives, but they may not be
+complete, meaning they may produce false positives. They scale better, but
+the false positives can be pretty annoying.
 
-**What are the key findings?**
-Local robustness
+One of the main incomplete methods is abstract interpretation. Things get very
+weird very fast--this is all about zonotopes and using over approximation of sets
+to say things about stability. There is weird stuff going on with cell splitting 
+and merging that seems like a to grasp. But, apparently it works. 
+
+Next, they spend some time talking about other machine learning methods and
+the formal methods that have been applied to them. Of particular interest to me
+is the formal method application to support vector machines and decision trees. 
 
 # Third Pass
 **Recreation Notes:**