From a6ec4288a2232988b130b2f00bb2565f81706966 Mon Sep 17 00:00:00 2001
From: YurenHao0426 <blackhao0426@gmail.com>
Date: Mon, 29 Jun 2026 12:15:51 -0500
Subject: Recursive reasoning dynamics: analysis pipeline, paper drafts, toy
 models

Failure=more-chaotic (task-general under validity labeling) reduces to convergence/completeness
detection; mechanism (transient chaos vs multistability vs input-induced) under investigation.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
---
 external/GradientFlossing/README.md    | 79 ++++++++++++++++++++++++++++++++++
 external/GradientFlossing/packages.txt |  6 +++
 2 files changed, 85 insertions(+)
 create mode 100644 external/GradientFlossing/README.md
 create mode 100644 external/GradientFlossing/packages.txt

(limited to 'external/GradientFlossing')

diff --git a/external/GradientFlossing/README.md b/external/GradientFlossing/README.md
new file mode 100644
index 0000000..962c955
--- /dev/null
+++ b/external/GradientFlossing/README.md
@@ -0,0 +1,79 @@
+# Gradient Flossing: Improving Gradient Descent through Dynamic Control of Jacobians
+
+This repository contains the implementation code for manuscript: <br>
+__Gradient Flossing: Improving Gradient Descent through Dynamic Control of Jacobians__ <br>
+## Overview
+In this work we show that RNN training can be improved by pushing Lyapunov exponents of the forward pass to zero during or before training.
+
+## Installation
+
+#### Prerequisites
+- Download [Julia](https://julialang.org/downloads/) 
+
+#### Dependencies
+- Julia (1.6)
+- Flux, BackwardsLinalg
+
+## Getting started
+To install the required packages, run the following in the julia REPL after installing Julia:
+
+```
+using Pkg
+
+for pkg in ["Flux", "BackwardsLinalg"]
+    Pkg.add(pkg)
+end
+```
+
+For example, to train an RNN on tracking delayed XOR task, run:
+```
+include("GradientFlossing_ExampleCode.jl")
+# setting parameters:
+N, E, Ef, Ei, Ep, Ni, B, S, T, Tp, Ti, sIC, sIn, sNet, sONS, lr, b1, b2, IC, g, gbar, I1, delay, wsS, wsM, wrS, wrM, bS, bM, nLE, task, intype, Lwnt=
+80, 3001, 100, 500, 500, 2, 16, 1, 300, 55, 300, 1,1,1,1, 0.001f0, 0.9, 0.999, 1, 1.0, 0.0, 1.0,10, 1.0f0, 0.0f0, 1.0f0, 0.0f0, 0.1f0, 0.0f0,75, -1, 3, 0.0
+
+trainRNNflossing(N, E, Ef, Ei, Ep, Ni, B, S, T, Tp, Ti, sIC, sIn, sNet, sONS, lr, b1, b2, IC, g, gbar, I1, delay, wsS, wsM, wrS, wrM, bS, bM, nLE, task, intype, Lwnt)
+```
+
+## Repository Overview
+_GradientFlossing_ExampleCode.jl_:\
+Example scripts for training networks with gradient flossing before training, with gradient flossing before and during training and without gradient flossing.
+
+
+_GradientFlossing_XOR.jl_:\
+Generates input and target output for copy task and delayed XOR task.
+
+<!---
+
+runOneStimulus.jl trains an RNN on tracking one OU-signal showing that the network becomes more tightly balanced over training epochs.\
+runTwoStimuli.jl trains an RNN on two OU-signal stimulus showing that the network becomes more tightly balanced over training epochs and breaks up into two weakly-connected subnetworks.\
+runTheeStimuli.jl trains an RNN on two OU-signal stimulus showing that the network becomes more tightly balanced over training epochs and breaks up into three weakly-connected subnetworks.\
+![Training RNN on two signals leads to balanced subpopulations](/figures/S=2.svg?raw=true "balanced subnetworks emerge  after runTheeStimuli.jl")
+-->
+
+
+<!---
+
+### Training dynamics of eigenvalues:
+Here is a visualization of the recurrent weight matrix and the eigenvalues throughout across training epochs.
+![Training dynamics of networks trained on multiple signals shows first tracking of global mean input](eigenvalue_movie_2D_task.gif)
+-->
+
+
+### Implementation details
+A full specification of packages used and their versions can be found in _packages.txt_ .\
+For learning rates the default ADAM parameters were used to avoid any impression of fine-tuning.\
+All simulations were run on a single CPU and took on the order of minutes to a few of hours.
+
+
+
+<!---
+### figures/
+Contains all figures of the main text and the supplement.
+-->
+
+
+<!---
+### tex/
+Contains the raw text of the main text and the supplement.
+-->
diff --git a/external/GradientFlossing/packages.txt b/external/GradientFlossing/packages.txt
new file mode 100644
index 0000000..e90facc
--- /dev/null
+++ b/external/GradientFlossing/packages.txt
@@ -0,0 +1,6 @@
+julia => v"1.6.7"
+
+[442b4e1a] BackwardsLinalg v0.1.1
+[587475ba] Flux v0.11.3
+[e6cf234a] RandomNumbers v1.5.3
+[e88e6eb3] Zygote v0.5.1
-- 
cgit v1.2.3