DSamuelHodge

# === Imports ===
import torch
import numpy as np
import matplotlib.pyplot as plt
from transformers import AutoModel, AutoTokenizer
import gudhi as gd
from sklearn.manifold import MDS
import warnings

warnings.filterwarnings("ignore")

DSamuelHodge

From Pairwise Attention to Many-Body Physics: The Hidden Phase Shift in Transformers

Derrick Hodge
Independent Researcher
derrick@hodgedomain.com

Abstract

We present evidence for a universal phase transition in transformer attention mechanisms that fundamentally alters their computational strategy based on input sequence length. Using Random Matrix Theory (RMT) baselines, spectral analysis, and information-theoretic measures, we demonstrate that transformers operate in two distinct regimes: a Local Interaction Regime for short sequences characterized by distributed pairwise processing, and a Collective Correlation Regime beyond a critical length $L_c$ featuring concentrated, non-local computation.

DSamuelHodge

# Topological Reasoning in Transformers: Semantic Loop Analysis
# Implementation of "Beyond Reinforcement Learning" - Geometric Theory of Transformer Reasoning

"""
ABSTRACT: 
We introduce a geometric theory of reasoning in Transformer models based on attention-induced 
topological structures. This notebook demonstrates that reasoning emerges from closed, high-energy 
attention loops—semantic circuits measurable through loop energy, holonomy, and attention geometry. 
This topological reasoning model enables prompt design and evaluation without external reward policies.

DSamuelHodge

Topological Reasoning in Transformers: Beyond Reinforcement Learning

Abstract

We introduce a geometric theory of reasoning in Transformer models based on attention-induced topological structures. Contrary to reinforcement learning-based paradigms that impose reasoning via reward optimization, we demonstrate that reasoning naturally emerges from closed, high-energy attention loops—semantic circuits measurable through loop energy, holonomy, and Ricci curvature. This topological reasoning model enables prompt design, evaluation, and model alignment without external reward policies.

---

1. Introduction

DSamuelHodge

import torch
import numpy as np
import pandas as pd
from scipy.linalg import svdvals
from transformers import AutoTokenizer, AutoModelForCausalLM
from transformers import logging as transformers_logging
import logging

# ──────────────────── CONFIGURATION PARAMETERS ────────────────────────────────
MODEL_NAME = "Qwen/Qwen2.5-0.5B"

DSamuelHodge

Core AEG Components in the Code

1. Complex Normalization Function

def normalize(self, z):
    rho = th.abs(z)
    theta = th.atan2(th.imag(z), th.real(z))
    return th.tanh(rho) * (th.cos(theta) + 1.0j * th.sin(theta))

This function maps complex values onto a curved manifold by:

DSamuelHodge

Acronyms and Notation Tables

Table 1: Definitions of acronyms used in HTSR

Acronym	Description
DNN	Deep Neural Network
ML	Machine Learning
SGD	Stochastic Gradient Descent
RMT	Random Matrix Theory

DSamuelHodge

WeightWatcher Advanced Usage Cheatsheet

🔍 Basic Analysis

Feature	Command	Description
Analyze Model Layers	watcher.analyze()	Analyze model layers for generalization, spectral properties, and overtraining.
Describe Model	watcher.describe(model=model)	Get model details without analyzing it.
Plot and Fit ESD	watcher.analyze(plot=True)	Plot the Empirical Spectral Density (ESD) of model layers and apply fits.
Generate Summary Statistics	summary = watcher.get_summary()	Generate summary statistics from analysis results to compare models.

DSamuelHodge

from manim import *

class GRPOExplanation(MovingCameraScene):
    def construct(self):
        # Title
        title = Text("DeepSeek-R1 Reinforcement Learning", font_size=36)
        subtitle = Text("Group Relative Policy Optimization (GRPO)", font_size=24)
        title_group = VGroup(title, subtitle).arrange(DOWN, buff=0.5)
        title_group.to_edge(UP, buff=1)

DSamuelHodge

import os
import math
from typing import List, Optional, Tuple, Union

import torch
import torch.nn.functional as F
from torch import nn

from transformers import AutoTokenizer, AutoModelForCausalLM, AutoConfig
from transformers.models.llama.modeling_llama import (