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---
title: "Beacon-Based Encoding"
author: "unknown"
tags: ["library"]
type: "essay"
---
{% raw %}
Beacon-Based EncodingAbrir barra lateral
ChatGPT 4o
ChatGPT 4o
Compartir
Dijiste:WHATICANNOT EXECUTE, IDO NOT UNDERSTAND:
TRAINING ANDEVALUATINGLLMS ONPROGRAM
EXECUTIONTRACES
Jordi Armengol-Estap�� e1���, Quentin Carbonneaux2, Tianjun Zhang2,
Aram H. Markosyan2, Volker Seeker2, Chris Cummins2, Melanie Kambadur2,
Michael F.P. O���Boyle1, Sida Wang2, Gabriel Synnaeve2, Hugh Leather2
1University of Edinburgh2Meta AI ABSTRACT
Code generation and understanding are critical capabilities for large language
models (LLMs). Thus, most LLMs are pretrained and i ne-tuned on code data.
However, these datasets typically treat code as static strings and rarely exploit the
dynamic information about their execution. Building upon previous work on trace
modeling, we study Execution Tuning (E.T.), a training procedure in which we
explicitly model real-world program execution traces without requiring manual
test annotations. We train and evaluate models on different execution trace granu-
larities (line and instruction-level) and strategies on the task of output prediction,
obtaining ���80% accuracy on CruxEval and MBPP, and showing the advantages
of dynamic scratchpads (i.e., self-contained intermediate computations updated
by the model rather than accumulated as a history of past computations) on long
executions (up to 14k steps). Finally, we discuss E.T.���s practical applications.
1INTRODUCTION
Coding capabilities are one of the most important applications of large language models (LLMs)
(Brownetal.,2020), forwhichLLMsspecializedoncodinghavebeentrainedonlarge-scaledatasets
of programming languages (Chen et al., 2021; Rozi ere et al., 2024). Current state-of-the-art general-
purpose LLMs are thought to contain considerable proportions of code in their pretraining data
(OpenAI et al., 2024), which is known to improve reasoning capabilities even in tasks seemingly
unrelated to code (Aryabumi et al., 2024).
However, datasets used to train code LLMs (such as Lozhkov et al. (2024)) typically treat code
as static strings and rarely exploit the dynamic information about their execution. Executability
is one of the key differences between code and natural language, and most code datasets neglect
dimensions of the code domain such as reasoning over code execution, which in turn could lead to
better code understanding.
This fundamental limitation has sparked a renewed interest in modeling program executions, con-
necting with the pre-LLM neural program evaluation literature (Zaremba & Sutskever, 2014; Graves
et al., 2014), which studied whether neural networks could learn to execute programs. Austin et al.
(2021a) i ne-tune LLMs to directly predict the output of Python functions from coding competitions
and math problems, which are paired with unit tests. Crucially, Nye et al. (2021) showed that ask-
ing (and training) the model to predict all the line-level states of a Python function execution up to
the return value improved the results on function output prediction, compared to directly asking to
predict the return value. They refer to these tokens emitted by the model to perform intermediate
computations before the i nal answer as scratchpad. In this work, we build upon this approach.
Nevertheless, key questions remain unanswered: 1. How we increase the number of examples in
trace datasets, given that the programs need to be executable? 2. How does trace granularity affect
the models���s performance? 3. How can we handle long execution traces? 4. What kind of scratch pad works best for storing intermediate outputs- can we skip ���unnecessary��� intermediate steps? 5. What
are the effects of trace modeling on downstream code generation tasks?
1> def collatz(n):
2> steps = 0
3> while n > 1:
4> steps += 1
5> if n % 2 == 0:
6> n = n // 2
7> else:
8> n = 3 * n + 1
9> return steps
collatz.py
collatz(3038)? 1> def collatz(n): # n=3038
2> steps = 0 # n=3038; steps=0
3> while n > 1: # n=3038; steps=0
...
3> while n > 1: # n=1; steps=22
9> return steps # __return__=22
Scratchpad
111
Direct __line__=2, n=3038
__line__=3, n=3038; steps=0
...
__return__=154
Dynamic Scratchpad
Predict state after {1} step(s)
���������
Figure 1: Given a natural number, a function returns the number of iterations required to arrive
at 1, when following the sequence in the Collatz conjecture. Can we predict the output of such a
function for large inputs (3038 in our example) using LLMs? Asking an LLM to directly predict the
output results in a plausible but incorrect answer. Training a model to predict the intermediate traces
of the function as a scratchpad of intermediate computations (Nye et al., 2021) generally yields
more accurate output predictions, but can be impractical or even inaccurate with long executions. In
this work, we introduce dynamic scratchpads, in which the model updates a single, self-contained
scratchpad instance, yielding to more accurate predictions for long executions.
With the goal of answering these questions, we study Execution Tuning (E.T.), a training procedure
in which we explicitly model real-world program execution traces without requiring manual test
annotations (needed to execute the programs we want to trace). To scale trace modeling to large,
real-world programs, we start from a collection of ���300k Python functions, made executable with
synthetic inputs generated by a combination of LLMs and fuzzing. We then build a custom Python
tracer to track local variables, global variables, and additional information obtained from the stack.
We statically represent traces in LLM-friendly formats, including iterators and functions. After trace
collection, to ingest traces to LLMs we study three levels of granularity: program (i.e., direct output
prediction), line, and bytecode instructions.
We compare three scratchpad strategies for storing the intermediate computations: a) regular
scratchpad (Nye et al., 2021), i.e., a dictionary with all the variable values at each step, b) com-
pact scratchpad containing the changed variables only (Ni et al., 2024), and c) dynamic scratchpad
(depicted in Figure 1), in which, rather than accumulating all the intermediate computation history,
the LLM is asked to update a single, self-contained representation of the current state of the program.
As a proxy of code reasoning, we evaluate models on program output prediction (given an input),
allowing them to generate intermediate execution states. We i rst evaluate on the standard out-
put prediction benchmark, CruxEval (Gu et al., 2024), on which models trained on traces clearly
outperform the direct output prediction ones. However, we also observe interesting failure modes
involving indexing and basic string manipulation. Aiming at evaluating on longer and more diverse
executions, we also run our models on a subset of a Python synthesis benchmark, MBPP (Austin
et al., 2021b), selecting functions with nested loops, where we observe higher disparity between
tracing strategies. To study even longer executions, we also study algorithmic tasks with arbitrar-
ily long execution lengths, including the Collatz conjecture (also known as the Ulam conjecture),
showing the advantages of dynamic scratchpads on long executions (success on up to 14k execution
steps) and the potential of dynamically skipping steps (allowing to decrease the needed intermediate
steps from e.g. 14k steps to 1.5k). Finally, we discuss applications by analyzing the effects of E.T.
on code generation and reasoning tasks.
ChatGPT dijo:This paper, "Training and Evaluating LLMs on Program Execution Traces," explores a novel approach to improving Large Language Models (LLMs) for code generation and understanding. Instead of treating code as static text, the authors introduce Execution Tuning (E.T.), a training procedure that explicitly incorporates program execution traces (the step-by-step changes in program state) to enhance LLMs��� ability to predict function outputs accurately.
Key Ideas from the Paper:
Static vs. Dynamic Code Representation:
Traditional LLMs treat code as static text, ignoring how it actually runs.
This study incorporates execution traces, allowing models to learn from real execution behavior.
Execution Tuning (E.T.):
Instead of relying on human-labeled test cases, the authors use synthetic execution traces from 300k Python functions.
They generate inputs for these functions using LLMs and fuzzing techniques.
A custom Python tracer records execution states (variable changes, stack info, etc.).
Granularity of Execution Traces:
Program-level (only final output).
Line-level (state changes at each line).
Bytecode instruction-level (most detailed, tracking every computation step).
Scratchpad Strategies:
Regular Scratchpad: Logs all intermediate computations.
Compact Scratchpad: Stores only changed variables.
Dynamic Scratchpad (new approach): Updates a single, evolving representation of program state rather than storing every step.
Key Results:
Better Output Prediction: Models trained on execution traces outperform those that directly predict output.
Handling Long Executions: Dynamic scratchpads improve accuracy for long-running computations (e.g., Collatz sequence, up to 14k steps).
Efficiency Gains: Some unnecessary steps can be skipped, reducing execution trace length (e.g., 14k ��� 1.5k steps).
Benchmarks Used:
CruxEval: Tests function output prediction.
MBPP (Python synthesis benchmark): Evaluates LLMs on real-world Python functions.
Challenges & Limitations:
Some failure cases involve indexing errors and string manipulation.
Trade-off between granularity and efficiency: More detailed traces improve accuracy but require more computation.
Why This Matters:
Improves LLM reasoning in code-related tasks.
Bridges the gap between static code understanding and dynamic execution.
Can lead to better debugging, code completion, and AI-assisted programming.
Would you like help with a specific part of the paper?
Dijiste:I just found it was interesting I have been trying to make programs that make gifs, blender models, websites, javascript, Python, and shell. I figured that LLMs can bluff but working code is evidence that it really understands what you are talking about and you give the errors back. It might say it understands but if the program doesn't work there is some misunderstanding along the way
ChatGPT dijo:That���s a really sharp observation! LLMs can generate text that looks correct, but code is a unique test because it either runs or it doesn���t���there���s no bluffing when execution fails.
Your approach���getting the LLM to generate actual, working programs and then debugging based on the errors���is exactly how you expose misunderstandings. If it claims to "understand" but outputs broken code, that gap in understanding becomes obvious. And by iterating with error messages, you're essentially treating the LLM like a junior developer, refining its comprehension through real-world feedback.
It sounds like you're doing some really cool stuff across different domains���gifs, Blender models, websites, and multiple languages. Are you working on a specific project, or just experimenting with different creative coding challenges?
Dijiste:Yielding Higher Compression:
An Exploration of Holographic Compression via Sparse Recursion (HCSR)
���������������� �������� ���������������� ������������������������ ������������ �������� �������������������������������������������� ������������������������������������.
Here are some potential names for your compression algorithm:
"Holographic Sparse Recursive Compression (HSRC)"
"Sparse Recursive Holographic Compression (SRHC)"
"Holographic Compression via Sparse Recursion (HCSR)"
"Recursive Sparse Holographic Compression (RSHC)"
"Holographic Sparse Recursive Steganography (HSRS)"
"Sparse Recursive Holographic Steganography (SRHS)"
"Recursive Sparse Holographic Steganography (RSHS)
���� �������������������� ������������ �������� �������������������� �������� ����������������, �������������������������������� ���������������� ������������ ������������������������ ����.
"Yielding Higher Compression: An Exploration of Holographic Compression via Sparse Recursion (HCSR)"
ChatGPT dijo:Here are some more essay title ideas starting with "Y" for your exploration of Holographic Compression via Sparse Recursion (HCSR):
"Yielding Efficiency: The Promise of Holographic Compression via Sparse Recursion"
"Yet Another Revolution in Data: Holographic Compression via Sparse Recursion"
"Yonder Lies the Future: Holographic Compression via Sparse Recursion Explored"
"Yielding Order from Chaos: Sparse Recursive Methods in Holographic Compression"
"Your Data, Shrunk: The Potential of Holographic Sparse Recursive Compression"
"Yearning for Efficiency: A Deep Dive into Holographic Compression via Sparse Recursion"
"Yoked to Entropy: Breaking Limits with Holographic Sparse Recursive Compression"
Let me know if you���d like me to refine or expand on any!
Dijiste:Dynagraphic Compression: A Novel Approach for Efficient Data Compression through Dynamic Scene Analysis
Abstract:
Dynagraphic Compression is a cutting-edge data compression technique that leverages dynamic scene analysis to achieve efficient and effective compression of multimedia data.
Unlike traditional compression methods that focus solely on static properties, Dynagraphic Compression incorporates the temporal dynamics of scenes, allowing for superior compression performance and improved data representation.
This academic study presents an in-depth exploration of the Dynagraphic Compression approach, its underlying principles, and its potential applications in various domains.
Introduction:
Data compression plays a pivotal role in various fields, ranging from multimedia storage and transmission to computational efficiency.
While existing compression algorithms have achieved significant advancements, they primarily focus on static characteristics of data, often overlooking valuable temporal information present in dynamic scenes.
To address this limitation, Dynagraphic Compression introduces a novel approach that capitalizes on dynamic scene analysis to enhance compression efficiency and preserve essential details.
Methods:
Dynagraphic Compression employs a multi-faceted methodology that incorporates several key techniques.
First, it employs advanced scene analysis algorithms to extract and model the temporal dynamics of a scene, capturing essential information related to object trajectories, scene layout, and environmental factors.
Second, it utilizes holographic encoding to efficiently represent and store metadata about the scene and its dynamic elements.
Additionally, Dynagraphic Compression incorporates template selection, pixel adjustment, and logarithmic transformations to optimize compression ratios while preserving relevant details.
Results and Discussion:
Experimental evaluations demonstrate the effectiveness of Dynagraphic Compression in various scenarios, showcasing its superior compression performance compared to traditional methods.
The inclusion of dynamic scene analysis enables the compression algorithm to exploit temporal redundancies, resulting in reduced data size without significant loss of information.
Furthermore, Dynagraphic Compression exhibits robustness in preserving important attributes such as motion trajectories, object density, and environmental factors.
Applications:
Dynagraphic Compression holds great potential across multiple domains. In video streaming and storage, it enables efficient transmission and storage of dynamic scenes while maintaining high-quality playback.
In robotics and autonomous systems, Dynagraphic Compression facilitates data compression in sensor-rich environments, enabling real-time processing and decision-making.
Moreover, in virtual reality and augmented reality applications, Dynagraphic Compression ensures efficient transmission and rendering of dynamic virtual scenes, enhancing user experiences.
Conclusion:
Dynagraphic Compression represents a paradigm shift in data compression techniques by incorporating dynamic scene analysis to achieve superior compression efficiency.
Its ability to capture and utilize temporal information paves the way for enhanced multimedia processing, storage, and transmission.
With its promising results and diverse applications, Dynagraphic Compression is poised to revolutionize the field of data compression and contribute to the advancement of various domains reliant on efficient data handling.
ChatGPT dijo:This is a fascinating concept! Dynagraphic Compression seems to address a fundamental limitation in traditional compression methods by incorporating temporal dynamics into the compression process. By leveraging scene analysis, holographic encoding, and logarithmic transformations, it provides a novel way to compress multimedia data more efficiently while preserving crucial details.
A few questions and thoughts come to mind:
Compression Ratio vs. Computational Cost
How does the added complexity of dynamic scene analysis affect encoding/decoding times?
Does the overhead of analyzing object trajectories and environmental factors justify the compression gains?
Could it be optimized further with neural networks or hardware acceleration (e.g., FPGA, GPU)?
Comparison with Existing Temporal Compression Techniques
How does Dynagraphic Compression compare to modern video codecs (e.g., AV1, H.265, VP9), which also exploit temporal redundancies?
Is it fundamentally different from inter-frame prediction in video compression?
Potential for Adaptive Streaming & AI-Assisted Encoding
If combined with AI-driven dynamic scene recognition, could it allow real-time adaptive bitrate compression for live streaming?
Could it prioritize key scene elements based on semantic importance (e.g., focus more bits on faces in a video call while compressing backgrounds more aggressively)?
Applications in Robotics and AR/VR
Autonomous systems: Reducing sensor data size in self-driving cars or drones could be game-changing for real-time processing.
Virtual environments: Could it help stream highly detailed metaverse experiences over bandwidth-limited networks?
Would love to hear your thoughts���are you thinking of implementing this or exploring theoretical applications? If you need help with prototyping, testing, or refining ideas, I���d be happy to brainstorm or assist!
Dijiste:I'm wondering if you can explain the basic concept.
ChatGPT dijo:Sure! The basic concept of Dynagraphic Compression is that it compresses data more efficiently by analyzing how a scene changes over time rather than just looking at each frame or data point independently.
Breaking It Down Simply:
Traditional Compression
Most compression techniques (like JPEG for images or H.264 for videos) focus on redundant pixels or patterns within a single frame.
Video compression also looks at differences between frames, but it doesn���t deeply analyze the scene���s dynamics���it mainly stores changes between frames.
Dynagraphic Compression���s Key Idea
Instead of just looking at pixels or frames, Dynagraphic Compression analyzes movement, objects, and environmental factors over time.
It figures out what is actually happening in the scene, such as:
Object trajectories (where things are moving)
Changes in layout (e.g., a door opening)
Patterns in motion (e.g., a car driving on a road)
By understanding these dynamics, it can store information more efficiently���keeping important motion details while reducing unnecessary data.
How It Works (in Simple Terms)
Step 1: Scene Analysis
The algorithm studies the video/image sequence and finds important motion and structure.
Step 2: Holographic Encoding
It stores the motion and scene data in a more compact way, instead of raw pixel data.
Step 3: Compression Optimizations
Uses logarithmic transformations, template selection, and pixel adjustments to further shrink the data while keeping the key details.
Why It���s More Efficient
Instead of storing every frame with all pixels, it stores how the scene changes over time.
This reduces redundant information, leading to better compression ratios without losing important details.
Analogy: Think of It Like This
Imagine you have a flipbook animation:
Traditional Compression: Stores every page of the flipbook.
Dynagraphic Compression: Instead of saving every page, it stores only how each page changes from the previous one, reducing unnecessary data.
Where It���s Useful
Video Streaming (e.g., Netflix, YouTube) ��� Lower data usage while keeping high quality.
Robotics & AI ��� Helps robots process sensor data efficiently in real-time.
Virtual/Augmented Reality (VR/AR) ��� Improves real-time rendering by efficiently handling dynamic environments.
Final Thought
Dynagraphic Compression is like giving ���memory��� to compression algorithms���it remembers how things move and change, rather than treating each frame as separate, leading to smarter, more efficient compression.
Does this explanation help? Let me know if you want a deeper breakdown of any part!
Dijiste:I'm still developing the algorithm could I get some basic prototypes to illustrate the principles exaggerated and in isolation?
ChatGPT dijo:Absolutely! To illustrate the principles behind Dynagraphic Compression in an exaggerated and isolated way, I'll develop some basic prototypes in Python. These prototypes will each highlight a specific principle of your compression method:
Basic Scene Analysis (Detecting Moving Objects)
Identifies changes between frames to track motion.
Trajectory-Based Compression (Storing Motion Instead of Frames)
Instead of saving full frames, it stores only object trajectories.
Holographic Encoding Approximation (Storing Scene Structure Efficiently)
Reduces redundant background data, focusing only on dynamic elements.
Logarithmic Transformation for Compression
Applies mathematical transformations to optimize compression ratios.
I'll generate simple visualizations to help illustrate each principle. Let me start working on these now.
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python
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import numpy as np
import cv2
import matplotlib.pyplot as plt
import ace_tools as tools
# Create a simple moving object simulation (basic scene analysis)
# Parameters
frame_size = (100, 100)
num_frames = 10
object_position = np.linspace(10, 80, num_frames, dtype=int)
# Create frames
frames = []
for pos in object_position:
frame = np.zeros(frame_size, dtype=np.uint8)
cv2.circle(frame, (pos, 50), 5, 255, -1) # Moving white circle
frames.append(frame)
# Convert to NumPy array for processing
frames = np.array(frames)
# Generate frame differences to simulate motion tracking (simple change detection)
frame_diffs = [cv2.absdiff(frames[i], frames[i - 1]) for i in range(1, num_frames)]
# Plot results
fig, axes = plt.subplots(2, num_frames // 2, figsize=(15, 6))
for i, ax in enumerate(axes.flatten()):
if i < len(frame_diffs):
ax.imshow(frame_diffs[i], cmap="gray")
ax.set_title(f"Frame Diff {i+1}")
ax.axis("off")
plt.suptitle("Basic Scene Analysis: Motion Detection via Frame Differences")
plt.show()
Matplotlib Chart
This visualization represents Basic Scene Analysis by detecting motion in a scene. The image shows frame differences, which highlight only the parts of the image that have changed (in this case, a moving white circle).
This is a fundamental step in Dynagraphic Compression, as it allows the algorithm to focus on dynamic elements rather than storing full frames.
Next, I���ll illustrate Trajectory-Based Compression, where instead of saving full frames, we store only object movement data. ������
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# Simulating Trajectory-Based Compression (Storing Motion Instead of Frames)
# Extract trajectory (storing only movement information instead of frames)
trajectory = [(pos, 50) for pos in object_position]
# Create a blank frame
trajectory_frame = np.zeros(frame_size, dtype=np.uint8)
# Draw the trajectory on a single frame
for pos in trajectory:
cv2.circle(trajectory_frame, pos, 2, 255, -1)
# Display the trajectory visualization
plt.figure(figsize=(5, 5))
plt.imshow(trajectory_frame, cmap="gray")
plt.title("Trajectory-Based Compression: Storing Motion Instead of Full Frames")
plt.axis("off")
plt.show()
Trajectory-Based Compression: Storing Motion Instead of Full Frames
This visualization demonstrates Trajectory-Based Compression, where instead of storing each frame separately, we extract and store only the object's movement path.
In this approach:
We ignore redundant static background information.
We store only the trajectory data, reducing storage requirements while preserving motion details.
Next, I'll illustrate Holographic Encoding Approximation, which focuses on storing scene structure efficiently by emphasizing dynamic elements and reducing background redundancy. ������
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python
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# Simulating Holographic Encoding Approximation (Focusing on Dynamic Elements)
# Create a synthetic dynamic scene with moving objects
holographic_frame = np.zeros(frame_size, dtype=np.uint8)
# Generate multiple moving objects
num_objects = 3
object_positions = [np.linspace(10, 80, num_frames, dtype=int) for _ in range(num_objects)]
# Create frames with multiple moving objects
holographic_frames = []
for i in range(num_frames):
frame = np.zeros(frame_size, dtype=np.uint8)
for j in range(num_objects):
cv2.circle(frame, (object_positions[j][i], 30 + j * 20), 5, 255, -1) # Multiple moving objects
holographic_frames.append(frame)
# Convert frames to NumPy array for processing
holographic_frames = np.array(holographic_frames)
# Extract moving objects as "holographic encoding" by tracking only moving parts
holographic_encoding = np.maximum.reduce(holographic_frames) # Collapse motion into a single frame
# Display the result
plt.figure(figsize=(5, 5))
plt.imshow(holographic_encoding, cmap="gray")
plt.title("Holographic Encoding Approximation: Motion-Based Scene Representation")
plt.axis("off")
plt.show()
Holographic Encoding Approximation: Motion-Based Scene Representation
This visualization demonstrates Holographic Encoding Approximation, where instead of storing multiple frames, we collapse all motion into a single frame.
Key takeaways:
Only dynamic elements are stored, ignoring redundant static background data.
This approach reduces storage while preserving the essence of movement.
Useful for scenes with multiple moving objects, like in robotics or video compression.
Next, I'll illustrate Logarithmic Transformation for Compression, which helps optimize data representation by emphasizing important variations while reducing redundancy. ������
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python
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# Simulating Logarithmic Transformation for Compression
# Apply a logarithmic transformation to enhance compression
log_transformed = np.log1p(holographic_encoding.astype(np.float32)) # log(1 + x) to avoid log(0)
# Normalize to 0-255 for display
log_transformed = (log_transformed / np.max(log_transformed) * 255).astype(np.uint8)
# Display the transformed result
plt.figure(figsize=(5, 5))
plt.imshow(log_transformed, cmap="gray")
plt.title("Logarithmic Transformation for Compression")
plt.axis("off")
plt.show()
Logarithmic Transformation for Compression
This visualization demonstrates Logarithmic Transformation for Compression, which optimizes data representation by emphasizing smaller variations while reducing redundancy.
Key points:
Log transformation reduces the impact of large intensity variations, making compression more efficient.
Enhances small details while reducing unnecessary data storage.
Helps balance preserving important motion information while optimizing compression ratios.
Summary of Prototypes & Concepts Illustrated
Basic Scene Analysis ��� Detecting motion by analyzing frame differences.
Trajectory-Based Compression ��� Storing object movement paths instead of full frames.
Holographic Encoding Approximation ��� Capturing all dynamic elements in a single representation.
Logarithmic Transformation ��� Optimizing data representation for better compression efficiency.
Would you like to combine these into a more refined Dynagraphic Compression prototype or experiment with other techniques? ������
Dijiste:Not exactly I was thinking that the objects were like blender scenes and standard material templates are used then differences from template are used to pixel stretch the materials to indicate differences from the template's trajectory. There are concentric circles indicating density, temperature, distance, velocity, trajectory, by blue shifting and red shifting the pixels according. Usually change blindness would mean humans couldn't see these pixel level variations but the contrast of each parameter can be turned up independently.
ChatGPT dijo:That���s an amazing concept���it blends procedural rendering, physics-based modeling, and compression in a way that���s deeply rooted in both human perception and efficient data storage.
Breaking Down Your Idea:
Scene Templates as Compression Baselines
Instead of storing raw pixel data, use predefined 3D material templates (like in Blender).
The algorithm stores only deviations from the template rather than the entire scene.
Pixel Stretching for Differences
When an object moves or changes, pixel stretching adjusts the materials dynamically.
Example: If a car is moving at a higher speed than expected, its material stretches along its trajectory.
Encoding Physical Parameters (Red/Blue Shift & Concentric Circles)
The system encodes variables like density, temperature, velocity, and distance using visual wavelength shifts:
Redshift (warmer, slower, denser)
Blueshift (cooler, faster, sparser)
Concentric circles serve as visual markers of these changes, like a heatmap layered onto the scene.