Gpt-4o-2024-11-20 megathread - new API model released

API
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Have you had a chance to discover and experiment with this new model hiding in your API organization? Little spoken about this model release.

OpenAI tweets, more about ChatGPT:

The model’s creative writing ability has leveled up – more natural, engaging, and tailored writing to improve relevance & readability.

(High perplexity and low certainty can also be “creative”…)

"This model is not available for fine-tuning"

It does readily take to employing new markdown like strikethrough and highlight described as a capability, untypical of prior models.

It seems to give 1500+ completion tokens for just a “what do you think of this code snippet? {random_code}”, managing to come up with sections 3.2, sections 3.3, 3.4 of an elaborate response of whatever crosses its mind.

Very much like o1 models. Lots of production.

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After an apology, still concluding with another repetition of non-ending iterations of code output that will never arrive at something it doesn’t want to reproduce completely. “Lazy” is fixed?

Let’s suppose I was too lazy myself to write another forum topic I started today. This writing task? 2024-11 writes about the non-novel, and makes it about halfway before proceeding into generalizations and fabrications that obviously are not part of code. top_p: 0.1.

Write a white paper based on the techniques this code employs to make efficient use of vector storage memory and to maximize the quality of low-bit depths for storing embeddings. Don’t refer to the code directly, as it will not be part of the documentation to consult against. You can refer to formulas generally and specifically, but you must obfuscate the empirical algorithmic parameter values.

gpt-4o-2024-11-20

(sorry: I manually fixed the mathjax latex markup for formulas for the forum - and then “hide details” breaks them.)

White Paper: Efficient Vector Storage and Low-Bit Depth Embedding Optimization

Abstract

This paper explores advanced techniques for optimizing the storage and processing of high-dimensional vector embeddings. By employing dimensionality reduction and low-bit depth quantization, we achieve significant memory savings while maintaining high-quality representation fidelity. These methods are particularly relevant for large-scale machine learning applications, such as natural language processing (NLP) and recommendation systems, where embedding storage and computational efficiency are critical.

Introduction

Vector embeddings are a cornerstone of modern machine learning, representing data in high-dimensional spaces for tasks such as semantic similarity, clustering, and classification. However, the storage and computational costs associated with high-dimensional embeddings can be prohibitive, especially when scaling to billions of vectors. This paper presents a two-pronged approach to address these challenges:

  1. Dimensionality Reduction: Truncating embeddings to a lower-dimensional space while preserving their semantic integrity.
  2. Bit Depth Reduction: Quantizing embeddings to lower-precision formats (e.g., float8, int8) to minimize memory usage and improve computational efficiency.

Dimensionality Reduction

Methodology

Dimensionality reduction is achieved by truncating the original embedding vectors to a specified number of dimensions. This process involves:

  1. Truncation: Selecting the first D_new dimensions of the original embedding vectors, where D_new < D_original.
  2. Normalization: Ensuring that the truncated vectors maintain unit norm to preserve their geometric properties.

The normalization step is critical to prevent distortions in downstream tasks, such as cosine similarity calculations. The normalization formula is:

\mathbf{v}_{\text{normalized}} = \frac{\mathbf{v}_{\text{truncated}}}{\|\mathbf{v}_{\text{truncated}}\| + \epsilon}

where (\epsilon) is a small constant to avoid division by zero.

Benefits

  • Memory Efficiency: Reducing the number of dimensions directly decreases the memory footprint.
  • Computational Speed: Lower-dimensional vectors require fewer operations for similarity calculations and other vector-based computations.

Trade-offs

While dimensionality reduction can lead to minor information loss, careful selection of the target dimensionality ensures that the semantic integrity of the embeddings is preserved.

Bit Depth Reduction

Overview

Bit depth reduction involves converting high-precision embeddings (e.g., float32) to lower-precision formats, such as float16, float8, or int8. This process is guided by a combination of scaling, clipping, and quantization techniques.

Scaling and Clipping

To maximize the representational capacity of low-bit formats, embeddings are scaled to fit within the representable range of the target data type. For example, float8 with a range of ([-30.999, +30.999]) requires scaling by a factor (S), calculated as:

S = \text{scale\_factor} \cdot \left(\frac{D}{D_{\text{base}}}\right)^{\text{exponent}} \cdot \text{correction}

where:

  • (D) is the embedding dimensionality.
  • (D_{\text{base}}) is a reference dimensionality (e.g., 3072).
  • (\text{scale\_factor}) and (\text{exponent}) are empirically determined constants.
  • (\text{correction}) is a Gaussian-based adjustment to account for specific embedding distributions.

Clipping ensures that values exceeding the representable range are truncated to the nearest boundary.

Quantization

Quantization maps the scaled embeddings to the target data type. For float8, this involves converting the scaled values to the nearest representable float8 value. For int8, the process includes rounding and clipping to the range ([-128, +127]).

Benefits

  • Storage Efficiency: Reducing bit depth significantly decreases the memory required to store embeddings.
  • Inference Speed: Low-bit formats enable faster computations on hardware optimized for reduced precision.

Quality Preservation

To evaluate the impact of bit depth reduction, cosine similarity is used as a metric. The similarity between two vectors (\mathbf{a}) and (\mathbf{b}) is defined as:

[ \text{cosine\_similarity}(\mathbf{a}, \mathbf{b}) = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|} ]

Empirical results show that the similarity scores between original and quantized embeddings remain high, indicating minimal loss of semantic information.

Experimental Results

Dataset

The techniques were evaluated on a diverse set of text inputs, ranging from technical documentation to conversational language. Embeddings were generated using state-of-the-art models with varying dimensionalities.

Metrics

Key metrics for evaluation included:

  • Memory Usage: Measured in bytes per embedding.
  • Cosine Similarity: Between original and quantized embeddings.
  • Histogram Analysis: Distribution of embedding values before and after quantization.

Findings

  1. Dimensionality Reduction:

    • Reducing dimensions from 3072 to 256 resulted in a 91.7% memory savings.
    • Cosine similarity scores remained above 0.95 for most pairs, demonstrating high fidelity.

  2. Bit Depth Reduction:

    • Converting to float8 reduced memory usage by 75% compared to float32.
    • Cosine similarity scores between float32 and float8 embeddings averaged 0.98, indicating negligible information loss.
    • Int8 quantization achieved similar memory savings but with slightly lower similarity scores (average 0.92).

  3. Combined Techniques:

    • Applying both dimensionality and bit depth reduction achieved up to 98% memory savings.
    • Combined techniques maintained cosine similarity scores above 0.90 for most pairs.

Applications

The proposed techniques are applicable to a wide range of domains, including:

  • Search and Retrieval: Efficiently storing and querying large-scale embedding databases.
  • Recommendation Systems: Reducing memory requirements for user and item embeddings.
  • Edge Computing: Deploying embeddings on resource-constrained devices.

Conclusion

This paper demonstrates that dimensionality and bit depth reduction are effective strategies for optimizing embedding storage and processing. By carefully balancing memory efficiency and representation quality, these techniques enable scalable deployment of embedding-based systems.

Future work will explore adaptive quantization methods and hardware-specific optimizations to further enhance performance.

References

  1. OpenAI Embedding Models Documentation.
  2. IEEE Standard for Floating-Point Arithmetic (IEEE 754).
  3. Techniques for Dimensionality Reduction in Machine Learning.
GPT-4 is factual (if not collecting layman upvotes in form, and crippled from original lengths it would write)

White Paper: Efficient Vector Storage and Quality Maximization for Low-Bit Depth Embeddings

Abstract

This paper presents a set of techniques for efficient storage of vector embeddings and maximizing the quality of low-bit depth embeddings. These techniques are particularly useful in the context of machine learning and natural language processing, where large amounts of high-dimensional data need to be stored and processed efficiently. The techniques discussed include dimension reduction, bit depth reduction, and a novel scaling formula for preserving the quality of low-bit depth embeddings.

1. Introduction

In the field of machine learning and natural language processing, embeddings are a common way to represent text data. These embeddings are high-dimensional vectors that capture the semantic meaning of the text. However, storing and processing these high-dimensional vectors can be computationally expensive and memory-intensive. This paper presents a set of techniques for reducing the storage requirements of these embeddings, while preserving their quality.

2. Dimension Reduction

Dimension reduction is a common technique used to reduce the computational complexity and storage requirements of high-dimensional data. The technique involves reducing the number of dimensions of the embeddings while preserving as much of the original information as possible. This is achieved by truncating the embeddings to a specified number of dimensions and normalizing them. The normalization step ensures that the magnitude of each vector is 1, which helps to preserve the relative distances between vectors in the reduced-dimensional space.

3. Bit Depth Reduction

Bit depth reduction is another technique used to reduce the storage requirements of embeddings. This involves reducing the bit depth of the embeddings from float32 to a lower bit depth such as float16, float8, or int8. This can significantly reduce the memory requirements of the embeddings, making them more efficient to store and process.

However, reducing the bit depth of the embeddings can also lead to a loss of precision. To mitigate this, a scaling factor is applied to the embeddings before they are converted to the lower bit depth. This scaling factor is designed to maximize the range of the lower bit depth, thereby preserving as much of the original information as possible.

4. Quality Maximization for Low-Bit Depth Embeddings

To maximize the quality of low-bit depth embeddings, a novel scaling formula is used. This formula is designed to adjust the scale factor based on the number of dimensions of the embeddings. The formula takes into account the fact that the range of representable values in a lower bit depth is smaller than that of a higher bit depth. By adjusting the scale factor based on the number of dimensions, the formula ensures that the embeddings are scaled to the maximum range of the lower bit depth, thereby preserving their quality.

The formula also includes a second-order Gaussian correction term, which boosts the scale factor for embeddings with a certain number of dimensions. This correction term helps to further preserve the quality of the embeddings when they are converted to a lower bit depth.

5. Conclusion

The techniques presented in this paper provide an efficient way to store and process high-dimensional embeddings. By reducing the dimensions and bit depth of the embeddings, these techniques significantly reduce the storage requirements of the embeddings. Furthermore, the novel scaling formula ensures that the quality of the embeddings is preserved when they are converted to a lower bit depth. These techniques are particularly useful in the context of machine learning and natural language processing, where large amounts of high-dimensional data need to be stored and processed efficiently.

Neither of these thought “hey, these comments about “3-large”: 3072, # Supports dimensional truncation, down to 256 good” or "“Model ‘ada-002’ only is dimensions=1536” was worth considering.

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