Quantized Fourier and Polynomial Features for Enhanced Tensor Network Models

Concepts de base

The author proposes quantizing Fourier and polynomial features to enhance tensor network models, increasing model flexibility without additional computational costs.

Résumé

The content discusses the quantization of Fourier and polynomial features to improve tensor network models. It explores the benefits of this approach in terms of model expressiveness, regularization, and generalization capabilities. Experimental results on various datasets demonstrate the effectiveness of quantized models compared to non-quantized counterparts.
The authors introduce a method to quantize Fourier and polynomial features in tensor network models. This allows for increased model flexibility without added computational costs. The study showcases how quantization enhances generalization capabilities and provides state-of-the-art results on various datasets.
Key points include:

Introduction to kernel machines using polynomial and Fourier features.
Proposal to exploit tensor structure in features by constraining model weights.
Quantization of features leading to higher VC-dimension bounds.
Experimental verification showing improved generalization with quantized models.
Regularizing effect observed through prioritizing salient features in data.
Benchmarking on large regression tasks showcasing superior performance.

Stats

We show that, for the same number of model parameters, the resulting quantized models have a higher bound on the VC-dimension as opposed to their non-quantized counterparts, at no additional computational cost while learning from identical features.
We verify experimentally how this additional tensorization regularizes the learning problem by prioritizing the most salient features in the data and how it provides models with increased generalization capabilities.

Citations

"We show that compared to their non-quantized counterparts, quantized models can be trained with no additional computational cost."
"Quantized tensor network models can provide state-of-the-art performance on large-scale real-life problems."

Idées clés tirées de

Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models

by Frederiek We... à arxiv.org 03-11-2024

https://arxiv.org/pdf/2309.05436.pdf

Questions plus approfondies

How does quantization impact overfitting or underfitting in complex datasets

Quantization can have a significant impact on overfitting or underfitting in complex datasets. When quantizing feature representations, the model is forced to prioritize and focus on the most salient features due to the limited number of parameters available for representation. This prioritization helps prevent overfitting by reducing the model's tendency to memorize noise or irrelevant details in the data. On the other hand, quantization can also lead to underfitting if not enough flexibility is retained in representing complex patterns within the data. In cases where there are intricate relationships that require more nuanced modeling, aggressive quantization may limit the model's ability to capture these complexities effectively.

What are potential drawbacks or limitations of using quantized feature representations

There are potential drawbacks and limitations associated with using quantized feature representations. One limitation is related to loss of information during quantization, as compressing continuous values into discrete levels can introduce approximation errors and reduce precision in representing features accurately. Additionally, aggressive quantization may result in oversimplification of complex patterns within the data, leading to underfitting issues where important nuances are overlooked due to constraints imposed by quantization levels. Moreover, selecting an inappropriate level of quantization could hinder model performance by either limiting its expressiveness or introducing unnecessary complexity without tangible benefits.

How might incorporating different types of tensor networks affect the performance of quantized models

Incorporating different types of tensor networks can have varying effects on the performance of quantized models. The choice of tensor network structure impacts how well a model can capture dependencies and interactions among features within high-dimensional data spaces efficiently. For instance:

Canonical Polyadic Decomposition (CPD): CPD constrains models with lower storage complexity but may struggle with capturing higher-order interactions.
Tensor Train (TT): TT allows for efficient computation while maintaining flexibility through hierarchical decomposition but requires careful selection of ranks for optimal performance.
Tensor Ring (TR): TR offers additional expressiveness compared to TT at increased computational costs.
By leveraging different tensor network structures alongside feature quantization, it becomes possible to tailor models based on specific dataset characteristics and balance between representational power and computational efficiency effectively.