Data Kernel Perspective Space Performance Guarantees for Synthetic Data from Transformer Models

TL;DR

The paper tackles the challenge of predicting and guaranteeing the quality of synthetic data produced by transformer models under data scarcity. It introduces Data Kernel Perspective Space (DKPS), a formalism that embeds multiple model outputs into a low-dimensional Euclidean space using MDS on a distance matrix derived from mean embeddings over a query set, enabling statistical guarantees on bias and variance. The authors apply DKPS to machine translation and contrastive preference optimization to reveal how synthetic data generated in batch vs sequential modes, and in-sample vs out-of-sample scenarios, differ in geometry and uncertainty, providing diagnostic tools for data provenance and debiasing. This framework offers a principled preprocessing and evaluation approach for synthetic data pipelines in NLP, with potential extensions to nonlinear embeddings and integration into downstream optimization schemes like CPO.

Abstract

Scarcity of labeled training data remains the long pole in the tent for building performant language technology and generative AI models. Transformer models -- particularly LLMs -- are increasingly being used to mitigate the data scarcity problem via synthetic data generation. However, because the models are black boxes, the properties of the synthetic data are difficult to predict. In practice it is common for language technology engineers to 'fiddle' with the LLM temperature setting and hope that what comes out the other end improves the downstream model. Faced with this uncertainty, here we propose Data Kernel Perspective Space (DKPS) to provide the foundation for mathematical analysis yielding concrete statistical guarantees for the quality of the outputs of transformer models. We first show the mathematical derivation of DKPS and how it provides performance guarantees. Next we show how DKPS performance guarantees can elucidate performance of a downstream task, such as neural machine translation models or LLMs trained using Contrastive Preference Optimization (CPO). Limitations of the current work and future research are also discussed.

Figures (13)

• Figure 1: For temperature $T=0.6$, we plot: (Left) Squared bias for the 10 batched synthetic translations with respect to the human translation; (Right) Estimated variance for the 10 synthetic translations. The upper row is the batched in-sample translations and the bottom the sequential in-sample translations. Points are colored by the number of words of English sentences.
• Figure 2: For temperature $T=0.6$, we plot: (Left) Squared bias for the 10 batched synthetic translations with respect to the human translation; (Right) Estimated variance for the 10 synthetic translations. The upper row is the batched in-sample translations and the bottom the sequential OOS translations. Points are colored by the number of words of English sentences.
• Figure 3: Convex hull of the points $\mathcal{C}_E$ (L) and $\mathcal{C}_Z$ (M and R). Below we show the ten closest OOS sentences to the mean of the English convex hull (the closest is denoted via an $*$, the second via a $\#$). Sentences in red (resp., black) font have their translations mapped outside (resp., inside) the convex hull of $\mathcal{C}_Z$. In the right panel, the translations of the ten sentences are plotted and numbered 1--10.
• Figure 4: Choosing 500 random sets $\mathcal{C}_E$, we plot the histogram for the number of the ten closest sentences to $\mathcal{HC}_E$ whose translations fall into $\mathcal{HC}_Z$. The mean is $5.47\pm 2$.
• Figure 5: Using MDS to embed the distance matrices in Figure \ref{['fig:Din']} into an appropriate $\mathbb{R}^d$, we show the pairs plot of the first three DKPS dimensions in each case. In the first two columns, the plot the batched and sequential models and the 10 translations are represented via numerals 1-10 (in the batched setting numbered according to their Sockeye rank) with the human translation model provided by the point labeled $H$. In the third column, the sequential translation models are provided by the black dots with a fitted Gaussian distribution in gray and mean show via the $x$. The batched are again numbered 1-10 (according to Sockeye rank).