Maximizing the Potential of Synthetic Data: Insights from Random Matrix Theory

Synthetic data has gained attention for training large language models, but poor-quality data can harm performance (see, e.g., Shumailov et al. (2023); Seddik et al. (2024)). A potential solution is data pruning, which retains only high-quality data based on a score function (human or machine feedback). Previous work Feng et al. (2024) analyzed models trained on synthetic data as sample size increases. We extend this by using random matrix theory to derive the performance of a binary classifier trained on a mix of real and pruned synthetic data in a high dimensional setting. Our findings identify conditions where synthetic data could improve performance, focusing on the quality of the generative model and verification strategy. We also show a smooth phase transition in synthetic label noise, contrasting with prior sharp behavior in infinite sample limits. Experiments with toy models and large language models validate our theoretical results.

Alignment with Preference Optimization Is All You Need for LLM Safety

We demonstrate that preference optimization methods can effectively enhance LLM safety. Applying various alignment techniques to the Falcon 11B model using safety datasets, we achieve a significant boost in global safety score (from $57.64\%$ to $99.90\%$) as measured by LlamaGuard 3 8B, competing with state-of-the-art models. On toxicity benchmarks, average scores in adversarial settings dropped from over $0.6$ to less than $0.07$. However, this safety improvement comes at the cost of reduced general capabilities, particularly in math, suggesting a trade-off. We identify noise contrastive alignment (Safe-NCA) as an optimal method for balancing safety and performance. Our study ultimately shows that alignment techniques can be sufficient for building safe and robust models.

Falcon2-11B Technical Report

We introduce Falcon2-11B, a foundation model trained on over five trillion tokens, and its multimodal counterpart, Falcon2-11B-vlm, which is a vision-to-text model. We report our findings during the training of the Falcon2-11B which follows a multi-stage approach where the early stages are distinguished by their context length and a final stage where we use a curated, high-quality dataset. Additionally, we report the effect of doubling the batch size mid-training and how training loss spikes are affected by the learning rate. The downstream performance of the foundation model is evaluated on established benchmarks, including multilingual and code datasets. The foundation model shows strong generalization across all the tasks which makes it suitable for downstream finetuning use cases. For the vision language model, we report the performance on several benchmarks and show that our model achieves a higher average score compared to open-source models of similar size. The model weights and code of both Falcon2-11B and Falcon2-11B-vlm are made available under a permissive license.

High-dimensional Learning with Noisy Labels

This paper provides theoretical insights into high-dimensional binary classification with class-conditional noisy labels. Specifically, we study the behavior of a linear classifier with a label noisiness aware loss function, when both the dimension of data $p$ and the sample size $n$ are large and comparable. Relying on random matrix theory by supposing a Gaussian mixture data model, the performance of the linear classifier when $p,n\to \infty$ is shown to converge towards a limit, involving scalar statistics of the data. Importantly, our findings show that the low-dimensional intuitions to handle label noise do not hold in high-dimension, in the sense that the optimal classifier in low-dimension dramatically fails in high-dimension. Based on our derivations, we design an optimized method that is shown to be provably more efficient in handling noisy labels in high dimensions. Our theoretical conclusions are further confirmed by experiments on real datasets, where we show that our optimized approach outperforms the considered baselines.

How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapse

The phenomenon of model collapse, introduced in (Shumailov et al., 2023), refers to the deterioration in performance that occurs when new models are trained on synthetic data generated from previously trained models. This recursive training loop makes the tails of the original distribution disappear, thereby making future-generation models forget about the initial (real) distribution. With the aim of rigorously understanding model collapse in language models, we consider in this paper a statistical model that allows us to characterize the impact of various recursive training scenarios. Specifically, we demonstrate that model collapse cannot be avoided when training solely on synthetic data. However, when mixing both real and synthetic data, we provide an estimate of a maximal amount of synthetic data below which model collapse can eventually be avoided. Our theoretical conclusions are further supported by empirical validations.

Investigating Regularization of Self-Play Language Models

This paper explores the effects of various forms of regularization in the context of language model alignment via self-play. While both reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) require to collect costly human-annotated pairwise preferences, the self-play fine-tuning (SPIN) approach replaces the rejected answers by data generated from the previous iterate. However, the SPIN method presents a performance instability issue in the learning phase, which can be mitigated by playing against a mixture of the two previous iterates. In the same vein, we propose in this work to address this issue from two perspectives: first, by incorporating an additional Kullback-Leibler (KL) regularization to stay at the proximity of the reference policy; second, by using the idea of fictitious play which smoothens the opponent policy across all previous iterations. In particular, we show that the KL-based regularizer boils down to replacing the previous policy by its geometric mixture with the base policy inside of the SPIN loss function. We finally discuss empirical results on MT-Bench as well as on the Hugging Face Open LLM Leaderboard.

Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

Do Vision and Language Encoders Represent the World Similarly?

Aligned text-image encoders such as CLIP have become the de facto model for vision-language tasks. Furthermore, modality-specific encoders achieve impressive performances in their respective domains. This raises a central question: does an alignment exist between uni-modal vision and language encoders since they fundamentally represent the same physical world? Analyzing the latent spaces structure of vision and language models on image-caption benchmarks using the Centered Kernel Alignment (CKA), we find that the representation spaces of unaligned and aligned encoders are semantically similar. In the absence of statistical similarity in aligned encoders like CLIP, we show that a possible matching of unaligned encoders exists without any training. We frame this as a seeded graph-matching problem exploiting the semantic similarity between graphs and propose two methods - a Fast Quadratic Assignment Problem optimization, and a novel localized CKA metric-based matching/retrieval. We demonstrate the effectiveness of this on several downstream tasks including cross-lingual, cross-domain caption matching and image classification.

On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis

This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r \beta_i{\mathcal{A}}_i + {\mathcal{W}}$ where $\beta_i\geq 0$ and the ${\mathcal{A}}_i$'s are unit-norm rank-one tensors such that $\left| \langle {\mathcal{A}}_i, {\mathcal{A}}_j \rangle \right| \in [0, 1]$ for $i\neq j$ and ${\mathcal{W}}$ is an additive noise term. Assuming that the dominant components are successively estimated from the noisy observation and subsequently subtracted, we leverage recent advances in random tensor theory in the regime of asymptotically large tensor dimensions to analytically characterize the estimated singular values and the alignment of estimated and true singular vectors at each step of the deflation procedure. Furthermore, this result can be used to construct estimators of the signal-to-noise ratios $\beta_i$ and the alignments between the estimated and true rank-1 signal components.

A Nested Matrix-Tensor Model for Noisy Multi-view Clustering

In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observations of each data point are acquired, with potentially non-uniform variances along the views. In this case, data can be naturally represented by an order-three tensor where the views are stacked. Given such a tensor, we consider the estimation of the hidden clusters via performing a best rank-one tensor approximation. In order to study the theoretical performance of this approach, we characterize the behavior of this best rank-one approximation in terms of the alignments of the obtained component vectors with the hidden model parameter vectors, in the large-dimensional regime. In particular, we show that our theoretical results allow us to anticipate the exact accuracy of the proposed clustering approach. Furthermore, numerical experiments indicate that leveraging our tensor-based approach yields better accuracy compared to a naive unfolding-based algorithm which ignores the underlying low-rank tensor structure. Our analysis unveils unexpected and non-trivial phase transition phenomena depending on the model parameters, ``interpolating'' between the typical behavior observed for the spiked matrix and tensor models.