What Makes Large Language Models Reason in (Multi-Turn) Code Generation?

Prompting techniques such as chain-of-thought have established themselves as a popular vehicle for improving the outputs of large language models (LLMs). For code generation, however, their exact mechanics and efficacy are under-explored. We thus investigate the effects of a wide range of prompting strategies with a focus on automatic re-prompting over multiple turns and computational requirements. After systematically decomposing reasoning, instruction, and execution feedback prompts, we conduct an extensive grid search on the competitive programming benchmarks CodeContests and TACO for multiple LLM families and sizes (Llama 3.0 and 3.1, 8B, 70B, 405B, and GPT-4o). Our study reveals strategies that consistently improve performance across all models with small and large sampling budgets. We then show how finetuning with such an optimal configuration allows models to internalize the induced reasoning process and obtain improvements in performance and scalability for multi-turn code generation.

Exploring Precision and Recall to assess the quality and diversity of LLMs

This paper introduces a novel evaluation framework for Large Language Models (LLMs) such as Llama-2 and Mistral, focusing on the adaptation of Precision and Recall metrics from image generation to text generation. This approach allows for a nuanced assessment of the quality and diversity of generated text without the need for aligned corpora. By conducting a comprehensive evaluation of state-of-the-art language models, the study reveals significant insights into their performance on open-ended generation tasks, which are not adequately captured by traditional benchmarks. The findings highlight a trade-off between the quality and diversity of generated samples, particularly when models are fine-tuned with human feedback. This work extends the toolkit for distribution-based NLP evaluation, offering insights into the practical capabilities and challenges faced by current LLMs in generating diverse and high-quality text.

Optimal Budgeted Rejection Sampling for Generative Models

Rejection sampling methods have recently been proposed to improve the performance of discriminator-based generative models. However, these methods are only optimal under an unlimited sampling budget, and are usually applied to a generator trained independently of the rejection procedure. We first propose an Optimal Budgeted Rejection Sampling (OBRS) scheme that is provably optimal with respect to \textit{any} $f$-divergence between the true distribution and the post-rejection distribution, for a given sampling budget. Second, we propose an end-to-end method that incorporates the sampling scheme into the training procedure to further enhance the model's overall performance. Through experiments and supporting theory, we show that the proposed methods are effective in significantly improving the quality and diversity of the samples.

Adversarial attacks for mixtures of classifiers

Mixtures of classifiers (a.k.a. randomized ensembles) have been proposed as a way to improve robustness against adversarial attacks. However, it has been shown that existing attacks are not well suited for this kind of classifiers. In this paper, we discuss the problem of attacking a mixture in a principled way and introduce two desirable properties of attacks based on a geometrical analysis of the problem (effectiveness and maximality). We then show that existing attacks do not meet both of these properties. Finally, we introduce a new attack called lattice climber attack with theoretical guarantees on the binary linear setting, and we demonstrate its performance by conducting experiments on synthetic and real datasets.

Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows

Achieving a balance between image quality (precision) and diversity (recall) is a significant challenge in the domain of generative models. Current state-of-the-art models primarily rely on optimizing heuristics, such as the Fr\'echet Inception Distance. While recent developments have introduced principled methods for evaluating precision and recall, they have yet to be successfully integrated into the training of generative models. Our main contribution is a novel training method for generative models, such as Generative Adversarial Networks and Normalizing Flows, which explicitly optimizes a user-defined trade-off between precision and recall. More precisely, we show that achieving a specified precision-recall trade-off corresponds to minimizing a unique $f$-divergence from a family we call the \mbox{\em PR-divergences}. Conversely, any $f$-divergence can be written as a linear combination of PR-divergences and corresponds to a weighted precision-recall trade-off. Through comprehensive evaluations, we show that our approach improves the performance of existing state-of-the-art models like BigGAN in terms of either precision or recall when tested on datasets such as ImageNet.

Randomization for adversarial robustness: the Good, the Bad and the Ugly

Deep neural networks are known to be vulnerable to adversarial attacks: A small perturbation that is imperceptible to a human can easily make a well-trained deep neural network misclassify. To defend against adversarial attacks, randomized classifiers have been proposed as a robust alternative to deterministic ones. In this work we show that in the binary classification setting, for any randomized classifier, there is always a deterministic classifier with better adversarial risk. In other words, randomization is not necessary for robustness. In many common randomization schemes, the deterministic classifiers with better risk are explicitly described: For example, we show that ensembles of classifiers are more robust than mixtures of classifiers, and randomized smoothing is more robust than input noise injection. Finally, experiments confirm our theoretical results with the two families of randomized classifiers we analyze.

Training Normalizing Flows with the Precision-Recall Divergence

Generative models can have distinct mode of failures like mode dropping and low quality samples, which cannot be captured by a single scalar metric. To address this, recent works propose evaluating generative models using precision and recall, where precision measures quality of samples and recall measures the coverage of the target distribution. Although a variety of discrepancy measures between the target and estimated distribution are used to train generative models, it is unclear what precision-recall trade-offs are achieved by various choices of the discrepancy measures. In this paper, we show that achieving a specified precision-recall trade-off corresponds to minimising -divergences from a family we call the {\em PR-divergences }. Conversely, any -divergence can be written as a linear combination of PR-divergences and therefore correspond to minimising a weighted precision-recall trade-off. Further, we propose a novel generative model that is able to train a normalizing flow to minimise any -divergence, and in particular, achieve a given precision-recall trade-off.

On the expressivity of bi-Lipschitz normalizing flows

An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Nowadays, most Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this paper, we discuss the expressivity of bi-Lipschitz Normalizing Flows and identify several target distributions that are difficult to approximate using such models. Then, we characterize the expressivity of bi-Lipschitz Normalizing Flows by giving several lower bounds on the Total Variation distance between these particularly unfavorable distributions and their best possible approximation. Finally, we discuss potential remedies which include using more complex latent distributions.

Advocating for Multiple Defense Strategies against Adversarial Examples

It has been empirically observed that defense mechanisms designed to protect neural networks against $\ell_\infty$ adversarial examples offer poor performance against $\ell_2$ adversarial examples and vice versa. In this paper we conduct a geometrical analysis that validates this observation. Then, we provide a number of empirical insights to illustrate the effect of this phenomenon in practice. Then, we review some of the existing defense mechanism that attempts to defend against multiple attacks by mixing defense strategies. Thanks to our numerical experiments, we discuss the relevance of this method and state open questions for the adversarial examples community.

Fast & Accurate Method for Bounding the Singular Values of Convolutional Layers with Application to Lipschitz Regularization

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz matrices, we introduce a new upper bound for convolutional layers that is both tight and easy to compute. Based on this result we devise an algorithm to train Lipschitz regularized Convolutional Neural Networks.