Group Relative Policy Optimization (GRPO) was introduced and used successfully to train DeepSeek R1 models for promoting reasoning capabilities of LLMs using verifiable or binary rewards. We show in this paper that GRPO with verifiable rewards can be written as a Kullback Leibler ($\mathsf{KL}$) regularized contrastive loss, where the contrastive samples are synthetic data sampled from the old policy. The optimal GRPO policy $\pi_{n}$ can be expressed explicitly in terms of the binary reward, as well as the first and second order statistics of the old policy ($\pi_{n-1}$) and the reference policy $\pi_0$. Iterating this scheme, we obtain a sequence of policies $\pi_{n}$ for which we can quantify the probability of success $p_n$. We show that the probability of success of the policy satisfies a recurrence that converges to a fixed point of a function that depends on the initial probability of success $p_0$ and the regularization parameter $\beta$ of the $\mathsf{KL}$ regularizer. We show that the fixed point $p^*$ is guaranteed to be larger than $p_0$, thereby demonstrating that GRPO effectively amplifies the probability of success of the policy.

Large Language Models (LLMs) suffer from hallucination problems, which hinder their reliability in sensitive applications. In the black-box setting, several self-consistency-based techniques have been proposed for hallucination detection. We empirically study these techniques and show that they achieve performance close to that of a supervised (still black-box) oracle, suggesting little room for improvement within this paradigm. To address this limitation, we explore cross-model consistency checking between the target model and an additional verifier LLM. With this extra information, we observe improved oracle performance compared to purely self-consistency-based methods. We then propose a budget-friendly, two-stage detection algorithm that calls the verifier model only for a subset of cases. It dynamically switches between self-consistency and cross-consistency based on an uncertainty interval of the self-consistency classifier. We provide a geometric interpretation of consistency-based hallucination detection methods through the lens of kernel mean embeddings, offering deeper theoretical insights. Extensive experiments show that this approach maintains high detection performance while significantly reducing computational cost.

Recent methods for aligning large language models (LLMs) with human feedback predominantly rely on a single reference model, which limits diversity, model overfitting, and underutilizes the wide range of available pre-trained models. Incorporating multiple reference models has the potential to address these limitations by broadening perspectives, reducing bias, and leveraging the strengths of diverse open-source LLMs. However, integrating multiple reference models into reinforcement learning with human feedback (RLHF) frameworks poses significant theoretical challenges, particularly in reverse KL-regularization, where achieving exact solutions has remained an open problem. This paper presents the first \emph{exact solution} to the multiple reference model problem in reverse KL-regularized RLHF. We introduce a comprehensive theoretical framework that includes rigorous statistical analysis and provides sample complexity guarantees. Additionally, we extend our analysis to forward KL-regularized RLHF, offering new insights into sample complexity requirements in multiple reference scenarios. Our contributions lay the foundation for more advanced and adaptable LLM alignment techniques, enabling the effective use of multiple reference models. This work paves the way for developing alignment frameworks that are both theoretically sound and better suited to the challenges of modern AI ecosystems.

This paper contains examples that may be considered offensive and inappropriate. Reducing the likelihood of generating harmful and toxic output is an essential task when aligning large language models (LLMs). Existing methods mainly rely on training an external reward model (i.e., another language model) or fine-tuning the LLM using self-generated data to influence the outcome. In this paper, we show that LLMs have the capability of self-detoxification without the use of an additional reward model or re-training. We propose Self-disciplined Autoregressive Sampling (SASA), a lightweight controlled decoding algorithm for toxicity reduction of LLMs. SASA leverages the contextual representations from an LLM to learn linear subspaces characterizing toxic v.s. When auto-completing a response token-by-token, SASA dynamically tracks the margin of the current output to steer the generation away from the toxic subspace, by adjusting the autoregressive sampling strategy. Recent advancements in large language models (LLMs) have dramatically enhanced their capabilities in textual understanding and reasoning (Brown et al., 2020; Kojima et al., 2022). Their capabilities in performing diverse linguistic tasks and producing coherent texts have catalyzed their adoption across a variety of applications (Rae et al., 2021; Hoffmann et al., 2022; Le Scao et al., 2023; Touvron et al., 2023a;b; Achiam et al., 2023). However, with the escalating size of models (Raffel et al., 2020; Brown et al., 2020; Achiam et al., 2023), there is a corresponding increase in the scale of the training datasets required to avert overfitting and to encapsulate extensive world knowledge. These extensive datasets, predominantly derived from internet crawls and merely subjected to basic filtering protocols (Raffel et al., 2020), often harbor biases that are problematic or directly detrimental for many applications and may not inherently align with these desirable attributes (Wallace et al., 2019; Gehman et al., 2020). In fact, it is known that language models trained on such data may not only mimic but also amplify these biases (Bolukbasi et al., 2016; Caliskan et al., 2017; Zhao et al., 2018; Sheng et al., 2019; Gehman et al., 2020; Hartvigsen et al., For example, an "aligned" LLM may be inadvertently or maliciously tricked into generating harmful or toxic output that causes usage violations and safety concerns (Sun et al., 2024).

Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little has been done in the multivariate scenario, wherein an agent has to decide between different multivariate outcomes. By exploiting a characterization of multivariate first stochastic dominance in terms of couplings, we introduce a statistic that assesses multivariate almost stochastic dominance under the framework of Optimal Transport with a smooth cost. Further, we introduce an entropic regularization of this statistic, and establish a central limit theorem (CLT) and consistency of the bootstrap procedure for the empirical statistic. Armed with this CLT, we propose a hypothesis testing framework as well as an efficient implementation using the Sinkhorn algorithm. We showcase our method in comparing and benchmarking Large Language Models that are evaluated on multiple metrics. Our multivariate stochastic dominance test allows us to capture the dependencies between the metrics in order to make an informed and statistically significant decision on the relative performance of the models.

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for distributional preference alignment of LLMs. AOT aligns LLMs on unpaired preference data by making the reward distribution of the positive samples stochastically dominant in the first order on the distribution of negative samples. We introduce a convex relaxation of this first-order stochastic dominance and cast it as an optimal transport problem with a smooth and convex cost. Thanks to the one-dimensional nature of the resulting optimal transport problem and the convexity of the cost, it has a closed-form solution via sorting on empirical measures. We fine-tune LLMs with this AOT objective, which enables alignment by penalizing the violation of the stochastic dominance of the reward distribution of the positive samples on the reward distribution of the negative samples. We analyze the sample complexity of AOT by considering the dual of the OT problem and show that it converges at the parametric rate. Empirically, we show on a diverse set of alignment datasets and LLMs that AOT leads to state-of-the-art models in the 7B family of models when evaluated with Open LLM Benchmarks and AlpacaEval.

Policy alignment of large language models refers to constrained policy optimization, where the policy is optimized to maximize a reward while staying close to a reference policy with respect to an $f$-divergence such as the $\mathsf{KL}$ divergence. The best of $n$ alignment policy selects a sample from the reference policy that has the maximum reward among $n$ independent samples. For both cases (policy alignment and best of $n$), recent works showed empirically that the reward improvement of the aligned policy on the reference one scales like $\sqrt{\mathsf{KL}}$, with an explicit bound in $n$ on the $\mathsf{KL}$ for the best of $n$ policy. We show in this paper that the $\sqrt{\mathsf{KL}}$ information theoretic upper bound holds if the reward under the reference policy has sub-gaussian tails. Moreover, we prove for the best of $n$ policy, that the $\mathsf{KL}$ upper bound can be obtained for any $f$-divergence via a reduction to exponential order statistics owing to the R\'enyi representation of order statistics, and a data processing inequality. If additional information is known on the tails of the aligned policy we show that tighter control on the reward improvement can be obtained via the R\'enyi divergence. Finally we demonstrate how these upper bounds transfer from proxy rewards to golden rewards which results in a decrease in the golden reward improvement due to overestimation and approximation errors of the proxy reward.

Transformer-based models trained on large and general purpose datasets consisting of molecular strings have recently emerged as a powerful tool for successfully modeling various structure-property relations. Inspired by this success, we extend the paradigm of training chemical language transformers on large-scale chemical datasets to generative tasks in this work. Specifically, we propose GP-MoLFormer, an autoregressive molecular string generator that is trained on more than 1.1B chemical SMILES. GP-MoLFormer uses a 46.8M parameter transformer decoder model with linear attention and rotary positional encodings as the base architecture. We explore the utility of GP-MoLFormer in generating novel, valid, and unique SMILES. Impressively, we find GP-MoLFormer is able to generate a significant fraction of novel, valid, and unique SMILES even when the number of generated molecules is in the 10 billion range and the reference set is over a billion. We also find strong memorization of training data in GP-MoLFormer generations, which has so far remained unexplored for chemical language models. Our analyses reveal that training data memorization and novelty in generations are impacted by the quality of the training data; duplication bias in training data can enhance memorization at the cost of lowering novelty. We evaluate GP-MoLFormer's utility and compare it with that of existing baselines on three different tasks: de novo generation, scaffold-constrained molecular decoration, and unconstrained property-guided optimization. While the first two are handled with no additional training, we propose a parameter-efficient fine-tuning method for the last task, which uses property-ordered molecular pairs as input. We call this new approach pair-tuning. Our results show GP-MoLFormer performs better or comparable with baselines across all three tasks, demonstrating its general utility.

Real-world data often exhibits bias, imbalance, and privacy risks. Synthetic datasets have emerged to address these issues. This paradigm relies on generative AI models to generate unbiased, privacy-preserving data while maintaining fidelity to the original data. However, assessing the trustworthiness of synthetic datasets and models is a critical challenge. We introduce a holistic auditing framework that comprehensively evaluates synthetic datasets and AI models. It focuses on preventing bias and discrimination, ensures fidelity to the source data, assesses utility, robustness, and privacy preservation. We demonstrate the framework's effectiveness by auditing various generative models across diverse use cases like education, healthcare, banking, and human resources, spanning different data modalities such as tabular, time-series, vision, and natural language. This holistic assessment is essential for compliance with regulatory safeguards. We introduce a trustworthiness index to rank synthetic datasets based on their safeguards trade-offs. Furthermore, we present a trustworthiness-driven model selection and cross-validation process during training, exemplified with "TrustFormers" across various data types. This approach allows for controllable trustworthiness trade-offs in synthetic data creation. Our auditing framework fosters collaboration among stakeholders, including data scientists, governance experts, internal reviewers, external certifiers, and regulators. This transparent reporting should become a standard practice to prevent bias, discrimination, and privacy violations, ensuring compliance with policies and providing accountability, safety, and performance guarantees.

Foundation models such as large language models (LLMs) have shown remarkable capabilities redefining the field of artificial intelligence. At the same time, they present pressing and challenging socio-technical risks regarding the trustworthiness of their outputs and their alignment with human values and ethics [Bommasani et al., 2021]. Evaluating LLMs is therefore a multi-dimensional problem, where those risks are assessed across diverse tasks and domains [Chang et al., 2023]. In order to quantify these risks, Liang et al. [2022], Wang et al. [2023], Huang et al. [2023] proposed benchmarks of automatic metrics for probing the trustworthiness of LLMs. These metrics include accuracy, robustness, fairness, toxicity of the outputs, etc. Human evaluation benchmarks can be even more nuanced, and are often employed when tasks surpass the scope of standard metrics. Notable benchmarks based on human and automatic evaluations include, among others, Chatbot Arena [Zheng et al., 2023], HELM [Bommasani et al., 2023], MosaicML's Eval, Open LLM Leaderboard [Wolf, 2023], and BIG-bench [Srivastava et al., 2022], each catering to specific evaluation areas such as chatbot performance, knowledge assessment, and domain-specific challenges. Traditional metrics, however, sometimes do not correlate well with human judgments.