Recent work has shown that large language models (LLMs) can iteratively improve their outputs by incorporating generated samples and their corresponding evaluation scores as in-context examples. Despite these empirical findings, the theoretical foundations underlying this phenomenon remain poorly understood. In this paper, we show that score-conditioned In-Context Learning (ICL) admits a structural correspondence to policy gradient optimization. We first provide a constructive proof that self-attention mechanisms can implement reward-weighted aggregation analogous to the REINFORCE algorithm under specific weight matrix configurations, and discuss the relationship between this construction and the behavior of pretrained transformers. The correspondence is directional in hidden-state space and holds exactly only under the stated simplifying conditions; we quantify its strength empirically. Within our simplified hidden-state model, we furthermore derive an exact upper bound on the distribution shift induced by a bounded attention update, yielding a trust-region-like analogy to KL-constrained policy optimization. We validate our theory through extensive experiments across multiple LLMs, demonstrating that LLMs effectively utilize score information to shift output distributions toward high-scoring exemplars, and that attention weights exhibit a strong correlation with example scores.
For any E-commerce website it is a nontrivial problem to build enduring advertisements that attract shoppers. It is hard to pass the creative quality bar of the website, especially at a large scale. We thus propose a programmatic solution to generate product advertising headlines using retail content. We propose a state of the art application of Reinforcement Learning (RL) Policy gradient methods on Transformer based Masked Language Models. Our method creates the advertising headline by jointly conditioning on multiple products that a seller wishes to advertise. We demonstrate that our method outperforms existing Transformer and LSTM + RL methods in overlap metrics and quality audits. We also show that our model-generated headlines outperform human submitted headlines in terms of both grammar and creative quality as determined by audits.
Michael Y. Li, Anthony Zhan, Kanishk Gandhi +2cs.LG cs.CL
Scaling inference compute, by generating many parallel attempts per problem, is a costly but reliable lever for improving language model capabilities. By default these attempts are generated independently, wasting inference compute on redundant solutions. This waste seems unavoidable. After all, independence is what makes parallel sampling trivial to scale. However, this tradeoff is not fundamental: there is a rich design space of samplers that generate correlated but exact samples entirely in parallel. We explore this design space as an avenue for improving sample efficiency in scaling inference compute and reinforcement learning (RL). Concretely, we introduce QuasiMoTTo, which uses correlated samples as a drop-in replacement for i.i.d. samples. To generate these samples, QuasiMoTTo uses a reparameterization of autoregressive sampling as inverse-CDF sampling and draws the underlying uniforms with quasi-Monte Carlo (QMC); because QMC spreads the uniforms out more evenly than i.i.d., the resulting samples cover the output space with far less redundancy. Even though the batch is correlated, each sample is marginally distributed according to the language model, so we can use the batch for policy-gradient training. Our empirical analysis focuses on understanding how efficiently QuasiMoTTo can turn compute into performance. To evaluate correlated samplers, whose dependence breaks standard pass@k estimators, we first develop an unbiased bootstrap estimator. Across four reasoning benchmarks, QuasiMoTTo matches i.i.d. pass@k accuracy with 25-47% fewer samples. Strikingly, QuasiMoTTo often saturates an upper bound on pass@k that holds for any marginal-preserving sampler. We also apply QuasiMoTTo to policy-gradient RL (GRPO) where it matches i.i.d. performance with 50% fewer training steps. These gains come from higher coverage, which yields a stronger learning signal per batch.
On-policy distillation (OPD) trains an LLM on states induced by the current or recent student policy: the student generates complete or partial rollouts, a teacher or self-teacher scores the resulting tokens under their generated contexts, and dense log-probability, logit, or distributional signals are converted into post-training updates. This survey studies OPD as a feedback-to-update problem rather than a single loss family. We develop a formula-driven taxonomy from two routes -- direct distributional losses and policy-gradient-style log-ratio updates -- and use it to organize core methods, verifier- or outcome-guided hybrids, industrial reports, framework implementations, failure modes, and stabilization recipes under explicit evidence boundaries. The taxonomy shows that OPD effectiveness depends not only on KL direction or teacher access, but also on state compatibility, support construction, temporal credit, vocabulary-level probability routing, gates and weights, and regularization. We further separate two mechanisms often conflated in sampled-token OPD stability discussions. Temporal credit asks how teacher-student log-ratio returns should weight sampled actions across a rollout; vocabulary routing asks where probability mass should move when negative feedback suppresses a sampled token. This distinction yields bias boundaries for immediate, return-to-go, discounted, and baseline-corrected estimators, motivates GAE-OPD as a value-based hypothesis for log-ratio returns, and motivates Counterfactual Routed OPD (CR-OPD) for routing probability mass toward teacher-supported, student-reachable alternatives. We close by mapping actionability diagnostics, failure mechanisms, case studies, open problems, and a reporting checklist onto the same feedback-to-update variables.
As deep language models (DLMs) are increasingly deployed in high-stakes domains such as healthcare, understanding their decision rationale becomes paramount for ensuring trust, safety, and accountability. However, achieving this vital level of interpretability is particularly challenging when these DLMs operate as black-box systems (e.g., via APIs), where access to internal model states (e.g., parameters, gradients) is restricted. Despite numerous efforts, existing explanation methods often fail to concurrently satisfy three key desiderata: (i) inference-time efficiency, (ii) black-box compatibility without inducing out-of-distribution behavior, and (iii) comprehensible explanations grounded in the input's linguistic structure. To address these challenges, we propose a method that explains predictions of DLMs by selecting a small, informative subset of input words. We formulate this as an amortized optimization problem, enabling efficient one-shot inference without the need for input-specific search. Our selection policy is trained via REINFORCE-style policy gradients, allowing discrete word selection in a fully gradient-free setting. To enhance interpretability and align with human linguistic intuition, we integrate graph-structured knowledge into this selection process, fostering linguistically coherent subsets that result in explanations both highly informative and cognitively meaningful to end-users. We evaluated our method on diverse DLM architectures and multiple real-world datasets. It consistently identifies word subsets with enhanced discriminative power and stronger alignment with linguistically salient cues, outperforming both conventional black-box compatible methods and gradient-based approaches that are given oracle access to the black-box model's gradients for a more challenging benchmark. Our code is available at here.