Deepak Agarwal

Jelena Markovic-Voronov, Wenhui Zhu, Bo Long et al.

We introduce a principled probabilistic framework for reward-guided decoding in large language models, addressing the limitations of standard decoding methods that optimize token-level likelihood rather than sequence-level quality. Our method defines a reward-augmented target distribution over complete sequences by combining model transition probabilities with prefix-dependent reward potentials. Importantly, the approach is training-free: it leaves model weights unchanged and instead modifies the inference distribution via reward potentials, with all gains arising purely from inference-time sampling. To sample from this distribution, we develop Sequential Monte Carlo algorithms, including a computationally efficient prefix-only variant and a lookahead variant whose intermediate targets match the exact marginals of the full sequence distribution. The framework also integrates resample-move updates with Metropolis-Hastings rejuvenation and supports block-wise generation, subsuming common decoding strategies such as temperature sampling and power-tempered objectives. Empirical results across three 7B models show significant gains. On code generation (HumanEval), our method improves base performance by up to 54.9% and surpasses the strongest sampling baselines by 9.1%-15.3%. On mathematical reasoning (MATH500), it achieves gains of up to 8.8%. Notably, it reaches 87.8% on HumanEval and 78.4% on MATH500 with Qwen2.5-7B, consistently outperforming the reinforcement learning method GRPO.

Deepak Agarwal, Dhyey Dharmendrakumar Mavani, Suyash Gupta et al.

Self-attention is usually described as a flexible, content-adaptive way to mix a token with information from its past. We re-interpret causal self-attention transformers, the backbone of modern foundation models, within a probabilistic framework, much like how classical PCA is extended to probabilistic PCA. However, this re-formulation reveals a surprising and deeper structural insight: due to a change-of-variables phenomenon, a barrier constraint emerges on the self-attention parameters. This induces a highly structured geometry on the token space, providing theoretical insights into the dynamics of LLM decoding. This reveals a boundary where attention becomes ill-conditioned, leading to a margin interpretation similar to classical support vector machines. Just like support vectors, this naturally gives rise to the concept of support tokens. Furthermore, we show that LLMs can be interpreted as a stochastic process over the power set of the token space, providing a rigorous probabilistic framework for sequence modeling. We propose a Bayesian framework and derive a MAP estimation objective that requires only a minimal modification to standard LLM training: the addition of a smooth log-barrier penalty to the usual cross-entropy loss. We demonstrate that this provides more robust models without sacrificing out-of-sample accuracy and that it is straightforward to incorporate in practice.

Bo Long, Deepak Agarwal, Jelena Markovic-Voronov et al.

The Transformer is the foundational building block of modern AI, yet offers no principled handling of \emph{uncertainty}, which is prevalent in real applications: cold-start tokens with sparse histories in sequential recommendation, heterogeneous signal quality in language models, and attention sinks induced by unconstrained softmax. Every token is treated with uniform confidence. We show this uniformity is a degenerate case of our \emph{Bayesian Filtering Transformer} (BFT): attention becomes precision-weighted kriging, the residual connection becomes a Kalman update with adaptive gain, and the FFN becomes a dynamics model propagating precision via a Jacobian--plus--process-noise rule. Observation precision comes from a parameter-free Restricted Maximum Likelihood (REML) estimator with a conjugate Bayesian prior. BFT replaces any Transformer layer with negligible overhead. On sequential recommendation, BFT applied to three major architectures yields significant gains on six benchmarks, with the largest improvements on cold-start users and rare items where uncertainty is highest. On supervised fine-tuning of large language models with noisy data, BFT improves robustness in two regimes: noisy supervision (token-label corruption in question answering) and noisy context (retrieval-augmented QA with real RAG distractors). A single principled modification -- restoring precision -- unlocks substantial headroom across both classical sequence-modeling and modern LLM regimes.

Weiwei Guo, Xiaowei Liu, Sida Wang et al.

Ranking is the most important component in a search system. Mostsearch systems deal with large amounts of natural language data,hence an effective ranking system requires a deep understandingof text semantics. Recently, deep learning based natural languageprocessing (deep NLP) models have generated promising results onranking systems. BERT is one of the most successful models thatlearn contextual embedding, which has been applied to capturecomplex query-document relations for search ranking. However,this is generally done by exhaustively interacting each query wordwith each document word, which is inefficient for online servingin search product systems. In this paper, we investigate how tobuild an efficient BERT-based ranking model for industry use cases.The solution is further extended to a general ranking framework,DeText, that is open sourced and can be applied to various rankingproductions. Offline and online experiments of DeText on threereal-world search systems present significant improvement overstate-of-the-art approaches.

Krishnaram Kenthapadi, Stuart Ambler, Liang Zhang et al.

The recently launched LinkedIn Salary product has been designed with the goal of providing compensation insights to the world's professionals and thereby helping them optimize their earning potential. We describe the overall design and architecture of the statistical modeling system underlying this product. We focus on the unique data mining challenges while designing and implementing the system, and describe the modeling components such as Bayesian hierarchical smoothing that help to compute and present robust compensation insights to users. We report on extensive evaluation with nearly one year of de-identified compensation data collected from over one million LinkedIn users, thereby demonstrating the efficacy of the statistical models. We also highlight the lessons learned through the deployment of our system at LinkedIn.

Deepak Agarwal, Bee-Chung Chen, Xuanhui Wang

Personalized article recommendation is important to improve user engagement on news sites. Existing work quantifies engagement primarily through click rates. We argue that quality of recommendations can be improved by incorporating different types of "post-read" engagement signals like sharing, commenting, printing and e-mailing article links. More specifically, we propose a multi-faceted ranking problem for recommending news articles where each facet corresponds to a ranking problem to maximize actions of a post-read action type. The key technical challenge is to estimate the rates of post-read action types by mitigating the impact of enormous data sparsity, we do so through several variations of factor models. To exploit correlations among post-read action types we also introduce a novel variant called locally augmented tensor (LAT) model. Through data obtained from a major news site in the US, we show that factor models significantly outperform a few baseline IR models and the LAT model significantly outperforms several other variations of factor models. Our findings show that it is possible to incorporate post-read signals that are commonly available on online news sites to improve quality of recommendations.

Rajiv Khanna, Liang Zhang, Deepak Agarwal et al.

Predicting user affinity to items is an important problem in applications like content optimization, computational advertising, and many more. While bilinear random effect models (matrix factorization) provide state-of-the-art performance when minimizing RMSE through a Gaussian response model on explicit ratings data, applying it to imbalanced binary response data presents additional challenges that we carefully study in this paper. Data in many applications usually consist of users' implicit response that are often binary -- clicking an item or not; the goal is to predict click rates, which is often combined with other measures to calculate utilities to rank items at runtime of the recommender systems. Because of the implicit nature, such data are usually much larger than explicit rating data and often have an imbalanced distribution with a small fraction of click events, making accurate click rate prediction difficult. In this paper, we address two problems. First, we show previous techniques to estimate bilinear random effect models with binary data are less accurate compared to our new approach based on adaptive rejection sampling, especially for imbalanced response. Second, we develop a parallel bilinear random effect model fitting framework using Map-Reduce paradigm that scales to massive datasets. Our parallel algorithm is based on a "divide and conquer" strategy coupled with an ensemble approach. Through experiments on the benchmark MovieLens data, a small Yahoo! Front Page data set, and a large Yahoo! Front Page data set that contains 8M users and 1B binary observations, we show that careful handling of binary response as well as identifiability issues are needed to achieve good performance for click rate prediction, and that the proposed adaptive rejection sampler and the partitioning as well as ensemble techniques significantly improve model performance.