Vedant Shah

Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models

Johan Samir Obando Ceron

Brian R. Bartoldson

Bhavya Kailkhura

Guillaume Lajoie

Glen Berseth

Nikolay Malkin

Moksh J. Jain

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference… (see more) to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. RSA exploits the rich information embedded in the reasoning chains -- not just the final answers -- and enables bootstrapping from partially correct intermediate steps within different chains of thought. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), while outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further demonstrate that training the model to combine solutions via a novel aggregation-aware reinforcement learning approach yields significant performance gains. Code available at https://github.com/HyperPotatoNeo/RSA.

2025-09-30

ArXiv (preprint)

Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models

Johan Samir Obando Ceron

Brian R. Bartoldson

Bhavya Kailkhura

Guillaume Lajoie

Glen Berseth

Nikolay Malkin

Moksh J. Jain

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference… (see more) to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. RSA exploits the rich information embedded in the reasoning chains -- not just the final answers -- and enables bootstrapping from partially correct intermediate steps within different chains of thought. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), while outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further demonstrate that training the model to combine solutions via a novel aggregation-aware reinforcement learning approach yields significant performance gains. Code available at https://github.com/HyperPotatoNeo/RSA.

2025-09-30

ArXiv (preprint)

Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models

Johan Samir Obando Ceron

Brian R. Bartoldson

Bhavya Kailkhura

Guillaume Lajoie

Glen Berseth

Nikolay Malkin

Moksh J. Jain

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference… (see more) to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. RSA exploits the rich information embedded in the reasoning chains -- not just the final answers -- and enables bootstrapping from partially correct intermediate steps within different chains of thought. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), while outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further demonstrate that training the model to combine solutions via a novel aggregation-aware reinforcement learning approach yields significant performance gains. Code available at https://github.com/HyperPotatoNeo/RSA.

2025-09-30

ArXiv (preprint)

Low Compute Unlearning via Sparse Representations

Frederik Träuble

Ashish Malik

Hugo Larochelle

Michael Curtis Mozer

Sanjeev Arora

Machine unlearning, which involves erasing knowledge about a \emph{forget set} from a trained model, can prove to be costly and infeasible … (see more)using existing techniques. We propose a low-compute unlearning technique based on a discrete representational bottleneck. We show that the proposed technique efficiently unlearns the forget set and incurs negligible damage to the model's performance on the rest of the dataset. We evaluate the proposed technique on the problem of class unlearning using four datasets: CIFAR-10, CIFAR-100, LACUNA-100 and ImageNet-1k. We compare the proposed technique to SCRUB, a state-of-the-art approach which uses knowledge distillation for unlearning. Across all four datasets, the proposed technique performs as well as, if not better than SCRUB while incurring almost no computational cost.

2025-09-15

TMLR (accepted)

openreview.net

General Causal Imputation via Synthetic Interventions

Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their inte… (see more)ractions. The task of causal imputation involves using this subset to predict unobserved interactions. Squires et al. (2022) have proposed two estimators for this task based on the synthetic interventions (SI) estimator: SI-A (for actions) and SI-C (for contexts). We extend their work and introduce a novel causal imputation estimator, generalized synthetic interventions (GSI). We prove the identifiability of this estimator for data generated from a more complex latent factor model. On synthetic and real data we show empirically that it recovers or outperforms their estimators.

2024-10-30

NeurIPS.cc/2024/Workshop/CRL (poster)

openreview.net

General Causal Imputation via Synthetic Interventions

2024-10-28

ArXiv (preprint)

General Causal Imputation via Synthetic Interventions

Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their inte… (see more)ractions. The task of causal imputation involves using this subset to predict unobserved interactions. Squires et al. (2022) have proposed two estimators for this task based on the synthetic interventions (SI) estimator: SI-A (for actions) and SI-C (for contexts). We extend their work and introduce a novel causal imputation estimator, generalized synthetic interventions (GSI). We prove the identifiability of this estimator for data generated from a more complex latent factor model. On synthetic and real data we show empirically that it recovers or outperforms their estimators.

2024-10-28

ArXiv (preprint)

AI-Assisted Generation of Difficult Math Questions

Dingli Yu

Kaifeng Lyu

Simon Park

Nan Rosemary Ke

Jiatong Yu

Yinghui He

Michael Curtis Mozer

James Lloyd McClelland

Sanjeev Arora

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH

2024-10-09

NeurIPS.cc/2024/Workshop/MATH-AI (accepted)

openreview.net

AI-Assisted Generation of Difficult Math Questions

Dingli Yu

Kaifeng Lyu

Simon Park

Nan Rosemary Ke

Michael Curtis Mozer

Sanjeev Arora

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH

2024-07-30

ArXiv (preprint)

AI-Assisted Generation of Difficult Math Questions

Dingli Yu

Kaifeng Lyu

Simon Park

Nan Rosemary Ke

Michael Curtis Mozer

Sanjeev Arora

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH

2024-07-30

ArXiv (preprint)

AI-Assisted Generation of Difficult Math Questions

Dingli Yu

Kaifeng Lyu

Simon Park

Nan Rosemary Ke

Michael Curtis Mozer

Sanjeev Arora

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet dem… (see more)and for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core"skills"from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an"out of distribution"task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH

2024-07-30

ArXiv (preprint)