arXiv subjects

Yuandong Tian

Publications and source records attributed to Yuandong Tian.

At least 37 records · Page 2Linked to original sources

arXiv2025

ParetoQ: Improving Scaling Laws in Extremely Low-bit LLM Quantization

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

cs.LG↗

arXiv2025

Composing Global Solutions to Reasoning Tasks via Algebraic Objects in Neural Nets

We prove rich algebraic structures of the solution space for 2-layer neural networks with quadratic activation and $L_2$ loss, trained on reasoning tasks in Abelian group (e.g., modular addition). Such a rich structure enables \emph{analytical} construction of global optimal solutions from partial solutions that only satisfy part of the loss, despite its high nonlinearity. We coin the framework as CoGS (\emph{\underline{Co}mposing \underline{G}lobal \underline{S}olutions}). Specifically, we show that the weight space over different numbers of hidden nodes of the 2-layer network is equipped with a semi-ring algebraic structure, and the loss function to be optimized consists of \emph{sum potentials}, which are ring homomorphisms, allowing partial solutions to be composed into global ones by ring addition and multiplication. Our experiments show that around $95\%$ of the solutions obtained by gradient descent match exactly our theoretical constructions. Although the global solutions constructed only required a small number of hidden nodes, our analysis on gradient dynamics shows that overparameterization asymptotically decouples training dynamics and is beneficial. We further show that training dynamics favors simpler solutions under weight decay, and thus high-order global solutions such as perfect memorization are unfavorable. The code is open sourced at https://github.com/facebookresearch/luckmatters/tree/yuandong3/ssl/real-dataset.

cs.LG↗

arXiv2025

Inpainting-Guided Policy Optimization for Diffusion Large Language Models

Masked diffusion large language models (dLLMs) are emerging as promising alternatives to autoregressive LLMs, offering competitive performance while supporting unique generation capabilities such as inpainting. We explore how inpainting can inform RL algorithm design for dLLMs. Aligning LLMs with reinforcement learning faces an exploration challenge: sparse reward signals and sample waste when models fail to discover correct solutions. While this inefficiency affects LLMs broadly, dLLMs offer a distinctive opportunity--their inpainting ability can guide exploration. We introduce IGPO (Inpainting Guided Policy Optimization), an RL framework that strategically inserts partial ground-truth reasoning traces during online sampling. Unlike providing full solutions, inpainting steers exploration toward promising trajectory spaces while preserving self-generated reasoning, bridging supervised fine-tuning and reinforcement learning. We apply IGPO to group-based optimization methods such as GRPO, where exploration failures cause zero advantages and gradients. IGPO restores meaningful gradients while improving sample efficiency. We also propose supervised fine-tuning on synthetically rewritten concise traces that better align with dLLM generation patterns. With additional techniques including entropy-based filtering, our training recipe yields substantial gains across three mathematical benchmarks--GSM8K, Math500, and AMC--achieving new state-of-the-art results for full-attention masked dLLMs.

cs.LG↗

arXiv2025

Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning

Large Language Models (LLMs) excel at reasoning and planning when trained on chainof-thought (CoT) data, where the step-by-step thought process is explicitly outlined by text tokens. However, this results in lengthy inputs where many words support textual coherence rather than core reasoning information, and processing these inputs consumes substantial computation resources. In this work, we propose a hybrid representation of the reasoning process, where we partially abstract away the initial reasoning steps using latent discrete tokens generated by VQ-VAE, significantly reducing the length of reasoning traces. We explore the use of latent trace abstractions in two scenarios: 1) training the model from scratch for the Keys-Finding Maze problem, 2) fine-tuning LLMs on this hybrid data with an extended vocabulary including unseen latent tokens, for both logical and mathematical reasoning problems. To facilitate effective learning, we introduce a simple training procedure that randomly mixes latent and text tokens, which enables fast adaptation to new latent tokens. Our approach consistently outperforms the baselines methods in various benchmarks.

cs.CL↗

arXiv2025

Deep Think with Confidence

Large Language Models (LLMs) have shown great potential in reasoning tasks through test-time scaling methods like self-consistency with majority voting. However, this approach often leads to diminishing returns in accuracy and high computational overhead. To address these challenges, we introduce Deep Think with Confidence (DeepConf), a simple yet powerful method that enhances both reasoning efficiency and performance at test time. DeepConf leverages model-internal confidence signals to dynamically filter out low-quality reasoning traces during or after generation. It requires no additional model training or hyperparameter tuning and can be seamlessly integrated into existing serving frameworks. We evaluate DeepConf across a variety of reasoning tasks and the latest open-source models, including Qwen 3 and GPT-OSS series. Notably, on challenging benchmarks such as AIME 2025, DeepConf@512 achieves up to 99.9% accuracy and reduces generated tokens by up to 84.7% compared to full parallel thinking.

cs.LG↗

arXiv2025

Dualformer: Controllable Fast and Slow Thinking by Learning with Randomized Reasoning Traces

In cognition theory, human thinking is governed by two systems: the fast and intuitive System 1 and the slower but more deliberative System 2. Analogously, Large Language Models (LLMs) can operate in two reasoning modes: outputting only the solutions (\emph{fast mode}) or both the reasoning chain and the final solution (\emph{slow mode}). We present \dualformer, a single Transformer model that seamlessly integrates both the fast and slow reasoning modes by training on randomized reasoning traces, where different parts of the traces are strategically dropped during training. At inference time, \dualformer can be easily configured to execute in either fast or slow mode, or automatically decide which mode to engage (\emph{auto mode}). It outperforms baselines in both performance and computational efficiency across all three modes: (1) in slow mode, \dualformer achieves $97.6\%$ optimal rate on unseen $30 \times 30$ maze tasks, surpassing the \searchformer baseline ($93.3\%$) trained on data with complete reasoning traces, with $45.5\%$ fewer reasoning steps; (2) in fast mode, \dualformer achieves $80\%$ optimal rate, significantly outperforming the Solution-Only model trained on solution-only data, which has an optimal rate of only $30\%$; (3) in auto mode, \dualformer achieves $96.6\%$ optimal rate with $59.9\%$ fewer steps than \searchformer. Moreover, \dualformer produces more diverse reasoning traces than \searchformer{}. For math reasoning problems, our techniques have also achieved improved performance with LLM fine-tuning, demonstrating its generalization beyond task-specific models. We open source our code at https://github.com/facebookresearch/dualformer.

cs.AI↗

arXiv2025

From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications

Large Language Models' (LLMs) weight matrices can often be expressed in low-rank form with potential to relax memory and compute resource requirements. Unlike prior efforts that focus on developing novel matrix decompositions, in this work we study the non-uniform low-rank properties of weight matrices in LLMs through the lens of stabilizing gradient subspace. First, we provide a theoretical framework to understand the stabilization of gradient subspaces through Hessian analysis. Second, we empirically establish an important relationship between gradient dynamics and low-rank expressiveness of weight matrices. Our findings reveal that different LLM components exhibit varying levels of converged low-rank structures, necessitating variable rank reduction across them to minimize drop in performance due to compression. Drawing on this result, we present Weight Low-Rank Projection(WeLore) that unifies weight compression and memory-efficient fine-tuning into one, in a data-agnostic and one-shot manner. When used as a compression technique, WeLore categorizes weight matrices into Low-rank Components (LRCs) and Non-Low-rank Components (N-LRCs) and suitably encodes them for minimum performance loss. Our gradient dynamics perspective illustrates that LRCs tend to have better fine-tuning capabilities and their standalone fine-tuning can closely mimic and sometimes outperform the training loss trajectory and performance of full fine-tuning with notable memory and compute footprint reduction. Codes are available at https://github.com/VITA-Group/WeLore.

cs.LG↗

arXiv2025

AdvPrompter: Fast Adaptive Adversarial Prompting for LLMs

Large Language Models (LLMs) are vulnerable to jailbreaking attacks that lead to generation of inappropriate or harmful content. Manual red-teaming requires a time-consuming search for adversarial prompts, whereas automatic adversarial prompt generation often leads to semantically meaningless attacks that do not scale well. In this paper, we present a novel method that uses another LLM, called AdvPrompter, to generate human-readable adversarial prompts in seconds. AdvPrompter, which is trained using an alternating optimization algorithm, generates suffixes that veil the input instruction without changing its meaning, such that the TargetLLM is lured to give a harmful response. Experimental results on popular open source TargetLLMs show highly competitive results on the AdvBench and HarmBench datasets, that also transfer to closed-source black-box LLMs. We also show that training on adversarial suffixes generated by AdvPrompter is a promising strategy for improving the robustness of LLMs to jailbreaking attacks.

cs.CR↗

arXiv2025

TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training

Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using tensor-parameterized layers to capture complex, multi-dimensional relationships. However, scaling neural operators to high-resolution problems leads to significant computational demands, making the training of industrial-scale models prohibitive. In this work, we introduce \textbf{TensorGRaD}, a novel method that directly addresses the memory challenges associated with optimizing large tensor-structured weights. Our approach, based on a \texit{robust tensor decomposition}, factorizes gradients as the sum of a low-rank tensor and a sparse one to efficiently capture information within optimizer states, including outliers. Additionally, we provide a recipe for mixed precision training of TensorGRaD, achieving further memory savings without sacrificing accuracy. We showcase the effectiveness of TensorGRaD on Fourier Neural Operators, a class of models crucial for solving partial differential equations (PDE). We provide theoretical guarantees for TensorGRaD, demonstrating its fundamental advantage over matrix-based gradient compression methods. We empirically demonstrate large improvements across various PDE tasks, including the challenging turbulent Navier-Stokes case at a Reynolds number of $10^5$. TensorGRaD reduces total memory usage by over $50\%$ while maintaining and sometimes even improving accuracy.

cs.LG↗

arXiv2025

GaLore 2: Large-Scale LLM Pre-Training by Gradient Low-Rank Projection

Large language models (LLMs) have revolutionized natural language understanding and generation but face significant memory bottlenecks during training. GaLore, Gradient Low-Rank Projection, addresses this issue by leveraging the inherent low-rank structure of weight gradients, enabling substantial memory savings without sacrificing performance. Recent works further extend GaLore from various aspects, including low-bit quantization and higher-order tensor structures. However, there are several remaining challenges for GaLore, such as the computational overhead of SVD for subspace updates and the integration with state-of-the-art training parallelization strategies (e.g., FSDP). In this paper, we present GaLore 2, an efficient and scalable GaLore framework that addresses these challenges and incorporates recent advancements. In addition, we demonstrate the scalability of GaLore 2 by pre-training Llama 7B from scratch using up to 500 billion training tokens, highlighting its potential impact on real LLM pre-training scenarios.

cs.LG↗

arXiv2025

R-Sparse: Rank-Aware Activation Sparsity for Efficient LLM Inference

Large Language Models (LLMs), while demonstrating remarkable capabilities across various applications, present significant challenges during inference due to their substantial model size, especially when deployed on edge devices. Activation sparsity offers a promising solution to reduce computation and memory movement, enabling more efficient inference, particularly for small-batch on-device applications. However, current approaches face limitations with non-ReLU activation function, which are foundational to most advanced LLMs, or require heavy continual training. Additionally, the difficulty in predicting active channels and limited achievable sparsity ratios constrain the effectiveness of activation sparsity-based methods. In this paper, we introduce R-Sparse, a training-free activation sparsity approach capable of achieving high sparsity levels in advanced LLMs. We conducted two preliminary investigations into how different components contribute to the output within a single linear layer and found two key observations: (i) the non-sparse components of the input function can be regarded as a few bias terms, and (ii) The full computation can be effectively approximated by an appropriate combination of input channels and weight singular values. Building on this, we replace the linear layers in LLMs with a rank-aware sparse inference method that leverages the sparsity of input channels and singular value components, eliminating the need for active channel prediction like the output sparsity based approaches. Experiments on Llama-2/3 and Mistral models across ten diverse tasks demonstrate that R-Sparse achieves comparable performance at 50% model-level sparsity, resulting in a significant 43% end-to-end efficient improvements with customized kernels.

cs.LG↗

arXiv2025

Param$Δ$ for Direct Weight Mixing: Post-Train Large Language Model at Zero Cost

The post-training phase of large language models is essential for enhancing capabilities such as instruction-following, reasoning, and alignment with human preferences. However, it demands extensive high-quality data and poses risks like overfitting, alongside significant computational costs due to repeated post-training and evaluation after each base model update. This paper introduces $ParamΔ$, a novel method that streamlines post-training by transferring knowledge from an existing post-trained model to a newly updated base model with ZERO additional training. By computing the difference between post-trained model weights ($Θ_\text{post}$) and base model weights ($Θ_\text{base}$), and adding this to the updated base model ($Θ'_\text{base}$), we define $ParamΔ$ Model as: $Θ_{\text{Param}Δ} = Θ_\text{post} - Θ_\text{base} + Θ'_\text{base}$. This approach surprisingly equips the new base model with post-trained capabilities, achieving performance comparable to direct post-training. We did analysis on LLama3, Llama3.1, Qwen, and DeepSeek-distilled models. Results indicate $ParamΔ$ Model effectively replicates traditional post-training. For example, the $ParamΔ$ Model obtained from 70B Llama3-inst, Llama3-base, Llama3.1-base models attains approximately 95\% of Llama3.1-inst model's performance on average. $ParamΔ$ brings a new perspective on how to fully leverage models in the open-weight community, where checkpoints for base and instruct models are readily available and frequently updated, by providing a cost-free framework to accelerate the iterative cycle of model development.

cs.CL↗

arXiv2025

SWEET-RL: Training Multi-Turn LLM Agents on Collaborative Reasoning Tasks

Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.

cs.LG↗

arXiv2025

SpinQuant: LLM quantization with learned rotations

Post-training quantization (PTQ) techniques applied to weights, activations, and the KV cache greatly reduce memory usage, latency, and power consumption of Large Language Models (LLMs), but may lead to large quantization errors when outliers are present. Rotating activation or weight matrices helps remove outliers and benefits quantization. In this work, we identify a collection of applicable rotation parameterizations that lead to identical outputs in full-precision Transformer architectures while enhancing quantization accuracy. In addition, we find that some random rotations lead to much better quantization than others, with an up to 13 points difference in downstream zero-shot reasoning performance. As a result, we propose SpinQuant, a novel approach that incorporates learned rotation matrices for optimal quantized network accuracy. With 4-bit quantization of weight, activation, and KV-cache, SpinQuant narrows the accuracy gap on zero-shot reasoning tasks with full precision to merely 2.9 points on the LLaMA-2 7B model, surpassing LLM-QAT by 19.1 points and SmoothQuant by 25.0 points. Furthermore, SpinQuant also outperforms concurrent work QuaRot, which applies random rotations to remove outliers. In particular, for LLaMA-3 8B models that are hard to quantize, SpinQuant reduces the gap to full precision by up to 45.1% relative to QuaRot. Code is available at https://github.com/facebookresearch/SpinQuant.

cs.LG↗

arXiv2025

LLM Pretraining with Continuous Concepts

Next token prediction has been the standard training objective used in large language model pretraining. Representations are learned as a result of optimizing for token-level perplexity. We propose Continuous Concept Mixing (CoCoMix), a novel pretraining framework that combines discrete next token prediction with continuous concepts. Specifically, CoCoMix predicts continuous concepts learned from a pretrained sparse autoencoder and mixes them into the model's hidden state by interleaving with token hidden representations. Through experiments on multiple benchmarks, including language modeling and downstream reasoning tasks, we show that CoCoMix is more sample efficient and consistently outperforms standard next token prediction, knowledge distillation and inserting pause tokens. We find that combining both concept learning and interleaving in an end-to-end framework is critical to performance gains. Furthermore, CoCoMix enhances interpretability and steerability by allowing direct inspection and modification of the predicted concept, offering a transparent way to guide the model's internal reasoning process.

cs.LG↗

arXiv2025

Spectral Journey: How Transformers Predict the Shortest Path

Decoder-only transformers lead to a step-change in capability of large language models. However, opinions are mixed as to whether they are really planning or reasoning. A path to making progress in this direction is to study the model's behavior in a setting with carefully controlled data. Then interpret the learned representations and reverse-engineer the computation performed internally. We study decoder-only transformer language models trained from scratch to predict shortest paths on simple, connected and undirected graphs. In this setting, the representations and the dynamics learned by the model are interpretable. We present three major results: (1) Two-layer decoder-only language models can learn to predict shortest paths on simple, connected graphs containing up to 10 nodes. (2) Models learn a graph embedding that is correlated with the spectral decomposition of the line graph. (3) Following the insights, we discover a novel approximate path-finding algorithm Spectral Line Navigator (SLN) that finds shortest path by greedily selecting nodes in the space of spectral embedding of the line graph.

cs.LG↗

arXiv2025

SHARP: Accelerating Language Model Inference by SHaring Adjacent layers with Recovery Parameters

While Large language models (LLMs) have advanced natural language processing tasks, their growing computational and memory demands make deployment on resource-constrained devices like mobile phones increasingly challenging. In this paper, we propose SHARP (SHaring Adjacent Layers with Recovery Parameters), a novel approach to accelerate LLM inference by sharing parameters across adjacent layers, thus reducing memory load overhead, while introducing low-rank recovery parameters to maintain performance. Inspired by observations that consecutive layers have similar outputs, SHARP employs a two-stage recovery process: Single Layer Warmup (SLW), and Supervised Fine-Tuning (SFT). The SLW stage aligns the outputs of the shared layers using L_2 loss, providing a good initialization for the following SFT stage to further restore the model performance. Extensive experiments demonstrate that SHARP can recover the model's perplexity on various in-distribution tasks using no more than 50k fine-tuning data while reducing the number of stored MLP parameters by 38% to 65%. We also conduct several ablation studies of SHARP and show that replacing layers towards the later parts of the model yields better performance retention, and that different recovery parameterizations perform similarly when parameter counts are matched. Furthermore, SHARP saves 42.8% in model storage and reduces the total inference time by 42.2% compared to the original Llama2-7b model on mobile devices. Our results highlight SHARP as an efficient solution for reducing inference costs in deploying LLMs without the need for pretraining-scale resources.

cs.LG↗

arXiv2025

GSM-Infinite: How Do Your LLMs Behave over Infinitely Increasing Context Length and Reasoning Complexity?

Long-context large language models (LLMs) have recently shown strong performance in information retrieval and long-document QA. However, to tackle the most challenging intellectual problems, LLMs must reason effectively in long and complex contexts (e.g., frontier mathematical research). Studying how LLMs handle increasing reasoning complexity and context length is essential, yet existing benchmarks lack a solid basis for quantitative evaluation. Inspired by the abstraction of GSM-8K problems as computational graphs, and the ability to introduce noise by adding unnecessary nodes and edges, we develop a grade school math problem generator capable of producing arithmetic problems with infinite difficulty and context length under fine-grained control. Using our newly synthesized GSM-Infinite benchmark, we comprehensively evaluate existing LLMs. We find a consistent sigmoid decline in reasoning performance as complexity increases, along with a systematic inference scaling trend: exponentially increasing inference computation yields only linear performance gains. These findings underscore the fundamental limitations of current long-context LLMs and the key challenges in scaling reasoning capabilities. Our GSM-Infinite benchmark provides a scalable and controllable testbed for systematically studying and advancing LLM reasoning in long and complex contexts.

cs.CL↗