arXiv subjects

Yin Tat Lee

Publications and source records attributed to Yin Tat Lee.

At least 19 recordsLinked to original sources

arXiv2025

Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Sampler

The development of efficient sampling algorithms catering to non-Euclidean geometries has been a challenging endeavor, as discretization techniques which succeed in the Euclidean setting do not readily carry over to more general settings. We develop a non-Euclidean analog of the recent proximal sampler of [LST21], which naturally induces regularization by an object known as the log-Laplace transform (LLT) of a density. We prove new mathematical properties (with an algorithmic flavor) of the LLT, such as strong convexity-smoothness duality and an isoperimetric inequality, which are used to prove a mixing time on our proximal sampler matching [LST21] under a warm start. As our main application, we show our warm-started sampler improves the value oracle complexity of differentially private convex optimization in $\ell_p$ and Schatten-$p$ norms for $p \in [1, 2]$ to match the Euclidean setting [GLL22], while retaining state-of-the-art excess risk bounds [GLLST23]. We find our investigation of the LLT to be a promising proof-of-concept of its utility as a tool for designing samplers, and outline directions for future exploration.

cs.DS↗

arXiv2025

Early science acceleration experiments with GPT-5

AI models like GPT-5 are an increasingly valuable tool for scientists, but many remain unaware of the capabilities of frontier AI. We present a collection of short case studies in which GPT-5 produced new, concrete steps in ongoing research across mathematics, physics, astronomy, computer science, biology, and materials science. In these examples, the authors highlight how AI accelerated their work, and where it fell short; where expert time was saved, and where human input was still key. We document the interactions of the human authors with GPT-5, as guiding examples of fruitful collaboration with AI. Of note, this paper includes four new results in mathematics (carefully verified by the human authors), underscoring how GPT-5 can help human mathematicians settle previously unsolved problems. These contributions are modest in scope but profound in implication, given the rate at which frontier AI is progressing.

cs.CL↗

arXiv2025

Upper and Lower Bounds on the Smoothed Complexity of the Simplex Method

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by Spielman and Teng (JACM '04) for this purpose, defines the smoothed complexity of solving a linear program with $d$ variables and $n$ constraints as the expected running time when Gaussian noise of variance $σ^2$ is added to the LP data. We prove that the smoothed complexity of the simplex method is $O(σ^{-3/2} d^{13/4}\log^{7/4} n)$, improving the dependence on $1/σ$ compared to the previous bound of $O(σ^{-2} d^2\sqrt{\log n})$. We accomplish this through a new analysis of the \emph{shadow bound}, key to earlier analyses as well. Illustrating the power of our new method, we use our method to prove a nearly tight upper bound on the smoothed complexity of two-dimensional polygons. We also establish the first non-trivial lower bound on the smoothed complexity of the simplex method, proving that the \emph{shadow vertex simplex method} requires at least $Ω\Big(\min \big(σ^{-1/2} d^{-1/2}\log^{-1/4} d,2^d \big) \Big)$ pivot steps with high probability. A key part of our analysis is a new variation on the extended formulation for the regular $2^k$-gon. We end with a numerical experiment that suggests this analysis could be further improved.

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arXiv2025

Pseudo-Asynchronous Local SGD: Robust and Efficient Data-Parallel Training

Following AI scaling trends, frontier models continue to grow in size and continue to be trained on larger datasets. Training these models requires huge investments in exascale computational resources, which has in turn driven developtment of distributed deep learning methods. Data parallelism is an essential approach to speed up training, but it requires frequent global communication between workers, which can bottleneck training at the largest scales. In this work, we propose a method called Pseudo-Asynchronous Local SGD (PALSGD) to improve the efficiency of data-parallel training. PALSGD is an extension of Local SGD (Stich, 2018) and DiLoCo (Douillard et al., 2023), designed to further reduce communication frequency by introducing a pseudo-synchronization mechanism. PALSGD allows the use of longer synchronization intervals compared to standard Local SGD. Despite the reduced communication frequency, the pseudo-synchronization approach ensures that model consistency is maintained, leading to performance results comparable to those achieved with more frequent synchronization. Furthermore, we provide a theoretical analysis of PALSGD, establishing its convergence and deriving its convergence rate. This analysis offers insights into the algorithm's behavior and performance guarantees. We evaluated PALSGD on image classification and language modeling tasks. Our results show that PALSGD achieves better performance in less time compared to existing methods like Distributed Data Parallel (DDP), and DiLoCo. Notably, PALSGD trains 18.4% faster than DDP on ImageNet-1K with ResNet-50, 24.4% faster than DDP on TinyStories with GPT-Neo-125M, and 21.1% faster than DDP on TinyStories with GPT-Neo-8M.

cs.LG↗

arXiv2024

Phi-4 Technical Report

We present phi-4, a 14-billion parameter language model developed with a training recipe that is centrally focused on data quality. Unlike most language models, where pre-training is based primarily on organic data sources such as web content or code, phi-4 strategically incorporates synthetic data throughout the training process. While previous models in the Phi family largely distill the capabilities of a teacher model (specifically GPT-4), phi-4 substantially surpasses its teacher model on STEM-focused QA capabilities, giving evidence that our data-generation and post-training techniques go beyond distillation. Despite minimal changes to the phi-3 architecture, phi-4 achieves strong performance relative to its size -- especially on reasoning-focused benchmarks -- due to improved data, training curriculum, and innovations in the post-training scheme.

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arXiv2024

Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone

We introduce phi-3-mini, a 3.8 billion parameter language model trained on 3.3 trillion tokens, whose overall performance, as measured by both academic benchmarks and internal testing, rivals that of models such as Mixtral 8x7B and GPT-3.5 (e.g., phi-3-mini achieves 69% on MMLU and 8.38 on MT-bench), despite being small enough to be deployed on a phone. Our training dataset is a scaled-up version of the one used for phi-2, composed of heavily filtered publicly available web data and synthetic data. The model is also further aligned for robustness, safety, and chat format. We also provide parameter-scaling results with a 7B, 14B models trained for 4.8T tokens, called phi-3-small, phi-3-medium, both significantly more capable than phi-3-mini (e.g., respectively 75%, 78% on MMLU, and 8.7, 8.9 on MT-bench). To enhance multilingual, multimodal, and long-context capabilities, we introduce three models in the phi-3.5 series: phi-3.5-mini, phi-3.5-MoE, and phi-3.5-Vision. The phi-3.5-MoE, a 16 x 3.8B MoE model with 6.6 billion active parameters, achieves superior performance in language reasoning, math, and code tasks compared to other open-source models of similar scale, such as Llama 3.1 and the Mixtral series, and on par with Gemini-1.5-Flash and GPT-4o-mini. Meanwhile, phi-3.5-Vision, a 4.2 billion parameter model derived from phi-3.5-mini, excels in reasoning tasks and is adept at handling both single-image and text prompts, as well as multi-image and text prompts.

cs.CL↗

arXiv2024

Reducing Isotropy and Volume to KLS: Faster Rounding and Volume Algorithms

We show that the volume of a convex body in $\mathbb{R}^{n}$ in the general membership oracle model can be computed to within relative error $\varepsilon$ using $\widetilde{O}(n^{3.5}ψ^{2} + n^3/\varepsilon^{2})$ oracle queries, where $ψ$ is the KLS constant. With the current bound of $ψ=\widetilde{O}(1)$, this gives an $\widetilde{O}(n^{3.5} + n^3/\varepsilon^{2})$ algorithm, improving on the Lovász-Vempala $\widetilde{O}(n^{4}/\varepsilon^{2})$ algorithm from 2003. The main new ingredient is an $\widetilde{O}(n^{3}ψ^{2})$ algorithm for isotropic transformation of a well-rounded convex body; we apply this iteratively to isotropicize a general convex body. Following this, we can apply the $\widetilde{O}(n^{3}/\varepsilon^{2})$ volume algorithm of Cousins and Vempala for well-rounded convex bodies. We also give an efficient implementation of the new algorithm for convex polytopes defined by $m$ inequalities in $\mathbb{R}^{n}$: polytope volume can be estimated in time $\widetilde{O}(mn^{c}/\varepsilon^{2})$ where $c<3.7$ depends on the current matrix multiplication exponent and improves on the previous best bound.

cs.DS↗

arXiv2024

Differentially Private Synthetic Data via Foundation Model APIs 2: Text

Text data has become extremely valuable due to the emergence of machine learning algorithms that learn from it. A lot of high-quality text data generated in the real world is private and therefore cannot be shared or used freely due to privacy concerns. Generating synthetic replicas of private text data with a formal privacy guarantee, i.e., differential privacy (DP), offers a promising and scalable solution. However, existing methods necessitate DP finetuning of large language models (LLMs) on private data to generate DP synthetic data. This approach is not viable for proprietary LLMs (e.g., GPT-3.5) and also demands considerable computational resources for open-source LLMs. Lin et al. (2024) recently introduced the Private Evolution (PE) algorithm to generate DP synthetic images with only API access to diffusion models. In this work, we propose an augmented PE algorithm, named Aug-PE, that applies to the complex setting of text. We use API access to an LLM and generate DP synthetic text without any model training. We conduct comprehensive experiments on three benchmark datasets. Our results demonstrate that Aug-PE produces DP synthetic text that yields competitive utility with the SOTA DP finetuning baselines. This underscores the feasibility of relying solely on API access of LLMs to produce high-quality DP synthetic texts, thereby facilitating more accessible routes to privacy-preserving LLM applications. Our code and data are available at https://github.com/AI-secure/aug-pe.

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arXiv2024

MathChat: Converse to Tackle Challenging Math Problems with LLM Agents

Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. LLMs, with their generalized ability, are used as a foundation model to build AI agents for different tasks. In this paper, we study the effectiveness of utilizing LLM agents to solve math problems through conversations. We propose MathChat, a conversational problem-solving framework designed for math problems. MathChat consists of an LLM agent and a user proxy agent which is responsible for tool execution and additional guidance. This synergy facilitates a collaborative problem-solving process, where the agents engage in a dialogue to solve the problems. We perform evaluation on difficult high school competition problems from the MATH dataset. Utilizing Python, we show that MathChat can further improve previous tool-using prompting methods by 6%.

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arXiv2024

The Power of Sampling: Dimension-free Risk Bounds in Private ERM

Differentially private empirical risk minimization (DP-ERM) is a fundamental problem in private optimization. While the theory of DP-ERM is well-studied, as large-scale models become prevalent, traditional DP-ERM methods face new challenges, including (1) the prohibitive dependence on the ambient dimension, (2) the highly non-smooth objective functions, (3) costly first-order gradient oracles. Such challenges demand rethinking existing DP-ERM methodologies. In this work, we show that the regularized exponential mechanism combined with existing samplers can address these challenges altogether: under the standard unconstrained domain and low-rank gradients assumptions, our algorithm can achieve rank-dependent risk bounds for non-smooth convex objectives using only zeroth order oracles, which was not accomplished by prior methods. This highlights the power of sampling in differential privacy. We further construct lower bounds, demonstrating that when gradients are full-rank, there is no separation between the constrained and unconstrained settings. Our lower bound is derived from a general black-box reduction from unconstrained to the constrained domain and an improved lower bound in the constrained setting, which might be of independent interest.

cs.LG↗

arXiv2024

Improving the Bit Complexity of Communication for Distributed Convex Optimization

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression, $p$-norm regression (for $1\leq p\leq 2$), linear programming, minimizing the sum of finitely many convex nonsmooth functions with varying supports, and low rank approximation; for a number of these fundamental problems our bounds are nearly optimal, as proven by our lower bounds. Among our techniques, we use the notion of block leverage scores, which have been relatively unexplored in this context, as well as dropping all but the ``middle" bits in Richardson-style algorithms. We also introduce a new communication problem for accurately approximating inner products and establish a lower bound using the spherical Radon transform. Our lower bound can be used to show the first separation of linear programming and linear systems in the distributed model when the number of constraints is polynomial, addressing an open question in prior work.

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arXiv2023

Can Generalist Foundation Models Outcompete Special-Purpose Tuning? Case Study in Medicine

Generalist foundation models such as GPT-4 have displayed surprising capabilities in a wide variety of domains and tasks. Yet, there is a prevalent assumption that they cannot match specialist capabilities of fine-tuned models. For example, most explorations to date on medical competency benchmarks have leveraged domain-specific training, as exemplified by efforts on BioGPT and Med-PaLM. We build on a prior study of GPT-4's capabilities on medical challenge benchmarks in the absence of special training. Rather than using simple prompting to highlight the model's out-of-the-box capabilities, we perform a systematic exploration of prompt engineering. We find that prompting innovation can unlock deeper specialist capabilities and show that GPT-4 easily tops prior leading results for medical benchmarks. The prompting methods we explore are general purpose, and make no specific use of domain expertise, removing the need for expert-curated content. Our experimental design carefully controls for overfitting during the prompt engineering process. We introduce Medprompt, based on a composition of several prompting strategies. With Medprompt, GPT-4 achieves state-of-the-art results on all nine of the benchmark datasets in the MultiMedQA suite. The method outperforms leading specialist models such as Med-PaLM 2 by a significant margin with an order of magnitude fewer calls to the model. Steering GPT-4 with Medprompt achieves a 27% reduction in error rate on the MedQA dataset over the best methods to date achieved with specialist models and surpasses a score of 90% for the first time. Beyond medical problems, we show the power of Medprompt to generalize to other domains and provide evidence for the broad applicability of the approach via studies of the strategy on exams in electrical engineering, machine learning, philosophy, accounting, law, nursing, and clinical psychology.

cs.CL↗

arXiv2023

Positional Description Matters for Transformers Arithmetic

Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is their naive reliance on positional information to solve arithmetic problems with a small number of digits, leading to poor performance on larger numbers. Herein, we delve deeper into the role of positional encoding, and propose several ways to fix the issue, either by modifying the positional encoding directly, or by modifying the representation of the arithmetic task to leverage standard positional encoding differently. We investigate the value of these modifications for three tasks: (i) classical multiplication, (ii) length extrapolation in addition, and (iii) addition in natural language context. For (i) we train a small model on a small dataset (100M parameters and 300k samples) with remarkable aptitude in (direct, no scratchpad) 15 digits multiplication and essentially perfect up to 12 digits, while usual training in this context would give a model failing at 4 digits multiplication. In the experiments on addition, we use a mere 120k samples to demonstrate: for (ii) extrapolation from 10 digits to testing on 12 digits numbers while usual training would have no extrapolation, and for (iii) almost perfect accuracy up to 5 digits while usual training would be correct only up to 3 digits (which is essentially memorization with a training set of 120k samples).

cs.CL↗

arXiv2023

Convex Minimization with Integer Minima in $\widetilde O(n^4)$ Time

Given a convex function $f$ on $\mathbb{R}^n$ with an integer minimizer, we show how to find an exact minimizer of $f$ using $O(n^2 \log n)$ calls to a separation oracle and $O(n^4 \log n)$ time. The previous best polynomial time algorithm for this problem given in [Jiang, SODA 2021, JACM 2022] achieves $O(n^2\log\log n/\log n)$ oracle complexity. However, the overall runtime of Jiang's algorithm is at least $\widetildeΩ(n^8)$, due to expensive sub-routines such as the Lenstra-Lenstra-Lovász (LLL) algorithm [Lenstra, Lenstra, Lovász, Math. Ann. 1982] and random walk based cutting plane method [Bertsimas, Vempala, JACM 2004]. Our significant speedup is obtained by a nontrivial combination of a faster version of the LLL algorithm due to [Neumaier, Stehlé, ISSAC 2016] that gives similar guarantees, the volumetric center cutting plane method (CPM) by [Vaidya, FOCS 1989] and its fast implementation given in [Jiang, Lee, Song, Wong, STOC 2020]. For the special case of submodular function minimization (SFM), our result implies a strongly polynomial time algorithm for this problem using $O(n^3 \log n)$ calls to an evaluation oracle and $O(n^4 \log n)$ additional arithmetic operations. Both the oracle complexity and the number of arithmetic operations of our more general algorithm are better than the previous best-known runtime algorithms for this specific problem given in [Lee, Sidford, Wong, FOCS 2015] and [Dadush, Végh, Zambelli, SODA 2018, MOR 2021].

cs.DS↗

arXiv2023

ReSQueing Parallel and Private Stochastic Convex Optimization

We introduce a new tool for stochastic convex optimization (SCO): a Reweighted Stochastic Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. Combining ReSQue with recent advances in ball oracle acceleration [CJJJLST20, ACJJS21], we develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings. For a SCO objective constrained to the unit ball in $\mathbb{R}^d$, we obtain the following results (up to polylogarithmic factors). We give a parallel algorithm obtaining optimization error $ε_{\text{opt}}$ with $d^{1/3}ε_{\text{opt}}^{-2/3}$ gradient oracle query depth and $d^{1/3}ε_{\text{opt}}^{-2/3} + ε_{\text{opt}}^{-2}$ gradient queries in total, assuming access to a bounded-variance stochastic gradient estimator. For $ε_{\text{opt}} \in [d^{-1}, d^{-1/4}]$, our algorithm matches the state-of-the-art oracle depth of [BJLLS19] while maintaining the optimal total work of stochastic gradient descent. Given $n$ samples of Lipschitz loss functions, prior works [BFTT19, BFGT20, AFKT21, KLL21] established that if $n \gtrsim d ε_{\text{dp}}^{-2}$, $(ε_{\text{dp}}, δ)$-differential privacy is attained at no asymptotic cost to the SCO utility. However, these prior works all required a superlinear number of gradient queries. We close this gap for sufficiently large $n \gtrsim d^2 ε_{\text{dp}}^{-3}$, by using ReSQue to design an algorithm with near-linear gradient query complexity in this regime.

math.OC↗

arXiv2023

Learning threshold neurons via the "edge of stability"

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al. (ICLR 2021), which exhibit startling new phenomena (the "edge of stability" or "unstable convergence") and potential benefits for generalization in the large learning rate regime. Despite a flurry of recent works on this topic, however, the latter effect is still poorly understood. In this paper, we take a step towards understanding genuinely non-convex training dynamics with large learning rates by performing a detailed analysis of gradient descent for simplified models of two-layer neural networks. For these models, we provably establish the edge of stability phenomenon and discover a sharp phase transition for the step size below which the neural network fails to learn "threshold-like" neurons (i.e., neurons with a non-zero first-layer bias). This elucidates one possible mechanism by which the edge of stability can in fact lead to better generalization, as threshold neurons are basic building blocks with useful inductive bias for many tasks.

cs.LG↗

arXiv2023

Automatic Prompt Optimization with "Gradient Descent" and Beam Search

Large Language Models (LLMs) have shown impressive performance as general purpose agents, but their abilities remain highly dependent on prompts which are hand written with onerous trial-and-error effort. We propose a simple and nonparametric solution to this problem, Automatic Prompt Optimization (APO), which is inspired by numerical gradient descent to automatically improve prompts, assuming access to training data and an LLM API. The algorithm uses minibatches of data to form natural language "gradients" that criticize the current prompt. The gradients are then "propagated" into the prompt by editing the prompt in the opposite semantic direction of the gradient. These gradient descent steps are guided by a beam search and bandit selection procedure which significantly improves algorithmic efficiency. Preliminary results across three benchmark NLP tasks and the novel problem of LLM jailbreak detection suggest that Automatic Prompt Optimization can outperform prior prompt editing techniques and improve an initial prompt's performance by up to 31%, by using data to rewrite vague task descriptions into more precise annotation instructions.

cs.CL↗

arXiv2023

Textbooks Are All You Need

We introduce phi-1, a new large language model for code, with significantly smaller size than competing models: phi-1 is a Transformer-based model with 1.3B parameters, trained for 4 days on 8 A100s, using a selection of ``textbook quality" data from the web (6B tokens) and synthetically generated textbooks and exercises with GPT-3.5 (1B tokens). Despite this small scale, phi-1 attains pass@1 accuracy 50.6% on HumanEval and 55.5% on MBPP. It also displays surprising emergent properties compared to phi-1-base, our model before our finetuning stage on a dataset of coding exercises, and phi-1-small, a smaller model with 350M parameters trained with the same pipeline as phi-1 that still achieves 45% on HumanEval.

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