Hongzhou Lin

Jui-Hui Chung, Hongzhou Lin, Lai Jiang et al.

Heavy supervised fine-tuning on a target domain can strongly suppress capabilities that were present in the base model. We study this phenomenon in formal mathematics using Goedel-Prover-V2, an open-source model heavily trained on 1.8 million formal-math examples. After domain specialization, the model almost completely loses its ability to produce valid tool calls, even when explicitly instructed to use tools, dropping from 89.4% function-calling accuracy in the base model to nearly 0%. We ask whether this agentic collapse is permanent or instead reversible. To answer this question, we fine-tune the specialized model on a small amount of Lean-specific tool-use data. Remarkably, as few as 100 agentic traces are sufficient to restore strong tool-calling behavior. Importantly, this recovery is not the result of reward hacking or benchmark-specific optimization: the recovery data is entirely drawn from the Lean setting, where the model uses natural-language queries to search the Mathlib library for relevant theorems and lemmas, yet the regained capability transfers well beyond that domain. In particular, these same 100 Lean-specific traces improve performance on the Berkeley Function Calling Leaderboard from near zero to 83.8%, approaching the base model's 89.4% despite the mismatch in task distribution and protocol. The recovered capability is also practically useful in-domain. On ProofNet, pass@32 improves from 21.51% to 25.81%. Together, these results show that heavy domain supervised fine-tuning can suppress general tool-use ability without permanently erasing it, and that a small amount of domain-specific agentic data can awaken dormant tool-use capabilities.

Qingyi Wang, Shenhao Wang, Yunhan Zheng et al.

Classical demand modeling analyzes travel behavior using only low-dimensional numeric data (i.e. sociodemographics and travel attributes) but not high-dimensional urban imagery. However, travel behavior depends on the factors represented by both numeric data and urban imagery, thus necessitating a synergetic framework to combine them. This study creates a theoretical framework of deep hybrid models with a crossing structure consisting of a mixing operator and a behavioral predictor, thus integrating the numeric and imagery data into a latent space. Empirically, this framework is applied to analyze travel mode choice using the MyDailyTravel Survey from Chicago as the numeric inputs and the satellite images as the imagery inputs. We found that deep hybrid models outperform both the traditional demand models and the recent deep learning in predicting the aggregate and disaggregate travel behavior with our supervision-as-mixing design. The latent space in deep hybrid models can be interpreted, because it reveals meaningful spatial and social patterns. The deep hybrid models can also generate new urban images that do not exist in reality and interpret them with economic theory, such as computing substitution patterns and social welfare changes. Overall, the deep hybrid models demonstrate the complementarity between the low-dimensional numeric and high-dimensional imagery data and between the traditional demand modeling and recent deep learning. It generalizes the latent classes and variables in classical hybrid demand models to a latent space, and leverages the computational power of deep learning for imagery while retaining the economic interpretability on the microeconomics foundation.

Yossi Arjevani, Joan Bruna, Bugra Can et al.

We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method, thereby providing a systematic way for deriving several well-known decentralized algorithms including EXTRA arXiv:1404.6264 and SSDA arXiv:1702.08704. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds. We provide experimental results that demonstrate the effectiveness of the proposed algorithm on highly ill-conditioned problems.

Jingzhao Zhang, Hongzhou Lin, Stefanie Jegelka et al.

We provide the first non-asymptotic analysis for finding stationary points of nonsmooth, nonconvex functions. In particular, we study the class of Hadamard semi-differentiable functions, perhaps the largest class of nonsmooth functions for which the chain rule of calculus holds. This class contains examples such as ReLU neural networks and others with non-differentiable activation functions. We first show that finding an $ε$-stationary point with first-order methods is impossible in finite time. We then introduce the notion of $(δ, ε)$-stationarity, which allows for an $ε$-approximate gradient to be the convex combination of generalized gradients evaluated at points within distance $δ$ to the solution. We propose a series of randomized first-order methods and analyze their complexity of finding a $(δ, ε)$-stationary point. Furthermore, we provide a lower bound and show that our stochastic algorithm has min-max optimal dependence on $δ$. Empirically, our methods perform well for training ReLU neural networks.

Yossi Arjevani, Amit Daniely, Stefanie Jegelka et al.

Recent advances in randomized incremental methods for minimizing $L$-smooth $μ$-strongly convex finite sums have culminated in tight complexity of $\tilde{O}((n+\sqrt{n L/μ})\log(1/ε))$ and $O(n+\sqrt{nL/ε})$, where $μ>0$ and $μ=0$, respectively, and $n$ denotes the number of individual functions. Unlike incremental methods, stochastic methods for finite sums do not rely on an explicit knowledge of which individual function is being addressed at each iteration, and as such, must perform at least $Ω(n^2)$ iterations to obtain $O(1/n^2)$-optimal solutions. In this work, we exploit the finite noise structure of finite sums to derive a matching $O(n^2)$-upper bound under the global oracle model, showing that this lower bound is indeed tight. Following a similar approach, we propose a novel adaptation of SVRG which is both \emph{compatible with stochastic oracles}, and achieves complexity bounds of $\tilde{O}((n^2+n\sqrt{L/μ})\log(1/ε))$ and $O(n\sqrt{L/ε})$, for $μ>0$ and $μ=0$, respectively. Our bounds hold w.h.p. and match in part existing lower bounds of $\tildeΩ(n^2+\sqrt{nL/μ}\log(1/ε))$ and $\tildeΩ(n^2+\sqrt{nL/ε})$, for $μ>0$ and $μ=0$, respectively.

Hongzhou Lin, Stefanie Jegelka

We demonstrate that a very deep ResNet with stacked modules with one neuron per hidden layer and ReLU activation functions can uniformly approximate any Lebesgue integrable function in $d$ dimensions, i.e. $\ell_1(\mathbb{R}^d)$. Because of the identity mapping inherent to ResNets, our network has alternating layers of dimension one and $d$. This stands in sharp contrast to fully connected networks, which are not universal approximators if their width is the input dimension $d$ [Lu et al, 2017; Hanin and Sellke, 2017]. Hence, our result implies an increase in representational power for narrow deep networks by the ResNet architecture.

Hongzhou Lin, Julien Mairal, Zaid Harchaoui

We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective function, and consists of approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. One of the keys to achieve acceleration in theory and in practice is to solve these sub-problems with appropriate accuracy by using the right stopping criterion and the right warm-start strategy. We give practical guidelines to use Catalyst and present a comprehensive analysis of its global complexity. We show that Catalyst applies to a large class of algorithms, including gradient descent, block coordinate descent, incremental algorithms such as SAG, SAGA, SDCA, SVRG, MISO/Finito, and their proximal variants. For all of these methods, we establish faster rates using the Catalyst acceleration, for strongly convex and non-strongly convex objectives. We conclude with extensive experiments showing that acceleration is useful in practice, especially for ill-conditioned problems.

Courtney Paquette, Hongzhou Lin, Dmitriy Drusvyatskiy et al.

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed approach allows one to use them on weakly convex objectives, which covers a large class of non-convex functions typically appearing in machine learning and signal processing. In general, the scheme is guaranteed to produce a stationary point with a worst-case efficiency typical of first-order methods, and when the objective turns out to be convex, it automatically accelerates in the sense of Nesterov and achieves near-optimal convergence rate in function values. These properties are achieved without assuming any knowledge about the convexity of the objective, by automatically adapting to the unknown weak convexity constant. We conclude the paper by showing promising experimental results obtained by applying our approach to incremental algorithms such as SVRG and SAGA for sparse matrix factorization and for learning neural networks.

Hongzhou Lin, Julien Mairal, Zaid Harchaoui

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic variance-reduced gradient descent algorithm (SVRG) and other randomized incremental optimization algorithms. QNing is also compatible with composite objectives, meaning that it has the ability to provide exactly sparse solutions when the objective involves a sparsity-inducing regularization. When combined with limited-memory BFGS rules, QNing is particularly effective to solve high-dimensional optimization problems, while enjoying a worst-case linear convergence rate for strongly convex problems. We present experimental results where QNing gives significant improvements over competing methods for training machine learning methods on large samples and in high dimensions.