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Optimization · Neural Network Optimization

Yuhao Zhou, Jintao Xu, Bingrui Li, Chenglong Bao, Chao Ding, Jun Zhu

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face a trade‑off between global and local convergence. Whether a parameter-free algorithm of this type can simultaneously achieve optimal global complexity and quadratic local convergence remains an open question. To bridge this long-standing gap, we propose a new class of regularizers constructed from the current and previous gradients, and leverage the conjugate gradient approach with a negative curvature monitor to solve the regularized Newton equation. The proposed algorithm is adaptive, requiring no prior knowledge of the Hessian Lipschitz constant, and achieves a global complexity of $O(\epsilon^{-\frac{3}{2}})$ in terms of the second-order oracle calls, and $\tilde O(\epsilon^{-\frac{7}{4}})$ for Hessian-vector products, respectively. When the iterates converge to a point where the Hessian is positive definite, the method exhibits quadratic local convergence. Preliminary numerical results, including training the physics-informed neural networks, illustrate the competitiveness of our algorithm.

Optimization · Neural Network Optimization

Adrian Bulat, Yassine Ouali, Georgios Tzimiropoulos

This work aims to compress the vision tokens of an LVLM into a representation that is simultaneously suitable for (a) generative and (b) discriminative tasks, (c) is nearly lossless, and (d) storage-efficient. To this end, we propose C&C, a novel compression method that leverages the LVLM itself for task-agnostic visual token compression. Unlike prior methods that perform token reduction on-the-fly, our approach offloads computation to a dedicated, upfront indexing stage, effectively decoupling compression from generation. This enables learning more powerful representations for generation during inference. At the core of C&C is a ``double-forward pass'' training strategy. During the first forward pass, the LLM (of the LVLM) creates a bottleneck by compressing the dense visual tokens into a few summary tokens. Subsequently, the second forward pass processes the language instruction(s) alongside the summary tokens, used as a direct replacement for the image ones. The training of C&C is guided by two key losses: an autoregressive loss applied after the second pass that provides a direct optimization objective for reconstructing the original information flow, and a contrastive loss applied after the first pass to bolster the representational strength of the summary tokens, particularly for discriminative tasks. Moreover, we propose stage-specific adapters for further enhancing performance. C&C produces highly informative compressed representations. An in-depth ablation study confirms the efficacy of our approach. For generative tasks, we achieve a 2x higher compression rate without compromising capabilities, setting a new state-of-the-art. For discriminative tasks, we establish new state-of-the-art results on image retrieval and compositionality benchmarks.

Deep Learning · Algorithms

Yusheng Zhao, Qixin Zhang, Xiao Luo, Weizhi Zhang, Zhiping Xiao, Wei Ju, Philip S Yu, Ming Zhang

Large language models (LLMs) have been used in many zero-shot learning problems, with their strong generalization ability. Recently, adopting LLMs in text-attributed graphs (TAGs) has drawn increasing attention. However, the adoption of LLMs faces two major challenges: limited information on graph structure and unreliable responses. LLMs struggle with text attributes isolated from the graph topology. Worse still, they yield unreliable predictions due to both information insufficiency and the inherent weakness of LLMs (e.g., hallucination). Towards this end, this paper proposes a novel method named Dynamic Text Bundling Supervision (DENSE) that queries LLMs with bundles of texts to obtain bundle-level labels and uses these labels to supervise graph neural networks. Specifically, we sample a set of bundles, each containing a set of nodes with corresponding texts of close proximity. We then query LLMs with the bundled texts to obtain the label of each bundle. Subsequently, the bundle labels are used to supervise the optimization of graph neural networks, and the bundles are further refined to exclude noisy items. To justify our design, we also provide theoretical analysis of the proposed method. Extensive experiments across ten datasets validate the effectiveness of the proposed method.

Deep Learning · Graph Neural Networks

Qipeng zhu, Jie Chen, Jian Pu, Junping Zhang

Graph Neural Networks (GNNs) are pivotal in graph classification but often struggle with generalization and overfitting. We introduce a unified and efficient Graph Multi-View (GMV) learning framework that integrates multi-view learning into GNNs to enhance robustness and efficiency. Leveraging the lottery ticket hypothesis, GMV activates diverse sub-networks within a single GNN through a novel training pipeline, which includes mixed-view generation, and multi-view decomposition and learning. This approach simultaneously broadens "views" from the data, model, and optimization perspectives during training to enhance the generalization capabilities of GNNs. During inference, GMV only incorporates additional prediction heads into standard GNNs, thereby achieving multi-view learning at minimal cost. Our experiments demonstrate that GMV surpasses other augmentation and ensemble techniques for GNNs and Graph Transformers across various graph classification scenarios.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Ioannis Mavrothalassitis, Pol Puigdemont, Noam Levi, Volkan Cevher

Contrary to common belief, we show that gradient ascent-based unconstrained optimization methods frequently fail to perform machine unlearning, a phenomenon we attribute to the inherent statistical dependence between the forget and retain data sets. This dependence, which can manifest itself even as simple correlations, undermines the misconception that these sets can be independently manipulated during unlearning. We provide empirical and theoretical evidence showing these methods often fail precisely due to this overlooked relationship. For random forget sets, this dependence means that degrading forget set metrics (which, for a retrained model, should mirror test set metrics) inevitably harms overall test performance. Going beyond random sets, we consider logistic regression as an instructive example where a critical failure mode emerges: inter-set dependence causes gradient descent-ascent iterations to progressively diverge from the ideal retrained model. Strikingly, these methods can converge to solutions that are not only far from the retrained ideal but are potentially even further from it than the original model itself, rendering the unlearning process actively detrimental. A toy example further illustrates how this dependence can trap models in inferior local minima, inescapable via finetuning. Our findings highlight that the presence of such statistical dependencies, even when manifest only as correlations, can be sufficient for ascent-based unlearning to fail. Our theoretical insights are corroborated by experiments on complex neural networks, demonstrating that these methods do not perform as expected in practice due to this unaddressed statistical interplay.

Optimization · Neural Network Optimization

Zhiwei Li, Yuesen Liao, Binrui Wu, Yuquan Zhou, Xupeng Shi, Dongsheng Jiang, Yin Li, Weizhong Zhang

Pruning is a commonly employed technique for deep neural networks (DNNs) aiming at compressing the model size to reduce computational and memory costs during inference. In contrast to conventional neural networks, large language models (LLMs) pose a unique challenge regarding pruning efficiency due to their substantial computational and memory demands. Existing methods, particularly optimization-based ones, often require considerable computational resources in gradient estimation because they cannot effectively leverage weight sparsity of the intermediate pruned network to lower compuation and memory costs in each iteration. The fundamental challenge lies in the need to frequently instantiate intermediate pruned sub-models to achieve these savings, a task that becomes infeasible even for moderately sized neural networks. To this end, this paper proposes a novel pruning method for DNNs that is both computationally and memory-efficient. Our key idea is to develop an effective reweighting mechanism that enables us to estimate the gradient of the pruned network in current iteration via reweigting the gradient estimated on an outdated intermediate sub-model instantiated at an earlier stage, thereby significantly reducing model instantiation frequency. We further develop a series of techniques, e.g., clipping and preconditioning matrix, to reduce the variance of gradient estimation and stabilize the optimization process. We conducted extensive experimental validation across various domains. Our approach achieves 50\% sparsity and a 1.58$\times$ speedup in forward pass on Llama2-7B model with only 6 GB of memory usage, outperforming state-of-the-art methods with respect to both perplexity and zero-shot performance. As a by-product, our method is highly suited for distributed sparse training and can achieve a 2 $\times$ speedup over the dense distributed baselines.

Optimization · Neural Network Optimization

Dmitriy Shopkhoev, Ammar Ali, Magauiya Zhussip, Valentin Malykh, Stamatios Lefkimmiatis, Nikos Komodakis, Sergey Zagoruyko

We introduce ReplaceMe, a generalized training-free depth pruning method that effectively replaces transformer blocks with a linear operation, while maintaining high performance for low compression ratios. In contrast to conventional pruning approaches that require additional training or fine-tuning, our approach requires only a small calibration dataset that is used to estimate a linear transformation, which approximates the pruned blocks. The estimated linear mapping can be seam- lessly merged with the remaining transformer blocks, eliminating the need for any additional network parameters. Our experiments show that ReplaceMe consistently outperforms other training-free approaches and remains highly competitive with state-of-the-art pruning methods that involve extensive retraining/fine-tuning and architectural modifications. Applied to several large language models (LLMs), ReplaceMe achieves up to 25% pruning while retaining approximately 90% of the original model’s performance on open benchmarks—without any training or healing steps, resulting in minimal computational overhead. We provide an open- source library implementing ReplaceMe alongside several state-of-the-art depth pruning techniques, available at https://github.com/mts-ai/ReplaceMe.

Optimization · Neural Network Optimization

Jiaqi Wang, Zhiguang Cao, Peng Zhao, Rui Cao, YuBin Xiao, YUAN JIANG, You Zhou

The rise of smart manufacturing under Industry 4.0 introduces mass customization and dynamic production, demanding more advanced and flexible scheduling techniques. The flexible job-shop scheduling problem (FJSP) has attracted significant attention due to its complex constraints and strong alignment with real-world production scenarios. Current deep reinforcement learning (DRL)-based approaches to FJSP predominantly employ constructive methods. While effective, they often fall short of reaching (near-)optimal solutions. In contrast, improvement-based methods iteratively explore the neighborhood of initial solutions and are more effective in approaching optimality. However, the flexible machine allocation in FJSP poses significant challenges to the application of this framework, including accurate state representation, effective policy learning, and efficient search strategies. To address these challenges, this paper proposes a $\textbf{M}$emory-enhanced $\textbf{I}$mprovement $\textbf{S}$earch framework with he$\textbf{t}$erogeneous gr$\textbf{a}$ph $\textbf{r}$epresentation—$\textit{MIStar}$. It employs a novel heterogeneous disjunctive graph that explicitly models the operation sequences on machines to accurately represent scheduling solutions. Moreover, a memory-enhanced heterogeneous graph neural network (MHGNN) is designed for feature extraction, leveraging historical trajectories to enhance the decision-making capability of the policy network. Finally, a parallel greedy search strategy is adopted to explore the solution space, enabling superior solutions with fewer iterations. Extensive experiments on synthetic data and public benchmarks demonstrate that $\textit{MIStar}$ significantly outperforms both traditional handcrafted improvement heuristics and state-of-the-art DRL-based constructive methods.

Optimization · Optimization and Learning under Uncertainty

Avrajit Ghosh, Bai Cong, Rio Yokota, Saiprasad Ravishankar, Rongrong Wang, Molei Tao, Mohammad Emtiyaz Khan, Thomas Möllenhoff

Variational Learning (VL) has recently gained popularity for training deep neural networks. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but little has been done to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient descent can find flat solutions and we extend this result to show that VL can find even flatter solutions. This result is obtained by controlling the shape of the variational posterior as well as the number of posterior samples used during training. The derivation follows in a similar fashion as in the standard EoS literature for deep learning, by first deriving a result for a quadratic problem and then extending it to deep neural networks. We empirically validate these findings on a wide variety of large networks, such as ResNet and ViT, to find that the theoretical results closely match the empirical ones. Ours is the first work to analyze the EoS dynamics of~VL.

Applications · Physics

Yiming Huang, Yajie Hao, Yuxuan Du, Jing Zhou, Xiao Yuan, Xiaoting Wang

Variational Quantum Algorithms (VQAs) are emerging as leading strategies with the potential to unlock practical applications and deliver significant advantages in the investigation of many-body quantum systems and quantum chemistry. A key challenge hindering the application of VQAs to large-scale problems is rooted in the no-cloning theorem in quantum mechanics, precluding standard backpropagation and leading to prohibitive quantum resource expenditure such as measurement cost. To address this challenge, we reformulate the training dynamics of VQAs as a non-linear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) to model this dynamical system efficiently. Given a small amount of training trajectory data collected from quantum devices, our protocol predicts the parameter updates of VQAs over multiple iterations on the classical side, dramatically reducing quantum resource costs. Through systematic numerical experiments, we demonstrate that our method achieves up to a 30x speedup compared to conventional methods and reduces quantum resource costs by as much as 90\% for tasks involving up to 40 qubits, including ground state preparation of different quantum systems, while maintaining competitive accuracy. Our approach complements existing techniques aimed at improving the efficiency of VQAs and further strengthens their potential for practical applications.

Optimization · Neural Network Optimization

Julian Kranz, Davide Gallon, Steffen Dereich, Arnulf Jentzen

We study gradient flows for loss landscapes of fully connected feedforward neural networks with commonly used continuously differentiable activation functions such as the logistic, hyperbolic tangent, softplus or GELU function. We prove that the gradient flow either converges to a critical point or diverges to infinity while the loss converges to an asymptotic critical value. Moreover, we prove the existence of a threshold $\varepsilon>0$ such that the loss value of any gradient flow initialized at most $\varepsilon$ above the optimal level converges to it. For polynomial target functions and sufficiently big architecture and data set, we prove that the optimal loss value is zero and can only be realized asymptotically. From this setting, we deduce our main result that any gradient flow with sufficiently good initialization diverges to infinity. Our proof heavily relies on the geometry of o-minimal structures. We confirm these theoretical findings with numerical experiments and extend our investigation to more realistic scenarios, where we observe an analogous behavior.

Applications · Physics

Hong Wang, Jie Wang, Minghao Ma, Haoran Shao, Haoyang Liu

Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed constants for specific scenarios. However, they rely on domain expertise and fail to consider the instance-wise features for individual problems, limiting their performance. In contrast, machine learning (ML) approaches, though promising, are hindered by high inference costs and limited interpretability. To combine the strengths of both approaches, we propose a symbolic discovery framework—namely, **Sym**bolic **Ma**trix **P**reconditioning (**SymMaP**)—to learn efficient symbolic expressions for preconditioning parameters. Specifically, we employ a neural network to search the high-dimensional discrete space for expressions that can accurately predict the optimal parameters. The learned expression allows for high inference efficiency and excellent interpretability (expressed in concise symbolic formulas), making it simple and reliable for deployment. Experimental results show that SymMaP consistently outperforms traditional strategies across various benchmarks.

Theory · Domain Adaptation and Transfer Learning

Shixuan Liu, Yue He, Haotian Wang, Wenjing Yang, Yunfei Wang, Peng Cui, Zhong Liu

Data-driven methods offer efficient and robust solutions for analyzing complex dynamical systems but rely on the assumption of I.I.D. data, driving the development of generalization techniques for handling environmental differences. These techniques, however, are limited by their dependence on environment labels, which are often unavailable during training due to data acquisition challenges, privacy concerns, and environmental variability, particularly in large public datasets and privacy-sensitive domains. In response, we propose DynaInfer, a novel method that infers environment specifications by analyzing prediction errors from fixed neural networks within each training round, enabling environment assignments directly from data. We prove our algorithm effectively solves the alternating optimization problem in unlabeled scenarios and validate it through extensive experiments across diverse dynamical systems. Results show that DynaInfer outperforms existing environment assignment techniques, converges rapidly to true labels, and even achieves superior performance when environment labels are available.

Deep Learning · Algorithms

Haotian Sun, Yitong Li, Yuchen Zhuang, Niao He, Hanjun Dai, Bo Dai

Contrastive Language-Image Pretraining (CLIP) has demonstrated strong zero-shot performance across diverse downstream text-image tasks. Existing CLIP methods typically optimize a contrastive objective using negative samples drawn from each minibatch. To achieve robust representation learning, these methods require extremely large batch sizes and escalate computational demands to hundreds or even thousands of GPUs. Prior approaches to mitigate this issue often compromise downstream performance, prolong training duration, or face scalability challenges with very large datasets. To overcome these limitations, we propose AmorLIP, an efficient CLIP pretraining framework that amortizes expensive computations involved in contrastive learning through lightweight neural networks, which substantially improves training efficiency and performance. Leveraging insights from a spectral factorization of energy-based models, we introduce novel amortization objectives along with practical techniques to improve training stability. Extensive experiments across 38 downstream tasks demonstrate the superior zero-shot classification and retrieval capabilities of AmorLIP, consistently outperforming standard CLIP baselines with substantial relative improvements of up to 12.24%.

Deep Learning · Algorithms

Haidong Kang, Lihong Lin, Hanling Wang

The success of computer vision tasks is mainly attributed to the architectural design of neural networks. This highlights the need to automatically design high-performance architectures via Neural Architecture Search (NAS). To accelerate the search process, training-free NAS is proposed, which aims to search high-performance architectures at initialization via zero-cost proxies (ZCPs). However, existing zero-cost proxies heavily rely on manual design, which is often labor-intensive and requires extensive expert knowledge. In addition, these crafted proxies often suffer from poor correlation with final model performance and high computational complexity, severely limiting NAS efficiency in real-world applications. To address those issues, this paper proposes a novel Large Language Models (LLMs)-driven $\underline{A}$utomatic $\underline{P}$roxy $\underline{D}$iscovery ($\textbf{APD}$) framework, which revolutionizes the design paradigm of ZCPs by leveraging LLMs to automatically discover optimal ZCPs for Training-Free NAS. Moreover, we utilize actor-critic based reinforcement learning to optimize prompts, enabling to generate better ZCPs in the next generation. We conduct extensive experiments on mainstream NAS benchmarks, demonstrating APD excels in both performance and efficiency. Besides, we firmly believe that our APD will dramatically benefit the deep learning community through providing novel paradigm of design algorithms via LLMs.

Deep Learning · Graph Neural Networks

Amir Ghazizadeh, Rickard Ewetz, Hao Zheng

The success of Graph Neural Networks (GNNs) leverages the homophily principle, where connected nodes share similar features and labels. However, this assumption breaks down in heterophilic graphs, where same-class nodes are often distributed across distant neighborhoods rather than immediate connections. Recent attempts expand the receptive field through multi-hop aggregation schemes that explicitly preserve intermediate representations from each hop distance. While effective at capturing heterophilic patterns, these methods require separate weight matrices per hop and feature concatenation, causing parameters to scale linearly with hop count. This leads to high computational complexity and GPU memory consumption. We propose Gated Multi-hop Message Passing (GAMMA), where nodes assess how relevant the aggregated information is from their k-hop neighbors. This assessment occurs through multiple refinement steps where the node compares each hop's embedding with its current representation, allowing it to focus on the most informative hops. During the forward pass, GAMMA finds the optimal mix of multi-hop information local to each node using a single feature vector without needing separate representations for each hop, thereby maintaining dimensionality comparable to single hop GNNs. In addition, we propose a weight sharing scheme that leverages a unified transformation for aggregated features from multiple hops so the global heterophilic patterns specific to each hop are learned during training. As such, GAMMA captures both global (per-hop) and local (per-node) heterophily patterns without high computation and memory overhead. Experiments show GAMMA matches or exceeds state-of-the-art heterophilic GNN accuracy, achieving up to $\approx20\times$ faster inference. Our code is publicly available at \url{https://github.com/amir-ghz/GAMMA}.

Optimization · Neural Network Optimization

Jincheol Yang, Jaemin Choi, Matti Zinke, Suk-Ju Kang

Monocular depth estimation has advanced significantly with foundation models like Depth Anything, leveraging large-scale transformer architectures for the superior generalization. However, the deployment on resource-constrained devices remains challenging due to the high computation and memory requirement. Existing quantization methods, such as post-training quantization and quantization-aware training, often face trade-offs between efficiency and accuracy, or require extensive labeled data for retraining. To address these limitations, we propose Quantization with Self-Compensating Auxiliary for Monocular Depth Estimation (QSCA), a novel framework for 4-bit post-training quantization of Monocular depth estimation models. Our method integrates a lightweight Self-Compensating Auxiliary (SCA) module into both transformer encoder and decoder blocks, enabling the quantized model to recover from performance degradation without requiring ground truth. This design enables fast adaptation while preserving structural and spatial consistency in predicted depth maps. To our knowledge, this is the first framework to successfully apply 4-bit quantization across all layers of large-scale monocular depth estimation models. Experimental results demonstrate that QSCA significantly improves quantized depth estimation performance. On the NYUv2 dataset, it achieves an 11\% improvement in $\delta_1$ accuracy over existing post-training quantization methods.

Optimization

Dian Meng, Zhiguang Cao, Jie Gao, Yaoxin Wu, Yaqing Hou

Neural solvers for the Vehicle Routing Problem (VRP) have typically relied on either node or edge inputs, limiting their flexibility and generalization in real-world scenarios. We propose UniteFormer, a unified neural solver that supports node-only, edge-only, and hybrid input types through a single model trained via joint edge-node modalities. UniteFormer introduces: (1) a mixed encoder that integrates graph convolutional networks and attention mechanisms to collaboratively process node and edge features, capturing cross-modal interactions between them; and (2) a parallel decoder enhanced with query mapping and a feed-forward layer for improved representation. The model is trained with REINFORCE by randomly sampling input types across batches. Experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that UniteFormer achieves state-of-the-art performance and generalizes effectively to TSPLib and CVRPLib instances. These results underscore UniteFormer’s ability to handle diverse input modalities and its strong potential to improve performance across various VRP tasks.

Theory · Learning Theory

Connall Garrod, Jonathan Keating

Neural collapse (NC) and its multi-layer variant, deep neural collapse (DNC), describe a structured geometry that occurs in the features and weights of trained deep networks. Recent theoretical work by Sukenik et al. using a deep unconstrained feature model (UFM) suggests that DNC is suboptimal under mean squared error (MSE) loss. They heuristically argue that this is due to low-rank bias induced by L2 regularization. In this work, we extend this result to deep UFMs trained with cross-entropy loss, showing that high-rank structures—including DNC—are not generally optimal. We characterize the associated low-rank bias, proving a fixed bound on the number of non-negligible singular values at global minima as network depth increases. We further analyze the loss surface, demonstrating that DNC is more prevalent in the landscape than other critical configurations, which we argue explains its frequent empirical appearance. Our results are validated through experiments in deep UFMs and deep neural networks.

Optimization · Neural Network Optimization

Yuesen Liao, Zhiwei Li, Binrui Wu, Zihao Cheng, Su Zhao, Shuai Chen, Weizhong Zhang

Sparse and low-rank matrix composite approximation has emerged as a promising paradigm for compressing large language models (LLMs), offering a more flexible pruning structure than conventional methods based solely on sparse matrices. The significant variation in weight redundancy across layers, along with the differing rank and sparsity structures of weight matrices, makes identifying the globally optimal pruning structure extremely challenging. Existing methods often depend on uniform or manually designed heuristic rules to allocate weight sparsity across layers, subsequently compressing each matrix using matrix approximation techniques. Given the above theoretical difficulty in global compression of LLMs and the limited computational and data resources available compared to the training phase, we argue that a collaboration between learning and matrix approximation is essential for effective compression. In this paper, we propose a novel LLM compression framework based on generalized bilevel optimization that naturally formulates an effective collaborative mechanism. Specifically, the outer loop frames the weight allocation task as a probabilistic optimization problem, enabling the automatic learning of both layer-wise sparsities and matrix-wise retained ranks, while the inner loop solves the corresponding sparsity and rank-constrained model compression problem via matrix approximation. Our main technical contributions include two key innovations for efficiently solving this bilevel optimization problem. First, we introduce a truncated Gaussian prior-based probabilistic parameterization integrated with a policy gradient estimator, which avoids expensive backpropagation and stabilizes the optimization process. Second, we design an adapted QR-based matrix approximation algorithm that significantly accelerates inner loop computations. Extensive experiments on Phi-3 and the LLama-2/3 family demonstrate the effectiveness of our method. Notably, it maintains over 95\% zero-shot accuracy under 50\% sparsity and achieves up to 2× inference speedup.