论文检索

Optimization · Non-Convex

Jiawei Xu, Yi Zheng, Chenghe Sun, Taiyu Zhou, Zuqi Zhang, Jie Li, Lirong Zheng, Zhuo Zou

Efficient deployment of deep neural networks increasingly relies on Post-Training Quantization (PTQ). Logarithmic PTQ, in particular, promises multiplier-free hardware efficiency, but its performance is often limited by the nonlinear and symmetric quantization grid and standard rounding-to-nearest (RTN) approach. While learnable rounding has significantly advanced linear PTQ, its application to the non-linear and often discrete nature of logarithmic domain remains unexplored. This paper introduces learnable Logarithmic Adaptive Rounding Techniques (LogART) that pioneer task-aware learnable rounding specifically for the logarithmic domain. LogART further extends the learnable rounding strategy to flexibly support outlier-aware, asymmetric, and hardware-friendly dynamic logarithmic bases, determined in a distribution-aware manner using an efficient search strategy. Extensive experiments demonstrate that LogART achieves state-of-the-art accuracy while maintaining efficiency in quantizing models across various architectures and ultra-low bitwidths, outperforming existing logarithmic PTQ methods and paving the way for more effective hardware deployment. The code is available at https://github.com/logart-lab/logart.

Applications · Language, Speech and Dialog

Xiaohe Bo, Rui Li, Zexu Sun, Quanyu Dai, Zeyu Zhang, Zihang Tian, Xu Chen, Zhenhua Dong

Prompt optimization and fine-tuning are two major approaches to improve the performance of Large Language Models (LLMs). They enhance the capabilities of LLMs from complementary perspectives: the former through explicit natural language, and the latter through implicit parameter updates. However, prior work has typically studied them in isolation, leaving their synergistic potential largely underexplored. To bridge this gap, in this paper, we introduce MetaTuner, a novel framework that jointly integrates prompt optimization and fine-tuning for LLM training. Specifically, we introduce two neural networks to generate prompts and parameters, respectively, while allowing them to share a common bottom encoding layer to enable knowledge sharing. By the guidance of the final supervised signals, our framework is optimized to discover the optimal combinations between the prompts and parameters. Given that prompt learning involves discrete optimization while fine-tuning operates in a continuous parameter space, we design a supervised regularization loss to train our framework effectively. Extensive experiments across diverse benchmarks show that our method consistently outperforms the baselines. To benefit the research community, we have released our project at https://github.com/BoXiaohe/MetaTuner.

Ambarish Moharil

This paper investigates how multilayer perceptrons (MLPs) can be represented in non-Euclidean spaces, with emphasis on the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting analysis to single checkpoints, we construct temporal parameter-graphs across $T$ snapshots of the optimization process. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based meta learning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal parameter-graphs in the Poincaré ball and learns from them while maintaining equivariance to within-snapshot neuron permutations and invariance to permutations of past snapshots. In doing so, it preserves functional equivalence across time and recovers the network’s latent geometry. Experiments on regression and classification tasks with trained MLPs show that hyperbolic temporal representations expose how structure emerges during training, offering intrinsic explanations of self-organisation in a given model training environment.

Optimization · Sampling and Optimization

Yesom Park, Shu Liu, Mo Zhou, Stanley J Osher

We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By leveraging the method of characteristics, we derive closed-form, bidirectional transport maps, thereby eliminating the need for numerical integration. The proposed method adopts a pure minimization framework: a single neural network is trained with a loss function derived from the method of characteristics of the HJ equation. This design guarantees convergence to the optimal map while eliminating adversarial training stages, thereby substantially reducing computational complexity. Furthermore, the framework naturally extends to a wide class of cost functions and supports class-conditional transport. Extensive experiments on diverse datasets demonstrate the accuracy, scalability, and efficiency of the proposed method, establishing it as a principled and versatile tool for OT applications with provable optimality.

Deep Learning · Graph Neural Networks

Weining Shi, Zhisen Wen, Qinggang Zhang, Chentao Zhang, Zhihong Zhang

Temporal graphs are commonly employed as conceptual models for capturing time-evolving interactions in real-world systems. Representation learning on such non-Euclidean data typically depends on aggregating information from neighbors, and the presence of temporal dynamics further complicates this process. However, neighbors often contain noisy information in practice, making the unreliable propagation of knowledge and may even lead to the model failure. Although existing methods employ adaptive spatiotemporal neighbor sampling strategies or temporal dependency modeling frameworks to enhance model robustness, their constrained sampling scope limits handling of severe noise and long-term dependencies. This limitation can be attributed to a fundamental cause: neglecting global evolution inherently overlooks the temporal regularities encoded in continuous dynamics. To address this, we propose the **T**emporal **G**raph **T**humbnail (**TGT**), encapsulating a temporal graph’s global evolutionary skeleton as a thumbnail to characterize temporal regularities and enhance model robustness. Specifically, we model the thumbnail by leveraging von Neumann graph entropy and node mutual information to extract essential evolutionary skeleton from the raw temporal graph, and subsequently use it to guide optimization for model learning. In addition to rigorous theoretical derivation, extensive experiments demonstrate that TGT achieves superior capability and robustness compared to baselines, particularly in rapidly evolving and noisy environments. The code is available at https://anonymous.4open.science/r/TGT-BDF2.

Optimization · Sampling and Optimization

Daniel Severo, Brian Karrer, Niklas Nolte

Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric families or neural networks with expensive variational inference procedures. In this work, we propose a novel approach that leverages alternative representations for permutations, including Lehmer codes, Fisher-Yates draws, and Insertion-Vectors. These representations form a bijection with the symmetric group, allowing for unconstrained learning using conventional deep learning techniques, and can represent any probability distribution over permutations. Our approach enables a trade-off between expressivity of the model family and computational requirements. In the least expressive and most computationally efficient case our method subsumes previous families of well established probabilistic models over permutations, including Mallow's and the Repeated Insertion Model. Experiments indicate our method significantly outperforms current approaches on the jigsaw puzzle benchmark, a common task for permutation learning. However, we argue this benchmark is limited in its ability to assess learning probability distributions, as the target is a delta distribution (i.e., a single correct solution exists). We therefore propose two additional benchmarks: learning cyclic permutations and re-ranking movies based on user preference. We show that our method learns non-trivial distributions even in the least expressive mode, while traditional models fail to even generate valid permutations in this setting.

Social Aspects · Fairness, Equity, Justice and Safety

Yi Yu, Qixin ZHANG, Shuhan YE, Xun Lin, Qianshan Wei, Kun Wang, Wenhan Yang, Dacheng Tao, Jiang Xudong

Spiking neural networks (SNNs) compute with discrete spikes and exploit temporal structure, yet most adversarial attacks change intensities or event counts instead of timing. We study a timing-only adversary that retimes existing spikes while preserving spike counts and amplitudes in event-driven SNNs, thus remaining rate-preserving. We formalize a capacity-1 spike-retiming threat model with a unified trio of budgets: per-spike jitter $B_{\infty}$, total delay $B_{1}$, and tamper count $B_{0}$. Feasible adversarial examples must satisfy timeline consistency and non-overlap, which makes the search space discrete and constrained. To optimize such retimings at scale, we use projected-in-the-loop (PIL) optimization: shift-probability logits yield a differentiable soft retiming for backpropagation, and a strict projection in the forward pass produces a feasible discrete schedule that satisfies capacity-1, non-overlap, and the chosen budget at every step. The objective maximizes task loss on the projected input and adds a capacity regularizer together with budget-aware penalties, which stabilizes gradients and aligns optimization with evaluation. Across event-driven benchmarks (CIFAR10-DVS, DVS-Gesture, N-MNIST) and diverse SNN architectures, we evaluate under binary and integer event grids and a range of retiming budgets, and also test models trained with timing-aware adversarial training designed to counter timing-only attacks. For example, on DVS-Gesture the attack attains high success (over 90\%) while touching fewer than 2\% of spikes under ${B}_{0}$. Taken together, our results show that spike retiming is a practical and stealthy attack surface that current defenses struggle to counter, providing a clear reference for temporal robustness in event-driven SNNs. Code is available at https://github.com/yuyi-sd/Spike-Retiming-Attacks.

Deep Learning · Algorithms

Ningfeng Yang, Tor Aamodt

Quantization-Aware Pre-Training (QAPT) is an effective technique to reduce the compute and memory overhead of Deep Neural Networks while improving their energy efficiency on edge devices. Existing QAPT methods produce models stored in compute-efficient data types (e.g. integers) that are not information theoretically optimal (ITO). On the other hand, existing ITO data types (e.g. Quantile/NormalFloat Quantization) are not compute-efficient. We propose BBQ, the first ITO quantization method that is also compute-efficient. BBQ builds on our key insight that since learning is domain-agnostic, the output of a quantizer does not need to reside in the same domain as its input. BBQ performs ITO quantization in its input domain, and returns its output in a compute-efficient domain where ITO data types are mapped to compute-efficient data types. Without sacrificing compute efficiency, BBQ outperforms prior SOTA QAPT methods by a perplexity reduction of up to 2 points for 4-bit models, up to 4 points for 3-bit models, up to 5 points for 2-bit models, and up to 18 points for 1-bit models. Code is available at https://github.com/1733116199/bbq.

Seyed Mohammad Eshtehardian, Mohammad Hossein Yassaee, Babak HosseinKhalaj

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional neural networks, offering enhanced interpretability based on the Kolmogorov-Arnold representation theorem. While their empirical success is growing, a theoretical understanding of their training dynamics remains nascent. This paper investigates the optimization of a two-layer KAN in the overparameterized regime, focusing on a simplified yet insightful setting where only the first-layer coefficients are trained via gradient descent. Our main result establishes that, provided the network is sufficiently wide, this training method is guaranteed to converge to a global minimum and achieve zero training error. Furthermore, we derive a novel, fine-grained convergence rate that explicitly connects the optimization speed to the structure of the data labels through the eigenspectrum of the KAN Tangent Kernel (KAN-TK). Our analysis reveals a key advantage of this architecture: guaranteed convergence is achieved with a hidden layer width of $m=\mathcal{O}(n^2)$, a significant polynomial improvement over the $m=\mathcal{O}(n^6)$ requirement for classic two-layer neural networks using ReLU activation functions and analyzed within the same Tangent Kernel framework. We validate our theoretical findings with numerical experiments that corroborate our predictions on convergence speed and the impact of label structure.

Optimization · Everything Else

Bruno Mlodozeniec, Pierre Ablin, Louis Béthune, Dan Busbridge, Michal Klein, Jason Ramapuram, marco cuturi

Hyperparameter tuning can dramatically impact training stability of large-scale models. Recent works on neural network parameterisations, such as μP, have shown that layer types and sizes should dictate how global hyperparameters should be rescaled in order to achieve efficient transfer across model sizes. On the other hand, the established practice for hyperparameter optimisation search is to look for optimal global base values that apply at some fixed model scale. We transfer hyperparameters across all scaling axes: width and depth, using an extension of CompleteP (Dey et al., 2025), training horizon, and batch size. Our study covers all optimisation hyperparameters of modern models: learning rates, Adam parameters, weight decay, initialisation scales, and residual block multipliers. Lastly, we demonstrate that hyperparameter transfer holds even in the per-layer hyperparameter regime. We characterise the empirical challenges of navigating the high-dimensional hyperparameter landscape, and propose practical guidelines for tackling this optimisation problem. We suggest a simplified parameterisation of the hyperparameter space that reduces the dimensionality of the search-space at no performance cost. Our experiments demonstrate training speed improvements when applying transferred hyperparameters to Large Language Models.

Yuhao Mao, Yani Zhang, Martin Vechev

Neural network certification methods heavily rely on convex relaxations to provide robustness guarantees. However, these relaxations are often imprecise: even the most accurate single-neuron relaxation is incomplete for general ReLU networks, a limitation known as the *single-neuron convex barrier*. While multi-neuron relaxations have been heuristically applied to address this issue, two central questions arise: (i) whether they overcome the convex barrier, and if not, (ii) whether they offer theoretical capabilities beyond those of single-neuron relaxations. In this work, we present the first rigorous analysis of the expressiveness of multi-neuron relaxations. Perhaps surprisingly, we show that they are inherently incomplete, even when allocated sufficient resources to capture finitely many neurons and layers optimally. This result extends the single-neuron barrier to a *universal convex barrier* for neural network certification. On the positive side, we show that completeness can be achieved by either (i) augmenting the network with a polynomial number of carefully designed ReLU neurons or (ii) partitioning the input domain into convex sub-polytopes, thereby distinguishing multi-neuron relaxations from single-neuron ones which are unable to realize the former and have worse partition complexity for the latter. Our findings establish a foundation for multi-neuron relaxations and point to new directions for certified robustness, including training methods tailored to multi-neuron relaxations and verification methods with multi-neuron relaxations as the main subroutine.

Theory · Domain Adaptation and Transfer Learning

aodi Li, Liansheng Zhuang, Xiao Long, Houqiang Li, Shafei Wang

This paper explores the geometric characteristics of loss landscapes to enhance domain generalization (DG) in deep neural networks. Existing methods mainly leverage the local flatness around minima for improved generalization. However, recent theoretical studies indicate that flatness does not universally guarantee better generalization. Instead, this paper investigates a global geometrical property for domain generalization, i.e., \emph{mode connectivity}, the phenomenon where distinct local minima are connected by continuous low-loss pathways. Different from flatness, mode connectivity enables transitions from poor to superior generalization models without leaving low-loss regions. To navigate these connected pathways effectively, this paper proposes a novel Billiard Optimization Algorithm (BOA), which discovers superior models by mimicking billiard dynamics. During this process, BOA operates within a low-dimensional Krylov subspace, aiming to alleviate the curse of dimensionality caused by the high-dimensional parameter space of deep models. Furthermore, this paper reveals that oracle test gradients strongly align with the Krylov subspace constructed from training gradients across diverse datasets and architectures. This alignment offers a powerful tool to bridge training and test domains, enabling the efficient discovery of superior models with limited training domains. Experiments on DomainBed demonstrate that BOA consistently outperforms existing sharpness-aware and DG methods across diverse datasets and architectures. Impressively, BOA even surpasses the sharpness-aware minimization by 3.6\% on VLCS when using a ViT-B/16 backbone.

Ali Behrouz, Meisam Razaviyayn, Peilin Zhong, Vahab Mirrokni

Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias—the natural tendency to prioritize certain events or stimuli—we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules with attentional bias. We define and formalize the concept of attentional bias as the internal memory objective deep learning architectures. We show that existing deep learning architectures leverage the same attentional bias based on $L_2$ loss function. Going beyond $L_2$ loss function, we present a set of alternative attentional bias configurations along with their effective approximations. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on the choice of attentional bias objective, retention gate, associative memory architecture, and memory learning algorithm. Our experiments show different designs yield models with varying strengths. Furthermore, our special instances of Miras achieve exceptional performance in language modeling, commonsense reasoning, recall intensive, and time series tasks, outperforming Transformers and other modern linear recurrent models.

Social Aspects · Trustworthy Machine Learning

Weijun Li, Ansh Arora, Xuanli He, Mark Dras, Qiongkai Xu

Backdoor attacks pose a serious threat to deep neural networks (DNNs), allowing adversaries to implant triggers for hidden behaviors in inference. Defending against such vulnerabilities is especially difficult in the post-training setting, since end-users lack training data or prior knowledge of the attacks. Model merging offers a cost-effective defense; however, latest methods like weight averaging (WAG) provide reasonable protection when multiple homologous models are available, but are less effective with fewer models and place heavy demands on defenders. We propose a module-switching defense (MSD) for disrupting backdoor shortcuts. We first validate its theoretical rationale and empirical effectiveness on two-layer networks, showing its capability of achieving higher backdoor divergence than WAG, and preserving utility. For deep models, we evaluate MSD on Transformer and CNN architectures and design an evolutionary algorithm to optimize fusion strategies with selective mechanisms to identify the most effective combinations. Experiments shown that MSD achieves stronger defense with fewer models in practical settings, and even under an underexplored case of collusive attacks among multiple models--where some models share same backdoors--switching strategies by MSD deliver superior robustness against diverse attacks.

Shahaf Bassan, Xuanxiang Huang, Guy Katz

Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and (2) *contrastive reasons*, which are subsets of input features that, when modified, alter a prediction. Prior studies have examined these explanations in different contexts, such as non-probabilistic versus probabilistic frameworks and local versus global settings. In this study, we introduce a unified framework for analyzing these explanations, demonstrating that they can all be characterized through the minimization of a unified probabilistic value function. We then prove that the complexity of these computations is influenced by three key properties of the value function: (1) *monotonicity*, (2) *submodularity*, and (3) *supermodularity* - which are three fundamental properties in *combinatorial optimization*. Our findings uncover some counterintuitive results regarding the nature of these properties within the explanation settings examined. For instance, although the *local* value functions do not exhibit monotonicity or submodularity/supermodularity whatsoever, we demonstrate that the *global* value functions do possess these properties. This distinction enables us to prove a series of novel polynomial-time results for computing various explanations with provable guarantees in the global explainability setting, across a range of ML models that span the interpretability spectrum, such as neural networks, decision trees, and tree ensembles. In contrast, we show that even highly simplified versions of these explanations become NP-hard to compute in the corresponding local explainability setting.

Deep Learning · Everything Else

Paulius Rauba, Mihaela van der Schaar

Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing approaches to this problem present a difficult choice: training a discrete collection of specialist models is computationally prohibitive, while dynamic methods like slimmable networks often lack the flexibility to be applied to large, pre-trained foundation models. In this work, we propose *Nested Subspace Networks (NSNs)*, a novel architectural paradigm that enables a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets at inference time. The core of our approach is to re-parameterize linear layers to satisfy a nested subspace property, such that the function computed at a given rank is a strict subspace of the function at any higher rank. We show that this entire hierarchy of models can be optimized jointly via an uncertainty-aware objective that learns to balance the contributions of different ranks based on their intrinsic difficulty. We demonstrate empirically that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier. For example, a single NSN-adapted model can achieve a 50\% reduction in inference FLOPs with only a 5 percentage point loss in accuracy. Our findings establish NSNs as a powerful framework for creating the next generation of adaptive foundation models.

Optimization · Everything Else

Ruobing Wang, Xin Li, Mingzhong Wang

We propose MILPnet, a multi-scale hybrid attention framework that models Mixed Integer Linear Programming (MILP) problems as geometric sequences rather than graphs. This approach directly addresses the challenge of Foldable MILP instances, a class of problems that graph-based models, specifically Graph Neural Networks (GNNs), fail to distinguish due to expressiveness limits imposed by the Weisfeiler-Lehman test. By representing MILPs through sequences of constraint and objective features, MILPnet captures both local and global geometric structure using a theoretically grounded multi-scale attention mechanism. We theoretically prove that MILPnet can approximate feasibility, optimal objective value, and optimal solution mappings over a measurable topological space with arbitrarily small error. Empirically, MILPnet outperforms graph-based methods in feasibility prediction accuracy and convergence speed on Foldable MILPs, while using significantly fewer parameters. It also generalizes effectively among problem scales and demonstrates strong performance on real-world MILP benchmarks when integrated into an end-to-end solver pipeline. Our code is available.

Social Aspects · Trustworthy Machine Learning

Keke Tang, Ziyong Du, Xiaofei Wang, Weilong Peng, Peican Zhu, Zhihong Tian

Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of semantic ambiguity, where classifiers are particularly prone to unwarranted high-confidence predictions. Motivated by this observation, we propose a principled framework to mitigate OOD overconfidence by leveraging the geometry of OT-induced singular boundaries. Specifically, we formulate an OT problem between a continuous base distribution and the latent embeddings of training data, and identify the resulting singular boundaries. By sampling near these boundaries, we construct a class of OOD inputs, termed optimal transport-induced OOD samples (OTIS), which are geometrically grounded and inherently semantically ambiguous. During training, a confidence suppression loss is applied to OTIS to guide the model toward more calibrated predictions in structurally uncertain regions. Extensive experiments show that our method significantly alleviates OOD overconfidence and outperforms state-of-the-art methods.

Theory · Optimization

Keitaro Sakamoto, Issei Sato

The training dynamics of deep neural networks often defy expectations, even as these models form the foundation of modern machine learning. Two prominent examples are grokking, where test performance improves abruptly long after the training loss has plateaued, and the information bottleneck principle, where models progressively discard input information irrelevant to the prediction task as training proceeds. However, the mechanisms underlying these phenomena and their relations remain poorly understood. In this work, we present a unified explanation of such late-phase phenomena through the lens of neural collapse, which characterizes the geometry of learned representations. We show that the contraction of population within-class variance is a key factor underlying both grokking and information bottleneck, and relate this measure to the neural collapse measure defined on the training set. By analyzing the dynamics of neural collapse, we show that distinct time scales between fitting the training set and the progression of neural collapse account for the behavior of the late-phase phenomena. Finally, we validate our theoretical findings on multiple datasets and architectures.

Optimization · Non-Convex

Juan Ramirez, Simon Lacoste-Julien

Constrained optimization is a powerful framework for enforcing requirements on neural networks. These constrained deep learning problems are typically solved using first-order methods on their min-max Lagrangian formulation, but such approaches often suffer from oscillations and can fail to find all local solutions. While the Augmented Lagrangian method (ALM) addresses these issues, practitioners often favor dual optimistic ascent schemes (PI control) on the standard Lagrangian, which perform well empirically but lack formal guarantees. In this paper, we establish a previously unknown equivalence between these approaches: dual optimistic ascent on the Lagrangian is equivalent to gradient descent-ascent on the Augmented Lagrangian. This finding allows us to transfer the robust theoretical guarantees of the ALM to the dual optimistic setting, proving it converges linearly to all local solutions. Furthermore, the equivalence provides principled guidance for tuning the optimism hyper-parameter. Our work closes a critical gap between the empirical success of dual optimistic methods and their theoretical foundation in the single-step, first-order regime commonly used in constrained deep learning.