ICLR 2025 Papers

International Conference on Learning Representations

Decision breakdown

3,703papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    2135.8%
  • Spotlight
    38010.3%
  • Poster
    3,11084.0%

Browse all papers

Scalable Extraction of Training Data from Aligned, Production Language Models

Milad Nasr, Javier Rando, Nicholas Carlini, Jonathan Hayase, Matthew Jagielski, A. Feder Cooper, Daphne Ippolito, Christopher A. Choquette-Choo, Florian Tramèr, Katherine Lee

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Large language models are prone to *memorizing* some of their training data. Memorized (and possibly sensitive) samples can then be extracted at generation time by adversarial or benign users. There is hope that *model alignment*---a standard training process that tunes a model to harmlessly follow user instructions---would mitigate the risk of extraction. However, we develop two novel attacks that undo a language model's alignment and recover thousands of training examples from popular proprietary aligned models such as OpenAI's ChatGPT. Our work highlights the limitations of existing safeguards to prevent training data leakage in production language models.

Poster
DAWN: Dynamic Frame Avatar with Non-autoregressive Diffusion Framework for Talking head Video Generation

Hanbo Cheng, Limin Lin, Chenyu Liu, Pengcheng Xia, Pengfei Hu, Jiefeng Ma, Jun Du, Jia Pan

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Talking head generation intends to produce vivid and realistic talking head videos from a single portrait and speech audio clip. Although significant progress has been made in diffusion-based talking head generation, almost all methods rely on autoregressive strategies, which suffer from limited context utilization beyond the current generation step, error accumulation, and slower generation speed. To address these challenges, we present DAWN (\textbf{D}ynamic frame \textbf{A}vatar \textbf{W}ith \textbf{N}on-autoregressive diffusion), a framework that enables all-at-once generation of dynamic-length video sequences. Specifically, it consists of two main components: (1) audio-driven holistic facial dynamics generation in the latent motion space, and (2) audio-driven head pose and blink generation. Extensive experiments demonstrate that our method generates authentic and vivid videos with precise lip motions, and natural pose/blink movements. Additionally, with a high generation speed, DAWN possesses strong extrapolation capabilities, ensuring the stable production of high-quality long videos. These results highlight the considerable promise and potential impact of DAWN in the field of talking head video generation. Furthermore, we hope that DAWN sparks further exploration of non-autoregressive approaches in diffusion models. Our code will be publicly available at \url{https://github.com/Hanbo-Cheng/DAWN-pytorch}.

Poster
Test-time Alignment of Diffusion Models without Reward Over-optimization

Sunwoo Kim, Minkyu Kim, Dongmin Park

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Diffusion models excel in generative tasks, but aligning them with specific objectives while maintaining their versatility remains challenging. Existing fine-tuning methods often suffer from reward over-optimization, while approximate guidance approaches fail to optimize target rewards effectively. Addressing these limitations, we propose a training-free, test-time method based on Sequential Monte Carlo (SMC) to sample from the reward-aligned target distribution. Our approach, tailored for diffusion sampling and incorporating tempering techniques, achieves comparable or superior target rewards to fine-tuning methods while preserving diversity and cross-reward generalization. We demonstrate its effectiveness in single-reward optimization, multi-objective scenarios, and online black-box optimization. This work offers a robust solution for aligning diffusion models with diverse downstream objectives without compromising their general capabilities. Code is available at https://github.com/krafton-ai/DAS.

Spotlight
SWEb: A Large Web Dataset for the Scandinavian Languages

Tobias Norlund, Tim Isbister, Amaru Cuba Gyllensten, Paul Gabriel dos Santos, Danila Petrelli, Ariel Ekgren, Magnus Sahlgren

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This paper presents the hitherto largest pretraining dataset for the Scandinavian languages: the Scandinavian WEb (SWEb), comprising over one trillion tokens. The paper details the collection and processing pipeline, and introduces a novel model-based text extractor that significantly reduces complexity in comparison with rule-based approaches. We also introduce a new cloze-style benchmark for evaluating language models in Swedish, and use this test to compare models trained on the SWEb data to models trained on FineWeb, with competitive results. All data, models and code are shared openly.

Poster
High-Precision Dichotomous Image Segmentation via Probing Diffusion Capacity

Qian Yu, Peng-Tao Jiang, Hao Zhang, Jinwei Chen, Bo Li, Lihe Zhang, Huchuan Lu

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In the realm of high-resolution (HR), fine-grained image segmentation, the primary challenge is balancing broad contextual awareness with the precision required for detailed object delineation, capturing intricate details and the finest edges of objects. Diffusion models, trained on vast datasets comprising billions of image-text pairs, such as SD V2.1, have revolutionized text-to-image synthesis by delivering exceptional quality, fine detail resolution, and strong contextual awareness, making them an attractive solution for high-resolution image segmentation. To this end, we propose DiffDIS, a diffusion-driven segmentation model that taps into the potential of the pre-trained U-Net within diffusion models, specifically designed for high-resolution, fine-grained object segmentation. By leveraging the robust generalization capabilities and rich, versatile image representation prior of the SD models, coupled with a task-specific stable one-step denoising approach, we significantly reduce the inference time while preserving high-fidelity, detailed generation. Additionally, we introduce an auxiliary edge generation task to not only enhance the preservation of fine details of the object boundaries, but reconcile the probabilistic nature of diffusion with the deterministic demands of segmentation. With these refined strategies in place, DiffDIS serves as a rapid object mask generation model, specifically optimized for generating detailed binary maps at high resolutions, while demonstrating impressive accuracy and swift processing. Experiments on the DIS5K dataset demonstrate the superiority of DiffDIS, achieving state-of-the-art results through a streamlined inference process. The source code will be publicly available at \href{https://github.com/qianyu-dlut/DiffDIS}{DiffDIS}.

Poster
MindSimulator: Exploring Brain Concept Localization via Synthetic fMRI

Guangyin Bao, Qi Zhang, Zixuan Gong, Zhuojia Wu, Duoqian Miao

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Concept-selective regions within the human cerebral cortex exhibit significant activation in response to specific visual stimuli associated with particular concepts. Precisely localizing these regions stands as a crucial long-term goal in neuroscience to grasp essential brain functions and mechanisms. Conventional experiment-driven approaches hinge on manually constructed visual stimulus collections and corresponding brain activity recordings, constraining the support and coverage of concept localization. Additionally, these stimuli often consist of concept objects in unnatural contexts and are potentially biased by subjective preferences, thus prompting concerns about the validity and generalizability of the identified regions. To address these limitations, we propose a data-driven exploration approach. By synthesizing extensive brain activity recordings, we statistically localize various concept-selective regions. Our proposed MindSimulator leverages advanced generative technologies to learn the probability distribution of brain activity conditioned on concept-oriented visual stimuli. This enables the creation of simulated brain recordings that reflect real neural response patterns. Using the synthetic recordings, we successfully localize several well-studied concept-selective regions and validate them against empirical findings, achieving promising prediction accuracy. The feasibility opens avenues for exploring novel concept-selective regions and provides prior hypotheses for future neuroscience research.

Poster
Neural Approximate Mirror Maps for Constrained Diffusion Models

Berthy Feng, Ricardo Baptista, Katherine Bouman

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Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-based (e.g., satisfying a PDE), geometric (e.g., respecting symmetry), or semantic (e.g., including a particular number of objects). When the training data all satisfy a certain constraint, enforcing this constraint on a diffusion model makes it more reliable for generating valid synthetic data and solving constrained inverse problems. However, existing methods for constrained diffusion models are restricted in the constraints they can handle. For instance, recent work proposed to learn mirror diffusion models (MDMs), but analytical mirror maps only exist for convex constraints and can be challenging to derive. We propose *neural approximate mirror maps* (NAMMs) for general, possibly non-convex constraints. Our approach only requires a differentiable distance function from the constraint set. We learn an approximate mirror map that transforms data into an unconstrained space and a corresponding approximate inverse that maps data back to the constraint set. A generative model, such as an MDM, can then be trained in the learned mirror space and its samples restored to the constraint set by the inverse map. We validate our approach on a variety of constraints, showing that compared to an unconstrained diffusion model, a NAMM-based MDM substantially improves constraint satisfaction. We also demonstrate how existing diffusion-based inverse-problem solvers can be easily applied in the learned mirror space to solve constrained inverse problems.

Poster
Towards Empowerment Gain through Causal Structure Learning in Model-Based Reinforcement Learning

Hongye Cao, Fan Feng, Meng Fang, Shaokang Dong, Tianpei Yang, Jing Huo, Yang Gao

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In Model-Based Reinforcement Learning (MBRL), incorporating causal structures into dynamics models provides agents with a structured understanding of the environments, enabling efficient decision. Empowerment as an intrinsic motivation enhances the ability of agents to actively control their environments by maximizing the mutual information between future states and actions. We posit that empowerment coupled with causal understanding can improve controllability, while enhanced empowerment gain can further facilitate causal reasoning in MBRL. To improve learning efficiency and controllability, we propose a novel framework, Empowerment through Causal Learning (ECL), where an agent with the awareness of causal dynamics models achieves empowerment-driven exploration and optimizes its causal structure for task learning. Specifically, ECL operates by first training a causal dynamics model of the environment based on collected data. We then maximize empowerment under the causal structure for exploration, simultaneously using data gathered through exploration to update causal dynamics model to be more controllable than dense dynamics model without causal structure. In downstream task learning, an intrinsic curiosity reward is included to balance the causality, mitigating overfitting. Importantly, ECL is method-agnostic and is capable of integrating various causal discovery methods. We evaluate ECL combined with $3$ causal discovery methods across $6$ environments including pixel-based tasks, demonstrating its superior performance compared to other causal MBRL methods, in terms of causal discovery, sample efficiency, and asymptotic performance.

Poster
DEPT: Decoupled Embeddings for Pre-training Language Models

Alex Iacob, Lorenzo Sani, Meghdad Kurmanji, William F. Shen, Xinchi Qiu, Dongqi Cai, Yan Gao, Nicholas Donald Lane

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Language Model pre-training uses broad data mixtures to enhance performance across domains and languages. However, training on such heterogeneous text corpora requires extensive and expensive efforts. Since these data sources vary significantly in lexical, syntactic, and semantic aspects, they cause negative interference or the ``curse of multilinguality''. To address these challenges we propose a communication-efficient pre-training framework, DEPT. Our method decouples embeddings from the transformer body while simultaneously training the latter on multiple data sources without requiring a shared vocabulary. DEPT can: (1) train robustly and effectively under significant data heterogeneity, (2) minimize token embedding parameters to only what the data source vocabulary requires, while cutting communication costs in direct proportion to both the communication frequency and the reduction in parameters, (3) enhance transformer body plasticity and generalization, improving both average perplexity (up to 20%) and downstream task performance, and (4) enable training with custom optimized vocabularies per data source. We demonstrate DEPT's potential via the first vocabulary-agnostic federated pre-training of billion-scale models, reducing communication costs by orders of magnitude and embedding memory by 4-5x.

Oral
Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence

Dharmesh Tailor, Alvaro Correia, Eric Nalisnick, Christos Louizos

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Uncertainty quantification is an important prerequisite for the deployment of deep learning models in safety-critical areas. Yet, this hinges on the uncertainty estimates being useful to the extent the prediction intervals are well-calibrated and sharp. In the absence of inherent uncertainty estimates (e.g. pretrained models predicting only point estimates), popular approaches that operate post-hoc include Laplace’s method and split conformal prediction (split-CP). However, Laplace’s method can be miscalibrated when the model is misspecified and split-CP requires sample splitting, and thus comes at the expense of statistical efficiency. In this work, we construct prediction intervals for neural network regressors post-hoc without held-out data. This is achieved by approximating the full conformal prediction method (full-CP). Whilst full-CP nominally requires retraining the model for every test point and candidate label, we propose to train just once and locally perturb model parameters using Gauss-Newton influence to approximate the effect of retraining. Coupled with linearization of the network, we express the absolute residual nonconformity score as a piecewise linear function of the candidate label allowing for an efficient procedure that avoids the exhaustive search over the output space. On standard regression benchmarks and bounding box localization, we show the resulting prediction intervals are locally-adaptive and often tighter than those of split-CP.

Poster
VoxDialogue: Can Spoken Dialogue Systems Understand Information Beyond Words?

Xize Cheng, Ruofan Hu, Xiaoda Yang, Jingyu Lu, Dongjie Fu, Zehan Wang, Shengpeng Ji, Rongjie Huang, Boyang Zhang, Tao Jin, Zhou Zhao

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With the rapid advancement of large models, voice assistants are gradually acquiring the ability to engage in open-ended daily conversations with humans. However, current spoken dialogue systems often overlook multi-modal information in audio beyond text, such as speech rate, volume, emphasis, and background sounds. Relying solely on Automatic Speech Recognition (ASR) can lead to the loss of valuable auditory cues, thereby weakening the system’s ability to generate contextually appropriate responses. To address this limitation, we propose \textbf{VoxDialogue}, a comprehensive benchmark for evaluating the ability of spoken dialogue systems to understand multi-modal information beyond text. Specifically, we have identified 12 attributes highly correlated with acoustic information beyond words and have meticulously designed corresponding spoken dialogue test sets for each attribute, encompassing a total of 4.5K multi-turn spoken dialogue samples. Finally, we evaluated several existing spoken dialogue models, analyzing their performance on the 12 attribute subsets of VoxDialogue. Experiments have shown that in spoken dialogue scenarios, many acoustic cues cannot be conveyed through textual information and must be directly interpreted from the audio input. In contrast, while direct spoken dialogue systems excel at processing acoustic signals, they still face limitations in handling complex dialogue tasks due to their restricted context understanding capabilities. All data and code will be open source at \url{https://voxdialogue.github.io/}.

Poster
Learning to Explore and Exploit with GNNs for Unsupervised Combinatorial Optimization

Utku Umur ACIKALIN, Aaron M Ferber, Carla P Gomes

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Combinatorial optimization (CO) problems are pervasive across various domains, but their NP-hard nature often necessitates problem-specific heuristic algorithms. Recent advancements in deep learning have led to the development of learning-based heuristics, yet these approaches often struggle with limited search capabilities. We introduce Explore-and-Exploit GNN ($X^2$GNN, pronounced x-squared GNN), a novel unsupervised neural framework that combines exploration and exploitation for combinatorial search optimization: i) Exploration - $X^2$GNN generates multiple solutions simultaneously, promoting diversity in the search space; (ii) Exploitation - $X^2$GNN employs neural stochastic iterative refinement to exploit partial existing solutions, guiding the search toward promising regions and helping escape local optima. By balancing exploration and exploitation, $X^2$GNN achieves superior performance and generalization on several graph CO problems including Max Cut, Max Independent Set, and Max Clique. Notably, for large Max Clique problems, $X^2$GNN consistently generates solutions within 1.2\% of optimality, while other state-of-the-art learning-based approaches struggle to reach within 22\% of optimal. Moreover, $X^2$GNN consistently generates better solutions than Gurobi on large graphs for all three problems under reasonable time budgets. Furthermore, $X^2$GNN exhibits exceptional generalization capabilities. For the Maximum Independent Set problem, $X^2$GNN outperforms state-of-the-art methods even when trained on smaller or out-of-distribution graphs compared to the test set. Our framework offers a more effective and flexible approach to neural combinatorial optimization, addressing a key challenge in the field and providing a promising direction for future research in learning-based heuristics for combinatorial optimization.

Poster
CyberHost: A One-stage Diffusion Framework for Audio-driven Talking Body Generation

Gaojie Lin, Jianwen Jiang, Chao Liang, Tianyun Zhong, Jiaqi Yang, Zerong Zheng, Yanbo Zheng

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Diffusion-based video generation technology has advanced significantly, catalyzing a proliferation of research in human animation. While breakthroughs have been made in driving human animation through various modalities for portraits, most of current solutions for human body animation still focus on video-driven methods, leaving audio-driven taking body generation relatively underexplored. In this paper, we introduce CyberHost, a one-stage audio-driven talking body generation framework that addresses common synthesis degradations in half-body animation, including hand integrity, identity consistency, and natural motion. CyberHost's key designs are twofold. Firstly, the Region Attention Module (RAM) maintains a set of learnable, implicit, identity-agnostic latent features and combines them with identity-specific local visual features to enhance the synthesis of critical local regions. Secondly, the Human-Prior-Guided Conditions introduce more human structural priors into the model, reducing uncertainty in generated motion patterns and thereby improving the stability of the generated videos. To our knowledge, CyberHost is the first one-stage audio-driven human diffusion model capable of zero-shot video generation for the human body. Extensive experiments demonstrate that CyberHost surpasses previous works in both quantitative and qualitative aspects. CyberHost can also be extended to video-driven and audio-video hybrid-driven scenarios, achieving similarly satisfactory results.

Oral
Differentiable Optimization of Similarity Scores Between Models and Brains

Nathan Cloos, Moufan Li, Markus Siegel, Scott L Brincat, Earl K Miller, Guangyu Robert Yang, Christopher J Cueva

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How do we know if two systems - biological or artificial - process information in a similar way? Similarity measures such as linear regression, Centered Kernel Alignment (CKA), Normalized Bures Similarity (NBS), and angular Procrustes distance, are often used to quantify this similarity. However, it is currently unclear what drives high similarity scores and even what constitutes a "good" score. Here, we introduce a novel tool to investigate these questions by differentiating through similarity measures to directly maximize the score. Surprisingly, we find that high similarity scores do not guarantee encoding task-relevant information in a manner consistent with neural data; and this is particularly acute for CKA and even some variations of cross-validated and regularized linear regression. We find no consistent threshold for a good similarity score - it depends on both the measure and the dataset. In addition, synthetic datasets optimized to maximize similarity scores initially learn the highest variance principal component of the target dataset, but some methods like angular Procrustes capture lower variance dimensions much earlier than methods like CKA. To shed light on this, we mathematically derive the sensitivity of CKA, angular Procrustes, and NBS to the variance of principal component dimensions, and explain the emphasis CKA places on high variance components. Finally, by jointly optimizing multiple similarity measures, we characterize their allowable ranges and reveal that some similarity measures are more constraining than others. While current measures offer a seemingly straightforward way to quantify the similarity between neural systems, our work underscores the need for careful interpretation. We hope the tools we developed will be used by practitioners to better understand current and future similarity measures.

Poster
SVDQuant: Absorbing Outliers by Low-Rank Component for 4-Bit Diffusion Models

Muyang Li, Yujun Lin, Zhekai Zhang, Tianle Cai, Xiuyu Li, junxian guo, Enze Xie, Chenlin Meng, Jun-Yan Zhu, Song Han

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Diffusion models can effectively generate high-quality images. However, as they scale, rising memory demands and higher latency pose substantial deployment challenges. In this work, we aim to accelerate diffusion models by quantizing their weights and activations to 4 bits. At such an aggressive level, both weights and activations are highly sensitive, where existing post-training quantization methods like smoothing become insufficient. To overcome this limitation, we propose *SVDQuant*, a new 4-bit quantization paradigm. Different from smoothing, which redistributes outliers between weights and activations, our approach *absorbs* these outliers using a low-rank branch. We first consolidate the outliers by shifting them from activations to weights. Then, we use a high-precision, low-rank branch to take in the weight outliers with Singular Value Decomposition (SVD), while a low-bit quantized branch handles the residuals. This process eases the quantization on both sides. However, naively running the low-rank branch independently incurs significant overhead due to extra data movement of activations, negating the quantization speedup. To address this, we co-design an inference engine *Nunchaku* that fuses the kernels of the low-rank branch into those of the low-bit branch to cut off redundant memory access. It can also seamlessly support off-the-shelf low-rank adapters (LoRAs) without re-quantization. Extensive experiments on SDXL, PixArt-$\Sigma$, and FLUX.1 validate the effectiveness of SVDQuant in preserving image quality. We reduce the memory usage for the 12B FLUX.1 models by 3.5×, achieving 3.0× speedup over the 4-bit weight-only quantization (W4A16) baseline on the 16GB laptop 4090 GPU with INT4 precision. On the latest RTX 5090 desktop with Blackwell architecture, we achieve a 3.1× speedup compared to the W4A16 model using NVFP4 precision. Our quantization library and inference engine are available at https://github.com/mit-han-lab/deepcompressor/ and https://github.com/mit-han-lab/nunchaku/, correspondingly.

Spotlight
Tracing Representation Progression: Analyzing and Enhancing Layer-Wise Similarity

Jiachen Jiang, Jinxin Zhou, Zhihui Zhu

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Analyzing the similarity of internal representations within and across different models has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such as those based on Centered Kernel Alignment (CKA), rely on statistical properties of the representations for a set of data points. In this paper, we focus on transformer models and study the similarity of representations between the hidden layers of individual transformers. In this context, we show that a simple sample-wise cosine similarity metric is capable of capturing the similarity and aligns with the complicated CKA. Our experimental results on common transformers reveal that representations across layers are positively correlated, with similarity increasing when layers get closer. We provide a theoretical justification for this phenomenon under the geodesic curve assumption for the learned transformer, a property that may approximately hold for residual networks. We then show that an increase in representation similarity implies an increase in predicted probability when directly applying the last-layer classifier to any hidden layer representation. This offers a justification for {\it saturation events}, where the model's top prediction remains unchanged across subsequent layers, indicating that the shallow layer has already learned the necessary knowledge. We then propose an aligned training method to improve the effectiveness of shallow layer by enhancing the similarity between internal representations, with trained models that enjoy the following properties: (1) more early saturation events, (2) layer-wise accuracies monotonically increase and reveal the minimal depth needed for the given task, (3) when served as multi-exit models, they achieve on-par performance with standard multi-exit architectures which consist of additional classifiers designed for early exiting in shallow layers. To our knowledge, our work is the first to show that one common classifier is sufficient for multi-exit models. We conduct experiments on both vision and NLP tasks to demonstrate the performance of the proposed aligned training.

Poster
The Pitfalls of Memorization: When Memorization Hurts Generalization

Reza Bayat, Mohammad Pezeshki, Elvis Dohmatob, David Lopez-Paz, Pascal Vincent

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Neural networks often learn simple explanations that fit the majority of the data while memorizing exceptions that deviate from these explanations. This behavior leads to poor generalization when the learned explanations rely on spurious correlations. In this work, we formalize $\textit{the interplay between memorization and generalization}$, showing that spurious correlations would particularly lead to poor generalization when are combined with memorization. Memorization can reduce training loss to zero, leaving no incentive to learn robust, generalizable patterns. To address this, we propose $\textit{memorization-aware training}$ (MAT), which uses held-out predictions as a signal of memorization to shift a model's logits. MAT encourages learning robust patterns invariant across distributions, improving generalization under distribution shifts.

Poster
RecFlow: An Industrial Full Flow Recommendation Dataset

Qi Liu, Kai Zheng, Rui Huang, Wuchao Li, Kuo Cai, Yuan Chai, Yanan Niu, Yiqun Hui, Bing Han, Na Mou, Hongning Wang, Wentian Bao, Yun En Yu, Guorui Zhou, Han Li, Yang Song, Defu Lian, Kun Gai

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Industrial recommendation systems (RS) rely on the multi-stage pipeline to balance effectiveness and efficiency when delivering items from a vast corpus to users. Existing RS benchmark datasets primarily focus on the exposure space, where novel RS algorithms are trained and evaluated. However, when these algorithms transition to real-world industrial RS, they face two critical challenges: (1) handling unexposed items—a significantly larger space than the exposed one, profoundly impacting their practical performance; and (2) overlooking the intricate interplay between multiple stages of the recommendation pipeline, resulting in suboptimal system performance. To bridge the gap between offline RS benchmarks and real-world online environments, we introduce RecFlow—an industrial full-flow recommendation dataset. Unlike existing datasets, RecFlow includes samples not only from the exposure space but also from unexposed items filtered at each stage of the RS funnel. RecFlow comprises 38 million interactions from 42,000 users across nearly 9 million items with additional 1.9 billion stage samples collected from 9.3 million online requests over 37 days and spanning 6 stages. Leveraging RecFlow, we conduct extensive experiments to demonstrate its potential in designing novel algorithms that enhance effectiveness by incorporating stage-specific samples. Some of these algorithms have already been deployed online at KuaiShou, consistently yielding significant gains. We propose RecFlow as the first comprehensive whole-pipeline benchmark dataset for the RS community, enabling research on algorithm design across the entire recommendation pipeline, including selection bias study, debiased algorithms, multi-stage consistency and optimality, multi-task recommendation, and user behavior modeling.

Poster
Decomposition Polyhedra of Piecewise Linear Functions

Marie-Charlotte Brandenburg, Moritz Leo Grillo, Christoph Hertrich

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In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Every CPWL function has infinitely many such decompositions, but for applications in optimization and neural network theory, it is crucial to find decompositions with as few linear pieces as possible. This is a highly challenging problem, as we further demonstrate by disproving a recently proposed approach by Tran and Wang [Minimal representations of tropical rational functions. Algebraic Statistics, 15(1):27–59, 2024]. To make the problem more tractable, we propose to fix an underlying polyhedral complex determining the possible locus of nonlinearity. Under this assumption, we prove that the set of decompositions forms a polyhedron that arises as intersection of two translated cones. We prove that irreducible decompositions correspond to the bounded faces of this polyhedron and minimal solutions must be vertices. We then identify cases with a unique minimal decomposition, and illustrate how our insights have consequences in the theory of submodular functions. Finally, we improve upon previous constructions of neural networks for a given convex CPWL function and apply our framework to obtain results in the nonconvex case.

Spotlight
When is Task Vector Provably Effective for Model Editing? A Generalization Analysis of Nonlinear Transformers

Hongkang Li, Yihua Zhang, Shuai Zhang, Pin-Yu Chen, Sijia Liu, Meng Wang

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Task arithmetic refers to editing the pre-trained model by adding a weighted sum of task vectors, each of which is the weight update from the pre-trained model to fine-tuned models for certain tasks. This approach recently gained attention as a computationally efficient inference method for model editing, e.g., multi-task learning, forgetting, and out-of-domain generalization capabilities. However, the theoretical understanding of why task vectors can execute various conceptual operations remains limited, due to the highly non-convexity of training Transformer-based models. To the best of our knowledge, this paper provides the first theoretical characterization of the generalization guarantees of task vector methods on nonlinear Transformers. We consider a conceptual learning setting, where each task is a binary classification problem based on a discriminative pattern. We theoretically prove the effectiveness of task addition in simultaneously learning a set of irrelevant or aligned tasks, as well as the success of task negation in unlearning one task from irrelevant or contradictory tasks. Moreover, we prove the proper selection of linear coefficients for task arithmetic to achieve guaranteed generalization to out-of-domain tasks. All of our theoretical results hold for both dense-weight parameters and their low-rank approximations. Although established in a conceptual setting, our theoretical findings were validated on a practical machine unlearning task using the large language model Phi-1.5 (1.3B).

Oral