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%

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SageAttention: Accurate 8-Bit Attention for Plug-and-play Inference Acceleration

Jintao Zhang, Jia wei, Pengle Zhang, Jun Zhu, Jianfei Chen

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The transformer architecture predominates across various models. As the heart of the transformer, attention has a computational complexity of $O(N^2)$, compared to $O(N)$ for linear transformations. When handling large sequence lengths, attention becomes the primary time-consuming component. Although quantization has proven to be an effective method for accelerating model inference, existing quantization methods primarily focus on optimizing the linear layer. In response, we first analyze the feasibility of quantization in attention detailedly. Following that, we propose SageAttention, a highly efficient and accurate quantization method for attention. The OPS (operations per second) of our approach outperforms FlashAttention2 and xformers by about 2.1x and 2.7x, respectively. SageAttention also achieves superior accuracy performance over FlashAttention3. Comprehensive experiments confirm that our approach incurs almost no end-to-end metrics loss across diverse models—including those for large language processing, image generation, and video generation. The code is available at https://github.com/thu-ml/SageAttention.

Poster
SIM: Surface-based fMRI Analysis for Inter-Subject Multimodal Decoding from Movie-Watching Experiments

Simon Dahan, Gabriel Bénédict, Logan Zane John Williams, Yourong Guo, Daniel Rueckert, Robert Leech, Emma Claire Robinson

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Current AI frameworks for brain decoding and encoding, typically train and test models within the same datasets. This limits their utility for cognitive training (neurofeedback) for which it would be useful to pool experiences across individuals to better simulate stimuli not sampled during training. A key obstacle to model generalisation is the degree of variability of inter-subject cortical organisation, which makes it difficult to align or compare cortical signals across participants. In this paper we address this through use of surface vision transformers, which build a generalisable model of cortical functional dynamics, through encoding the topography of cortical networks and their interactions as a moving image across a surface. This is then combined with tri-modal self-supervised contrastive (CLIP) alignment of audio, video, and fMRI modalities to enable the retrieval of visual and auditory stimuli from patterns of cortical activity (and vice-versa). We validate our approach on 7T task-fMRI data from 174 healthy participants engaged in the movie-watching experiment from the Human Connectome Project (HCP). Results show that it is possible to detect which movie clips an individual is watching purely from their brain activity, even for individuals and movies *not seen during training*. Further analysis of attention maps reveals that our model captures individual patterns of brain activity that reflect semantic and visual systems. This opens the door to future personalised simulations of brain function. Code \& pre-trained models will be made available at https://github.com/metrics-lab/sim.

Poster
OpenHands: An Open Platform for AI Software Developers as Generalist Agents

Xingyao Wang, Boxuan Li, Yufan Song, Frank F. Xu, Xiangru Tang, Mingchen Zhuge, Jiayi Pan, Yueqi Song, Bowen Li, Jaskirat Singh, Hoang H. Tran, Fuqiang Li, Ren Ma, Mingzhang Zheng, Bill Qian, Yanjun Shao, Niklas Muennighoff, Yizhe Zhang, Binyuan Hui, Junyang Lin, Robert Brennan, Hao Peng, Heng Ji, Graham Neubig

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Software is one of the most powerful tools that we humans have at our disposal; it allows a skilled programmer to interact with the world in complex and profound ways. At the same time, thanks to improvements in large language models (LLMs), there has also been a rapid development in AI agents that interact with and effect change in their surrounding environments. In this paper, we introduce OpenHands, a platform for the development of powerful and flexible AI agents that interact with the world in similar ways to a human developer: by writing code, interacting with a command line, and browsing the web. We describe how the platform allows for the implementation of new agents, utilization of various LLMs, safe interaction with sandboxed environments for code execution, and incorporation of evaluation benchmarks. Based on our currently incorporated benchmarks, we perform an evaluation of agents over 13 challenging tasks, including software engineering (e.g., SWE-Bench) and web browsing (e.g., WebArena), amongst others. Released under the permissive MIT license, OpenHands is a community project spanning academia and industry with more than 2K contributions from over 186 contributors in less than six months of development, and will improve going forward.

Poster
Procedural Synthesis of Synthesizable Molecules

Michael Sun, Alston Lo, Minghao Guo, Jie Chen, Connor W. Coley, Wojciech Matusik

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Designing synthetically accessible molecules and recommending analogs to unsynthesizable molecules are important problems for accelerating molecular discovery. We reconceptualize both problems using ideas from program synthesis. Drawing inspiration from syntax-guided synthesis approaches, we decouple the syntactic skeleton from the semantics of a synthetic tree to create a bilevel framework for reasoning about the combinatorial space of synthesis pathways. Given a molecule we aim to generate analogs for, we iteratively refine its skeletal characteristics via Markov Chain Monte Carlo simulations over the space of syntactic skeletons. Given a black-box oracle to optimize, we formulate a joint design space over syntactic templates and molecular descriptors and introduce evolutionary algorithms that optimize both syntactic and semantic dimensions synergistically. Our key insight is that once the syntactic skeleton is set, we can amortize over the search complexity of deriving the program's semantics by training policies to fully utilize the fixed horizon Markov Decision Process imposed by the syntactic template. We demonstrate performance advantages of our bilevel framework for synthesizable analog generation and synthesizable molecule design. Notably, our approach offers the user explicit control over the resources required to perform synthesis and biases the design space towards simpler solutions, making it particularly promising for autonomous synthesis platforms. Supporting code is at https://github.com/shiningsunnyday/SynthesisNet.

Poster
Resolution Attack: Exploiting Image Compression to Deceive Deep Neural Networks

Wangjia Yu, Xiaomeng Fu, Qiao Li, Jizhong Han, Xiaodan Zhang

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Model robustness is essential for ensuring the stability and reliability of machine learning systems. Despite extensive research on various aspects of model robustness, such as adversarial robustness and label noise robustness, the exploration of robustness towards different resolutions, remains less explored. To address this gap, we introduce a novel form of attack: the resolution attack. This attack aims to deceive both classifiers and human observers by generating images that exhibit different semantics across different resolutions. To implement the resolution attack, we propose an automated framework capable of generating dual-semantic images in a zero-shot manner. Specifically, we leverage large-scale diffusion models for their comprehensive ability to construct images and propose a staged denoising strategy to achieve a smoother transition across resolutions. Through the proposed framework, we conduct resolution attacks against various off-the-shelf classifiers. The experimental results exhibit high attack success rate, which not only validates the effectiveness of our proposed framework but also reveals the vulnerability of current classifiers towards different resolutions. Additionally, our framework, which incorporates features from two distinct objects, serves as a competitive tool for applications such as face swapping and facial camouflage. The code is available at https://github.com/ywj1/resolution-attack.

Poster
Oryx MLLM: On-Demand Spatial-Temporal Understanding at Arbitrary Resolution

Zuyan Liu, Yuhao Dong, Ziwei Liu, Winston Hu, Jiwen Lu, Yongming Rao

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Visual data comes in various forms, ranging from small icons of just a few pixels to long videos spanning hours. Existing multi-modal LLMs usually standardize these diverse visual inputs to fixed-resolution images or patches for visual encoders and yield similar numbers of tokens for LLMs. This approach is non-optimal for multimodal understanding and inefficient for processing inputs with long and short visual contents. To solve the problem, we propose Oryx, a unified multimodal architecture for the spatial-temporal understanding of images, videos, and multi-view 3D scenes. Oryx offers an on-demand solution to seamlessly and efficiently process visual inputs with arbitrary spatial sizes and temporal lengths through two core innovations: 1) a pre-trained OryxViT model that can encode images at any resolution into LLM-friendly visual representations; 2) a dynamic compressor module that supports 1x to 16x compression on visual tokens by request. These designs enable Oryx to accommodate extremely long visual contexts, such as videos, with lower resolution and high compression while maintaining high recognition precision for tasks like document understanding with native resolution and no compression. Beyond the architectural improvements, enhanced data curation and specialized training on long-context retrieval and spatial-aware data help Oryx achieve strong capabilities in image, video, and 3D multimodal understanding simultaneously.

Poster
A Sanity Check for AI-generated Image Detection

Shilin Yan, Ouxiang Li, Jiayin Cai, Yanbin Hao, Xiaolong Jiang, Yao Hu, Weidi Xie

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With the rapid development of generative models, discerning AI-generated content has evoked increasing attention from both industry and academia. In this paper, we conduct a sanity check on whether the task of AI-generated image detection has been solved. To start with, we present Chameleon dataset, consisting of AI-generated images that are genuinely challenging for human perception. To quantify the generalization of existing methods, we evaluate 9 off-the-shelf AI-generated image detectors on Chameleon dataset. Upon analysis, almost all models misclassify AI-generated images as real ones. Later, we propose AIDE AI-generated Image DEtector with Hybrid Features, which leverages multiple experts to simultaneously extract visual artifacts and noise patterns. Specifically, to capture the high-level semantics, we utilize CLIP to compute the visual embedding. This effectively enables the model to discern AI-generated images based on semantics and contextual information. Secondly, we select the highest and lowest frequency patches in the image, and compute the low-level patchwise features, aiming to detect AI-generated images by low-level artifacts, for example, noise patterns, anti-aliasing effects. While evaluating on existing benchmarks, for example, AIGCDetectBenchmark and GenImage, AIDE achieves +3.5% and +4.6% improvements to state-of-the-art methods, and on our proposed challenging Chameleon benchmarks, it also achieves promising results, despite the problem of detecting AI-generated images remains far from being solved.

Poster
Deep Random Features for Scalable Interpolation of Spatiotemporal Data

Weibin Chen, Azhir Mahmood, Michel Tsamados, So Takao

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The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes (GPs) are candidate model choices for interpolation. However, due to their poor scalability, they usually rely on inducing points for inference, which restricts their expressivity. Moreover, commonly imposed assumptions such as stationarity prevents them from capturing complex patterns in the data. While deep GPs can overcome this issue, training and making inference with them are difficult, again requiring crude approximations via inducing points. In this work, we instead approach the problem through Bayesian deep learning, where spatiotemporal fields are represented by deep neural networks, whose layers share the inductive bias of stationary GPs on the plane/sphere via random feature expansions. This allows one to (1) capture high frequency patterns in the data, and (2) use mini-batched gradient descent for large scale training. We experiment on various remote sensing data at local/global scales, showing that our approach produce competitive or superior results to existing methods, with well-calibrated uncertainties.

Poster
Meta-Continual Learning of Neural Fields

Seungyoon Woo, Junhyeog Yun, Gunhee Kim

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Neural Fields (NF) have gained prominence as a versatile framework for complex data representation. This work unveils a new problem setting termed Meta-Continual Learning of Neural Fields (MCL-NF) and introduces a novel strategy that employs a modular architecture combined with optimization-based meta-learning. Focused on overcoming the limitations of existing methods for continual learning of neural fields, such as catastrophic forgetting and slow convergence, our strategy achieves high-quality reconstruction with significantly improved learning speed. We further introduce Fisher Information Maximization loss for neural radiance fields (FIM-NeRF), which maximizes information gains at the sample level to enhance learning generalization, with proved convergence guarantee and generalization bound. We perform extensive evaluations across image, audio, video reconstruction, and view synthesis tasks on six diverse datasets, demonstrating our method’s superiority in reconstruction quality and speed over existing MCL and CL-NF approaches. Notably, our approach attains rapid adaptation of neural fields for city-scale NeRF rendering with reduced parameter requirement.

Poster
SmartRAG: Jointly Learn RAG-Related Tasks From the Environment Feedback

Jingsheng Gao, Linxu Li, Ke Ji, Weiyuan Li, Yixin Lian, Yuzhuo Fu, Bin Dai

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RAG systems consist of multiple modules to work together. However, these modules are usually separately trained. We argue that a system like RAG that incorporates multiple modules should be jointly optimized to achieve optimal performance. To demonstrate this, we design a specific pipeline called SmartRAG that includes a policy network and a retriever. The policy network can serve as 1) a decision maker that decides when to retrieve, 2) a query rewriter to generate a query most suited to the retriever and 3) an answer generator that produces the final response with/without the observations. We then propose to jointly optimize the whole system using a reinforcement learning algorithm, with the reward designed to encourage the system to achieve the highest performance with minimal retrieval cost. When jointly optimized, each module can be aware of how other modules are working and thus find the best way to work together as a complete system. Empirical results demonstrate that the jointly optimized system can achieve better performance than separately optimized counterparts.

Poster
Erasing Concept Combination from Text-to-Image Diffusion Model

hongyi nie, Quanming Yao, Yang Liu, Zhen Wang, Yatao Bian

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Advancements in the text-to-image diffusion model have raised security concerns due to their potential to generate images with inappropriate themes such as societal biases and copyright infringements. Current studies have made notable progress in preventing the model from generating images containing specific high-risk visual concepts. However, these methods neglect the issue that inappropriate themes may also arise from the combination of benign visual concepts. A crucial challenge arises because the same image theme can be represented through multiple distinct visual concept combinations, and the model's ability to generate individual concepts may become distorted when processing these combinations. Consequently, effectively erasing such visual concept combinations from the diffusion model remains a formidable challenge. To tackle this problem, we formalize the problem as the Concept Combination Erasing (CCE) problem and propose a Concept Graph-based high-level Feature Decoupling framework (CoGFD) to address CCE. CoGFD identifies and decomposes visual concept combinations with a consistent image theme from an LLM-induced concept logic graph, and erases these combinations through decoupling co-occurrent high-level features. These techniques enable CoGFD to eliminate undesirable visual concept combinations while minimizing adverse effects on the generative fidelity of related individual concepts, outperforming state-of-the-art baselines. Extensive experiments across diverse visual concept combination scenarios verify the effectiveness of CoGFD.

Poster
SparsyFed: Sparse Adaptive Federated Learning

Adriano Guastella, Lorenzo Sani, Alex Iacob, Alessio Mora, Paolo Bellavista, Nicholas Donald Lane

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Sparse training is often adopted in cross-device federated learning (FL) environments where constrained devices collaboratively train a machine learning model on private data by exchanging pseudo-gradients across heterogeneous networks. Although sparse training methods can reduce communication overhead and computational burden in FL, they are often not used in practice for the following key reasons: (1) data heterogeneity makes it harder for clients to reach consensus on sparse models compared to dense ones, requiring longer training; (2) methods for obtaining sparse masks lack adaptivity to accommodate very heterogeneous data distributions, crucial in cross-device FL; and (3) additional hyperparameters are required, which are notably challenging to tune in FL. This paper presents SparsyFed, a practical federated sparse training method that critically addresses the problems above. Previous works have only solved one or two of these challenges at the expense of introducing new trade-offs, such as clients’ consensus on masks versus sparsity pattern adaptivity. We show that SparsyFed simultaneously (1) can produce 95% sparse models, with negligible degradation in accuracy, while only needing a single hyperparameter, (2) achieves a per-round weight regrowth 200 times smaller than previous methods, and (3) allows the sparse masks to adapt to highly heterogeneous data distributions and outperform all baselines under such conditions.

Poster
Model-based Offline Reinforcement Learning with Lower Expectile Q-Learning

Kwanyoung Park, Youngwoon Lee

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Model-based offline reinforcement learning (RL) is a compelling approach that addresses the challenge of learning from limited, static data by generating imaginary trajectories using learned models. However, these approaches often struggle with inaccurate value estimation from model rollouts. In this paper, we introduce a novel model-based offline RL method, Lower Expectile Q-learning (LEQ), which provides a low-bias model-based value estimation via lower expectile regression of $\lambda$-returns. Our empirical results show that LEQ significantly outperforms previous model-based offline RL methods on long-horizon tasks, such as the D4RL AntMaze tasks, matching or surpassing the performance of model-free approaches and sequence modeling approaches. Furthermore, LEQ matches the performance of state-of-the-art model-based and model-free methods in dense-reward environments across both state-based tasks (NeoRL and D4RL) and pixel-based tasks (V-D4RL), showing that LEQ works robustly across diverse domains. Our ablation studies demonstrate that lower expectile regression, $\lambda$-returns, and critic training on offline data are all crucial for LEQ.

Poster
Maintaining Structural Integrity in Parameter Spaces for Parameter Efficient Fine-tuning

Chongjie Si, Xuehui Wang, Xue Yang, Zhengqin Xu, Qingyun Li, Jifeng Dai, Yu Qiao, Xiaokang Yang, Wei Shen

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Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix adaptations. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, designed for various dimensional parameter space. Specifically, our method asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. It effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile models it via low-rank tensor adaptation. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate the effectiveness of our method.

Poster
Arithmetic Without Algorithms: Language Models Solve Math with a Bag of Heuristics

Yaniv Nikankin, Anja Reusch, Aaron Mueller, Yonatan Belinkov

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Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types---such as neurons that activate when an operand falls within a certain range---and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a ``bag of heuristics''.

Poster
Bayesian Treatment of the Spectrum of the Empirical Kernel in (Sub)Linear-Width Neural Networks

Ouns El Harzli, Bernardo Cuenca Grau

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We study Bayesian neural networks (BNNs) in the theoretical limits of infinitely increasing number of training examples, network width and input space dimension. Our findings establish new bridges between kernel-theoretic approaches and techniques derived from statistical mechanics through the correspondence between Mercer's eigenvalues and limiting spectral distributions of covariance matrices studied in random matrix theory. Our theoretical contributions first consist in novel integral formulas that accurately describe the predictors of BNNs in the asymptotic linear-width and sublinear-width regimes. Moreover, we extend the recently developed renormalisation theory of deep linear neural networks, enabling a rigorous explanation of the mounting empirical evidence that hints at the theory's applicability to nonlinear BNNs with ReLU activations in the linear-width regime. From a practical standpoint, our results introduce a novel technique for estimating the predictor statistics of a trained BNN that is applicable to the sublinear-width regime where the predictions of the renormalisation theory are inaccurate.

Poster
Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization

Xi Lin, Yilu Liu, Xiaoyuan Zhang, Fei Liu, Zhenkun Wang, Qingfu Zhang

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Multi-objective optimization can be found in many real-world applications where some conflicting objectives can not be optimized by a single solution. Existing optimization methods often focus on finding a set of Pareto solutions with different optimal trade-offs among the objectives. However, the required number of solutions to well approximate the whole Pareto optimal set could be exponentially large with respect to the number of objectives, which makes these methods unsuitable for handling many optimization objectives. In this work, instead of finding a dense set of Pareto solutions, we propose a novel Tchebycheff set scalarization method to find a few representative solutions (e.g., 5) to cover a large number of objectives (e.g., $>100$) in a collaborative and complementary manner. In this way, each objective can be well addressed by at least one solution in the small solution set. In addition, we further develop a smooth Tchebycheff set scalarization approach for efficient optimization with good theoretical guarantees. Experimental studies on different problems with many optimization objectives demonstrate the effectiveness of our proposed method.

Poster
TPO: Aligning Large Language Models with Multi-branch & Multi-step Preference Trees

Weibin Liao, Xu Chu, Yasha Wang

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In the domain of complex reasoning tasks, such as mathematical reasoning, recent advancements have proposed the use of Direct Preference Optimization (DPO) to suppress output of dispreferred responses, thereby enhancing the long-chain reasoning capabilities of large language models (LLMs). To this end, these studies employed LLMs to generate preference trees via Tree-of-thoughts (ToT) and sample the paired preference responses required by the DPO algorithm. However, the DPO algorithm based on binary preference optimization is unable to learn multiple responses with varying degrees of preference/dispreference that provided by the preference trees, resulting in incomplete preference learning. In this work, we introduce Tree Preference Optimization (TPO), that does not sample paired preference responses from the preference tree; instead, it directly learns from the entire preference tree during the fine-tuning. Specifically, TPO formulates the language model alignment as a Preference List Ranking problem, where the policy can potentially learn more effectively from a ranked preference list of responses given the prompt. In addition, to further assist LLMs in identifying discriminative steps within long-chain reasoning and increase the relative reward margin in the preference list, TPO utilizes Adaptive Step Reward to adjust the reward values of each step in trajectory for performing fine-grained preference optimization. We carry out extensive experiments on mathematical reasoning tasks to evaluate TPO. The experimental results indicate that TPO consistently outperforms DPO across five public large language models on four datasets.

Poster
Direct Distributional Optimization for Provable Alignment of Diffusion Models

Ryotaro Kawata, Kazusato Oko, Atsushi Nitanda, Taiji Suzuki

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We introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. We first formulate the problem as a generic regularized loss minimization over probability distributions and directly optimize the distribution using the Dual Averaging method. Next, we enable sampling from the learned distribution by approximating its score function via Doob's $h$-transform technique. The proposed framework is supported by rigorous convergence guarantees and an end-to-end bound on the sampling error, which imply that when the original distribution's score is known accurately, the complexity of sampling from shifted distributions is independent of isoperimetric conditions. This framework is broadly applicable to general distribution optimization problems, including alignment tasks in Reinforcement Learning with Human Feedback (RLHF), Direct Preference Optimization (DPO), and Kahneman-Tversky Optimization (KTO). We empirically validate its performance on synthetic and image datasets using the DPO objective.

Poster
TRENDy: Temporal Regression of Effective Nonlinear Dynamics

Matt Ricci, Guy Pelc, Zoe Piran, Noa Moriel, Mor Nitzan

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Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable parameters induce qualitative changes in system behavior called bifurcations. This endeavor is particularly difficult in realistic settings where governing partial differential equations (PDEs) are unknown and data is limited and noisy. To address this challenge, we propose TRENDy (Temporal Regression of Effective Nonlinear Dynamics), an equation-free approach to learning low-dimensional, predictive models of spatiotemporal dynamics. TRENDy first maps input data to a low-dimensional space of effective dynamics through a cascade of multiscale filtering operations. Our key insight is the recognition that these effective dynamics can be fit by a neural ordinary differential equation (NODE) having the same parameter space as the input PDE. The preceding filtering operations strongly regularize the phase space of the NODE, making TRENDy significantly more robust to noise compared to existing methods. We train TRENDy to predict the effective dynamics of synthetic and real data representing dynamics from across the physical and life sciences. We then demonstrate how we can automatically locate both Turing and Hopf bifurcations in unseen regions of parameter space. We finally apply our method to the analysis of spatial patterning of the ocellated lizard through development. We found that TRENDy's predicted effective state not only accurately predicts spatial changes over time but also identifies distinct pattern features unique to different anatomical regions, such as the tail, neck, and body--an insight that highlights the potential influence of surface geometry on reaction-diffusion mechanisms and their role in driving spatially varying pattern dynamics.

Poster