NeurIPS 2024 Papers

Conference on Neural Information Processing Systems

Decision breakdown

4,562papers

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

  • Oral
    721.6%
  • Spotlight
    3828.4%
  • Poster
    4,06489.1%
  • Other / unlabeled
    441.0%

Browse all papers

SEA: State-Exchange Attention for High-Fidelity Physics Based Transformers

Parsa Esmati, Amirhossein Dadashzadeh, Vahid Goodarzi Ardakani, Nicolas Larrosa, Nicolò Grilli

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Current approaches using sequential networks have shown promise in estimating field variables for dynamical systems, but they are often limited by high rollout errors. The unresolved issue of rollout error accumulation results in unreliable estimations as the network predicts further into the future, with each step's error compounding and leading to an increase in inaccuracy. Here, we introduce the State-Exchange Attention (SEA) module, a novel transformer-based module enabling information exchange between encoded fields through multi-head cross-attention. The cross-field multidirectional information exchange design enables all state variables in the system to exchange information with one another, capturing physical relationships and symmetries between fields. Additionally, we introduce an efficient ViT-like mesh autoencoder to generate spatially coherent mesh embeddings for a large number of meshing cells. The SEA integrated transformer demonstrates the state-of-the-art rollout error compared to other competitive baselines. Specifically, we outperform PbGMR-GMUS Transformer-RealNVP and GMR-GMUS Transformer, with a reduction in error of 88% and 91%, respectively. Furthermore, we demonstrate that the SEA module alone can reduce errors by 97% for state variables that are highly dependent on other states of the system. The repository for this work is available at: https://github.com/ParsaEsmati/SEA

Poster
Improving the Learning Capability of Small-size Image Restoration Network by Deep Fourier Shifting

man zhou

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State-of-the-art image restoration methods currently face challenges in terms of computational requirements and performance, making them impractical for deployment on edge devices such as phones and resource-limited devices. As a result, there is a need to develop alternative solutions with efficient designs that can achieve comparable performance to transformer or large-kernel methods. This motivates our research to explore techniques for improving the capability of small-size image restoration standing on the success secret of large receptive filed. Targeting at expanding receptive filed, spatial-shift operator tailored for efficient spatial communication and has achieved remarkable advances in high-level image classification tasks, like $S^2$-MLP and ShiftVit. However, its potential has rarely been explored in low-level image restoration tasks. The underlying reason behind this obstacle is that image restoration is sensitive to the spatial shift that occurs due to severe region-aware information loss, which exhibits a different behavior from high-level tasks. To address this challenge and unleash the potential of spatial shift for image restoration, we propose an information-lossless shifting operator, i.e., Deep Fourier Shifting, that is customized for image restoration. To develop our proposed operator, we first revisit the principle of shift operator and apply it to the Fourier domain, where the shift operator can be modeled in an information-lossless Fourier cycling manner. Inspired by Fourier cycling, we design two variants of Deep Fourier Shifting, namely the amplitude-phase variant and the real-imaginary variant. These variants are generic operators that can be directly plugged into existing image restoration networks as a drop-in replacement for the standard convolution unit, consuming fewer parameters. Extensive experiments across multiple low-level tasks including image denoising, low-light image enhancement, guided image super-resolution, and image de-blurring demonstrate consistent performance gains obtained by our Deep Fourier Shifting while reducing the computation burden. Additionally, ablation studies verify the robustness of the shift displacement with stable performance improvement.

Poster
Can Transformers Smell Like Humans?

Farzaneh Taleb, Miguel Vasco, Antonio H. Ribeiro, Mårten Björkman, Danica Kragic

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The human brain encodes stimuli from the environment into representations that form a sensory perception of the world. Despite recent advances in understanding visual and auditory perception, olfactory perception remains an under-explored topic in the machine learning community due to the lack of large-scale datasets annotated with labels of human olfactory perception. In this work, we ask the question of whether pre-trained transformer models of chemical structures encode representations that are aligned with human olfactory perception, i.e., can transformers smell like humans? We demonstrate that representations encoded from transformers pre-trained on general chemical structures are highly aligned with human olfactory perception. We use multiple datasets and different types of perceptual representations to show that the representations encoded by transformer models are able to predict: (i) labels associated with odorants‌‌ provided by experts; (ii) continuous ratings provided by human participants with respect to pre-defined descriptors; and (iii) similarity ratings between odorants provided by human participants. Finally, we evaluate the extent to which this alignment is associated with physicochemical features of odorants known to be relevant for olfactory decoding.

Spotlight
The Edge-of-Reach Problem in Offline Model-Based Reinforcement Learning

Anya Sims, Cong Lu, Jakob Nicolaus Foerster, Yee Whye Teh

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Offline reinforcement learning (RL) aims to train agents from pre-collected datasets. However, this comes with the added challenge of estimating the value of behaviors not covered in the dataset. Model-based methods offer a potential solution by training an approximate dynamics model, which then allows collection of additional synthetic data via rollouts in this model. The prevailing theory treats this approach as online RL in an approximate dynamics model, and any remaining performance gap is therefore understood as being due to dynamics model errors. In this paper, we analyze this assumption and investigate how popular algorithms perform as the learned dynamics model is improved. In contrast to both intuition and theory, if the learned dynamics model is replaced by the true error-free dynamics, existing model-based methods completely fail. This reveals a key oversight: The theoretical foundations assume sampling of full horizon rollouts in the learned dynamics model; however, in practice, the number of model-rollout steps is aggressively reduced to prevent accumulating errors. We show that this truncation of rollouts results in a set of edge-of-reach states at which we are effectively "bootstrapping from the void." This triggers pathological value overestimation and complete performance collapse. We term this the edge-of-reach problem. Based on this new insight, we fill important gaps in existing theory, and reveal how prior model-based methods are primarily addressing the edge-of-reach problem, rather than model-inaccuracy as claimed. Finally, we propose Reach-Aware Value Learning (RAVL), a simple and robust method that directly addresses the edge-of-reach problem and hence - unlike existing methods - does not fail as the dynamics model is improved. Since world models will inevitably improve, we believe this is a key step towards future-proofing offline RL.

Poster
Decoding-Time Language Model Alignment with Multiple Objectives

Ruizhe Shi, Yifang Chen, Yushi Hu, Alisa Liu, Hannaneh Hajishirzi, Noah A. Smith, Simon Shaolei Du

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Aligning language models (LMs) to human preferences has emerged as a critical pursuit, enabling these models to better serve diverse user needs. Existing methods primarily focus on optimizing LMs for a single reward function, limiting their adaptability to varied objectives. Here, we propose $\textbf{multi-objective decoding~(MOD)}$, a decoding-time algorithm that outputs the next token from a linear combination of predictions of all base models, for any given weighting over different objectives. We exploit a common form among a family of $f$-divergence regularized alignment approaches (such as PPO, DPO, and their variants) to identify a closed-form solution by Legendre transform, and derive an efficient decoding strategy. Theoretically, we show why existing approaches can be sub-optimal even in natural settings and obtain optimality guarantees for our method. Empirical results demonstrate the effectiveness of the algorithm. For example, compared to a parameter-merging baseline, MOD achieves 12.8\% overall reward improvement when equally optimizing towards $3$ objectives. Moreover, we experiment with MOD on combining three fully-finetuned LMs of different model sizes, each aimed at different objectives such as safety, coding, and general user preference. Unlike traditional methods that require careful curation of a mixture of datasets to achieve comprehensive improvement, we can quickly experiment with preference weightings using MOD to find the best combination of models. Our best combination reduces toxicity on Toxigen to nearly 0\% and achieves 7.9--33.3\% improvement across three other metrics ($\textit{i.e.}$, Codex@1, GSM-COT, BBH-COT).

Poster
Learning-Augmented Algorithms for the Bahncard Problem

Hailiang Zhao, Xueyan Tang, Peng Chen, Shuiguang Deng

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In this paper, we study learning-augmented algorithms for the Bahncard problem. The Bahncard problem is a generalization of the ski-rental problem, where a traveler needs to irrevocably and repeatedly decide between a cheap short-term solution and an expensive long-term one with an unknown future. Even though the problem is canonical, only a primal-dual-based learning-augmented algorithm was explicitly designed for it. We develop a new learning-augmented algorithm, named PFSUM, that incorporates both history and short-term future to improve online decision making. We derive the competitive ratio of PFSUM as a function of the prediction error and conduct extensive experiments to show that PFSUM outperforms the primal-dual-based algorithm.

Poster
EGonc : Energy-based Open-Set Node Classification with substitute Unknowns

Qin ZHANG, Zelin Shi, Shirui Pan, Junyang Chen, Huisi Wu, Xiaojun Chen

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Open-set Classification (OSC) is a critical requirement for safely deploying machine learning models in the open world, which aims to classify samples from known classes and reject samples from out-of-distribution (OOD). Existing methods exploit the feature space of trained network and attempt at estimating the uncertainty in the predictions. However, softmax-based neural networks are found to be overly confident in their predictions even on data they have never seen before and the immense diversity of the OOD examples also makes such methods fragile. To this end, we follow the idea of estimating the underlying density of the training data to decide whether a given input is close to the in-distribution (IND) data and adopt Energy-based models (EBMs) as density estimators. A novel energy-based generative open-set node classification method, \textit{EGonc}, is proposed to achieve open-set graph learning. Specifically, we generate substitute unknowns to mimic the distribution of real open-set samples firstly, based on the information of graph structures. Then, an additional energy logit representing the virtual OOD class is learned from the residual of the feature against the principal space, and matched with the original logits by a constant scaling. This virtual logit serves as the indicator of OOD-ness. EGonc has nice theoretical properties that guarantee an overall distinguishable margin between the detection scores for IND and OOD samples. Comprehensive experimental evaluations of EGonc also demonstrate its superiority.

Poster
Global Rewards in Restless Multi-Armed Bandits

Naveen Janaki Raman, Zheyuan Ryan Shi, Fei Fang

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Restless multi-armed bandits (RMAB) extend multi-armed bandits so arm pulls impact future arm states. Despite the success of RMABs, a key limiting assumption is the separability of rewards into a sum across arms. We address this deficiency by proposing restless-multi-armed bandit with global rewards (RMAB-G), a generalization of RMABs to global non-separable rewards. To solve RMAB-G, we develop the Linear-Whittle and Shapley-Whittle indices, which extend Whittle indices from RMABs to RMAB-Gs. We prove approximation bounds which demonstrate how Linear and Shapley-Whittle indices fail for non-linear rewards. To overcome this limitation, we propose two sets of adaptive policies: the first computes indices iteratively and the second combines indices with Monte-Carlo Tree Search (MCTS). Empirically, we demonstrate that adaptive policies outperform both pre-computed index policies and baselines in synthetic and real-world food rescue datasets.

Poster
NanoBaseLib: A Multi-Task Benchmark Dataset for Nanopore Sequencing

Guangzhao Cheng, Chengbo Fu, Lu Cheng

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Nanopore sequencing is the third-generation sequencing technology with capabilities of generating long-read sequences and directly measuring modifications on DNA/RNA molecules, which makes it ideal for biological applications such as human Telomere-to-Telomere (T2T) genome assembly, Ebola virus surveillance and COVID-19 mRNA vaccine development. However, accuracies of computational methods in various tasks of Nanopore sequencing data analysis are far from satisfactory. For instance, the base calling accuracy of Nanopore RNA sequencing is $\sim$90\%, while the aim is $\sim$99.9\%. This highlights an urgent need of contributions from the machine learning community. A bottleneck that prevents machine learning researchers from entering this field is the lack of a large integrated benchmark dataset. To this end, we present NanoBaseLib, a comprehensive multi-task benchmark dataset. It integrates 16 public datasets with over 30 million reads for four critical tasks in Nanopore data analysis. To facilitate method development, we have preprocessed all the raw data using a uniform workflow, stored all the intermediate results in uniform formats, analysed test datasets with various baseline methods for four benchmark tasks, and developed a software package to easily access these results. NanoBaseLib is available at https://nanobaselib.github.io.

Poster
Revisiting Few-Shot Object Detection with Vision-Language Models

Anish Madan, Neehar Peri, Shu Kong, Deva Ramanan

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The era of vision-language models (VLMs) trained on web-scale datasets challenges conventional formulations of “open-world" perception. In this work, we revisit the task of few-shot object detection (FSOD) in the context of recent foundational VLMs. First, we point out that zero-shot predictions from VLMs such as GroundingDINO significantly outperform state-of-the-art few-shot detectors (48 vs. 33 AP) on COCO. Despite their strong zero-shot performance, such foundation models may still be sub-optimal. For example, trucks on the web may be defined differently from trucks for a target applications such as autonomous vehicle perception. We argue that the task of few-shot recognition can be reformulated as aligning foundation models to target concepts using a few examples. Interestingly, such examples can be multi-modal, using both text and visual cues, mimicking instructions that are often given to human annotators when defining a target concept of interest. Concretely, we propose Foundational FSOD, a new benchmark protocol that evaluates detectors pre-trained on any external data and fine-tuned on multi-modal (text and visual) K-shot examples per target class. We repurpose nuImages for Foundational FSOD, benchmark several popular open-source VLMs, and provide an empirical analysis of state-of-the-art methods. Lastly, we discuss our recent CVPR 2024 Foundational FSOD competition and share insights from the community. Notably, the winning team significantly outperforms our baseline by 23.3 mAP!

Poster
On the Inductive Bias of Stacking Towards Improving Reasoning

Nikunj Saunshi, Stefani Karp, Shankar Krishnan, Sobhan Miryoosefi, Sashank J. Reddi, Sanjiv Kumar

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Given the increasing scale of model sizes, efficient training strategies like gradual stacking have garnered interest. Stacking enables efficient training by gradually growing the depth of a model in stages and using layers from a smaller model in an earlier stage to initialize the next stage. Although efficient for training, the model biases induced by such growing approaches are largely unexplored. In this work, we examine this fundamental aspect of gradual stacking, going beyond its efficiency benefits. We propose a variant of gradual stacking called MIDAS that can speed up language model training by up to 40\%. Furthermore we discover an intriguing phenomenon: MIDAS is not only training-efficient but surprisingly also has an inductive bias towards improving downstream tasks, especially tasks that require reasoning abilities like reading comprehension and math problems, despite having similar or slightly worse perplexity compared to baseline training. To further analyze this inductive bias, we construct {\em reasoning primitives} – simple synthetic tasks that are building blocks for reasoning – and find that a model pretrained with stacking is significantly better than standard pretraining on these primitives, with and without fine-tuning. This provides stronger and more robust evidence for this inductive bias towards reasoning. These findings of training efficiency and inductive bias towards reasoning are verified at 1B, 2B and 8B parameter language models. Finally, we conjecture the underlying reason for this inductive bias by exploring the connection of stacking to looped models and provide strong supporting empirical analysis.

Poster
Faster Local Solvers for Graph Diffusion Equations

Jiahe Bai, Baojian Zhou, Deqing Yang, Yanghua Xiao

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Efficient computation of graph diffusion equations (GDEs), such as Personalized PageRank, Katz centrality, and the Heat kernel, is crucial for clustering, training neural networks, and many other graph-related problems. Standard iterative methods require accessing the whole graph per iteration, making them time-consuming for large-scale graphs. While existing local solvers approximate diffusion vectors through heuristic local updates, they often operate sequentially and are typically designed for specific diffusion types, limiting their applicability. Given that diffusion vectors are highly localizable, as measured by the participation ratio, this paper introduces a novel framework for approximately solving GDEs using a local diffusion process. This framework reveals the suboptimality of existing local solvers. Furthermore, our approach effectively localizes standard iterative solvers by designing simple and provably sublinear time algorithms. These new local solvers are highly parallelizable, making them well-suited for implementation on GPUs. We demonstrate the effectiveness of our framework in quickly obtaining approximate diffusion vectors, achieving up to a hundred-fold speed improvement, and its applicability to large-scale dynamic graphs. Our framework could also facilitate more efficient local message-passing mechanisms for GNNs.

Poster
Instruction Embedding: Latent Representations of Instructions Towards Task Identification

Yiwei Li, Jiayi Shi, Shaoxiong Feng, Peiwen Yuan, Xinglin Wang, Boyuan Pan, Heda Wang, Yao Hu, Kan Li

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Instruction data is crucial for improving the capability of Large Language Models (LLMs) to align with human-level performance. Recent research LIMA demonstrates that alignment is essentially a process where the model adapts instructions' interaction style or format to solve various tasks, leveraging pre-trained knowledge and skills. Therefore, for instructional data, the most important aspect is the task it represents, rather than the specific semantics and knowledge information. The latent representations of instructions play roles for some instruction-related tasks like data selection and demonstrations retrieval. However, they are always derived from text embeddings, encompass overall semantic information that influences the representation of task categories. In this work, we introduce a new concept, instruction embedding, and construct Instruction Embedding Benchmark (IEB) for its training and evaluation. Then, we propose a baseline Prompt-based Instruction Embedding (PIE) method to make the representations more attention on tasks. The evaluation of PIE, alongside other embedding methods on IEB with two designed tasks, demonstrates its superior performance in accurately identifying task categories. Moreover, the application of instruction embeddings in four downstream tasks showcases its effectiveness and suitability for instruction-related tasks.

Poster
A Swiss Army Knife for Heterogeneous Federated Learning: Flexible Coupling via Trace Norm

Tianchi Liao, Lele Fu, Jialong Chen, Zhen Wang, Zibin Zheng, Chuan Chen

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The heterogeneity issue in federated learning (FL) has attracted increasing attention, which is attempted to be addressed by most existing methods. Currently, due to systems and objectives heterogeneity, enabling clients to hold models of different architectures and tasks of different demands has become an important direction in FL. Most existing FL methods are based on the homogeneity assumption, namely, different clients have the same architectural models with the same tasks, which are unable to handle complex and multivariate data and tasks. To flexibly address these heterogeneity limitations, we propose a novel federated multi-task learning framework with the help of tensor trace norm, FedSAK. Specifically, it treats each client as a task and splits the local model into a feature extractor and a prediction head. Clients can flexibly choose shared structures based on heterogeneous situations and upload them to the server, which learns correlations among client models by mining model low-rank structures through tensor trace norm. Furthermore, we derive convergence and generalization bounds under non-convex settings. Evaluated on 6 real-world datasets compared to 13 advanced FL models, FedSAK demonstrates superior performance.

Poster
Handling Learnwares from Heterogeneous Feature Spaces with Explicit Label Exploitation

Peng Tan, Hai-Tian Liu, Zhi-Hao Tan, Zhi-Hua Zhou

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The learnware paradigm aims to help users leverage numerous existing high-performing models instead of starting from scratch, where a learnware consists of a well-trained model and the specification describing its capability. Numerous learnwares are accommodated by a learnware dock system. When users solve tasks with the system, models that fully match the task feature space are often rare or even unavailable. However, models with heterogeneous feature space can still be helpful. This paper finds that label information, particularly model outputs, is helpful yet previously less exploited in the accommodation of heterogeneous learnwares. We extend the specification to better leverage model pseudo-labels and subsequently enrich the unified embedding space for better specification evolvement. With label information, the learnware identification can also be improved by additionally comparing conditional distributions. Experiments demonstrate that, even without a model explicitly tailored to user tasks, the system can effectively handle tasks by leveraging models from diverse feature spaces.

Poster
InfoRM: Mitigating Reward Hacking in RLHF via Information-Theoretic Reward Modeling

Yuchun Miao, Sen Zhang, Liang Ding, Rong Bao, Lefei Zhang, Dacheng Tao

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Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models with human values, reward hacking, also termed reward overoptimization, remains a critical challenge. This issue primarily arises from reward misgeneralization, where reward models (RMs) compute reward using spurious features that are irrelevant to human preferences. In this work, we tackle this problem from an information-theoretic perspective and propose a framework for reward modeling, namely InfoRM, by introducing a variational information bottleneck objective to filter out irrelevant information. Notably, we further identify a correlation between overoptimization and outliers in the IB latent space of InfoRM, establishing it as a promising tool for detecting reward overoptimization. Inspired by this finding, we propose the Cluster Separation Index (CSI), which quantifies deviations in the IB latent space, as an indicator of reward overoptimization to facilitate the development of online mitigation strategies. Extensive experiments on a wide range of settings and RM scales (70M, 440M, 1.4B, and 7B) demonstrate the effectiveness of InfoRM. Further analyses reveal that InfoRM's overoptimization detection mechanism is not only effective but also robust across a broad range of datasets, signifying a notable advancement in the field of RLHF. The code will be released upon acceptance.

Poster
GS-Hider: Hiding Messages into 3D Gaussian Splatting

Xuanyu Zhang, Jiarui Meng, Runyi Li, Zhipei Xu, Yongbing Zhang, Jian Zhang

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3D Gaussian Splatting (3DGS) has already become the emerging research focus in the fields of 3D scene reconstruction and novel view synthesis. Given that training a 3DGS requires a significant amount of time and computational cost, it is crucial to protect the copyright, integrity, and privacy of such 3D assets. Steganography, as a crucial technique for encrypted transmission and copyright protection, has been extensively studied. However, it still lacks profound exploration targeted at 3DGS. Unlike its predecessor NeRF, 3DGS possesses two distinct features: 1) explicit 3D representation; and 2) real-time rendering speeds. These characteristics result in the 3DGS point cloud files being public and transparent, with each Gaussian point having a clear physical significance. Therefore, ensuring the security and fidelity of the original 3D scene while embedding information into the 3DGS point cloud files is an extremely challenging task. To solve the above-mentioned issue, we first propose a steganography framework for 3DGS, dubbed GS-Hider, which can embed 3D scenes and images into original GS point clouds in an invisible manner and accurately extract the hidden messages. Specifically, we design a coupled secured feature attribute to replace the original 3DGS's spherical harmonics coefficients and then use a scene decoder and a message decoder to disentangle the original RGB scene and the hidden message. Extensive experiments demonstrated that the proposed GS-Hider can effectively conceal multimodal messages without compromising rendering quality and possesses exceptional security, robustness, capacity, and flexibility. Our project is available at: https://xuanyuzhang21.github.io/project/gshider.

Poster
SimPO: Simple Preference Optimization with a Reference-Free Reward

Yu Meng, Mengzhou Xia, Danqi Chen

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Direct Preference Optimization (DPO) is a widely used offline preference optimization algorithm that reparameterizes reward functions in reinforcement learning from human feedback (RLHF) to enhance simplicity and training stability. In this work, we propose SimPO, a simpler yet more effective approach. The effectiveness of SimPO is attributed to a key design: using the _average_ log probability of a sequence as the implicit reward. This reward formulation better aligns with model generation and eliminates the need for a reference model, making it more compute and memory efficient. Additionally, we introduce a target reward margin to the Bradley-Terry objective to encourage a larger margin between the winning and losing responses, further improving the algorithm's performance. We compare SimPO to DPO and its latest variants across various state-of-the-art training setups, including both base and instruction-tuned models such as Mistral, Llama 3, and Gemma 2. We evaluate on extensive chat-based evaluation benchmarks, including AlpacaEval 2, MT-Bench, and Arena-Hard. Our results demonstrate that SimPO consistently and significantly outperforms existing approaches without substantially increasing response length. Specifically, SimPO outperforms DPO by up to 6.4 points on AlpacaEval 2 and by up to 7.5 points on Arena-Hard. Our top-performing model, built on Gemma-2-9B-it, achieves a 72.4\% length-controlled win rate on AlpacaEval 2, a 59.1\% win rate on Arena-Hard, and ranks 1st on Chatbot Arena among $<$10B models with real user votes.

Poster
Lexicon3D: Probing Visual Foundation Models for Complex 3D Scene Understanding

Yunze Man, Shuhong Zheng, Zhipeng Bao, Martial Hebert, Liangyan Gui, Yu-Xiong Wang

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Complex 3D scene understanding has gained increasing attention, with scene encoding strategies built on top of visual foundation models playing a crucial role in this success. However, the optimal scene encoding strategies for various scenarios remain unclear, particularly compared to their image-based counterparts. To address this issue, we present the first comprehensive study that probes various visual encoding models for 3D scene understanding, identifying the strengths and limitations of each model across different scenarios. Our evaluation spans seven vision foundation encoders, including image, video, and 3D foundation models. We evaluate these models in four tasks: Vision-Language Scene Reasoning, Visual Grounding, Segmentation, and Registration, each focusing on different aspects of scene understanding. Our evaluation yields key intriguing findings: Unsupervised image foundation models demonstrate superior overall performance, video models excel in object-level tasks, diffusion models benefit geometric tasks, language-pretrained models show unexpected limitations in language-related tasks, and the mixture-of-vision-expert (MoVE) strategy leads to consistent performance improvement. These insights challenge some conventional understandings, provide novel perspectives on leveraging visual foundation models, and highlight the need for more flexible encoder selection in future vision-language and scene understanding tasks.

Poster
Theoretical Foundations of Deep Selective State-Space Models

Nicola Muca Cirone, Antonio Orvieto, Benjamin Walker, Cristopher Salvi, Terry Lyons

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Structured state-space models (SSMs) are gaining popularity as effective foundational architectures for sequential data, demonstrating outstanding performance across a diverse set of domains alongside desirable scalability properties. Recent developments show that if the linear recurrence powering SSMs allows for a selectivity mechanism leveraging multiplicative interactions between inputs and hidden states (e.g. Mamba, GLA, Hawk/Griffin, HGRN2), then the resulting architecture can surpass attention-powered foundation models trained on text in both accuracy and efficiency, at scales of billion parameters. In this paper, we give theoretical grounding to the selectivity mechanism, often linked to in-context learning, using tools from Rough Path Theory. We provide a framework for the theoretical analysis of generalized selective SSMs, fully characterizing their expressive power and identifying the gating mechanism as the crucial architectural choice. Our analysis provides a closed-form description of the expressive powers of modern SSMs, such as Mamba, quantifying theoretically the drastic improvement in performance from the previous generation of models, such as S4. Our theory not only motivates the success of modern selective state-space models, but also provides a solid framework to understand the expressive power of future SSM variants. In particular, it suggests cross-channel interactions could play a vital role in future improvements.

Poster