ICLR 2025 论文列表

International Conference on Learning Representations

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3,703篇论文

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On the Optimization and Generalization of Two-layer Transformers with Sign Gradient Descent

Bingrui Li, Wei Huang, Andi Han, Zhanpeng Zhou, Taiji Suzuki, Jun Zhu, Jianfei Chen

展开摘要

The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it optimizes transformers remains a challenging task. Fortunately, Sign Gradient Descent (SignGD) serves as an effective surrogate for Adam. Despite its simplicity, theoretical understanding of how SignGD optimizes transformers still lags behind. In this work, we study how SignGD optimizes a two-layer transformer -- consisting of a softmax attention layer with trainable query-key parameterization followed by a linear layer -- on a linearly separable noisy dataset. We identify four stages in the training dynamics, each exhibiting intriguing behaviors. Based on the training dynamics, we prove the fast convergence but poor generalization of the learned transformer on the noisy dataset. We also show that Adam behaves similarly to SignGD in terms of both optimization and generalization in this setting. Additionally, we find that the poor generalization of SignGD is not solely due to data noise, suggesting that both SignGD and Adam requires high-quality data for real-world tasks. Finally, experiments on synthetic and real-world datasets empirically support our theoretical results.

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Towards a Unified and Verified Understanding of Group-Operation Networks

Wilson Wu, Louis Jaburi, Jacob Drori, Jason Gross

展开摘要

A recent line of work in mechanistic interpretability has focused on reverse-engineering the computation performed by neural networks trained on the binary operation of finite groups. We investigate the internals of one-hidden-layer neural networks trained on this task, revealing previously unidentified structure and producing a more complete description of such models in a step towards unifying the explanations of previous works (Chughtai et al., 2023; Stander et al., 2024). Notably, these models approximate equivariance in each input argument. We verify that our explanation applies to a large fraction of networks trained on this task by translating it into a compact proof of model performance, a quantitative evaluation of the extent to which we faithfully and concisely explain model internals. In the main text, we focus on the symmetric group S5. For models trained on this group, our explanation yields a guarantee of model accuracy that runs 3x faster than brute force and gives a >=95% accuracy bound for 45% of the models we trained. We were unable to obtain nontrivial non-vacuous accuracy bounds using only explanations from previous works.

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DenseMatcher: Learning 3D Semantic Correspondence for Category-Level Manipulation from a Single Demo

Junzhe Zhu, Yuanchen Ju, Junyi Zhang, Muhan Wang, Zhecheng Yuan, Kaizhe Hu, Huazhe Xu

展开摘要

Dense 3D correspondence can enhance robotic manipulation by enabling the generalization of spatial, functional, and dynamic information from one object to an unseen counterpart. Compared to shape correspondence, semantic correspondence is more effective in generalizing across different object categories. To this end, we present DenseMatcher, a method capable of computing 3D correspondences between in-the-wild objects that share similar structures. DenseMatcher first computes vertex features by projecting multiview 2D features onto meshes and refining them with a 3D network, and subsequently finds dense correspondences with the obtained features using functional map. In addition, we craft the first 3D matching dataset that contains colored object meshes across diverse categories. We demonstrate the downstream effectiveness of DenseMatcher in (i) robotic manipulation, where it achieves cross-instance and cross-category generalization on long-horizon complex manipulation tasks from observing only one demo; (ii) zero-shot color mapping between digital assets, where appearance can be transferred between different objects with relatable geometry. More details and demonstrations can be found at https://tea-lab.github.io/DenseMatcher/.

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Don't flatten, tokenize! Unlocking the key to SoftMoE's efficacy in deep RL

Ghada Sokar, Johan Samir Obando Ceron, Aaron Courville, Hugo Larochelle, Pablo Samuel Castro

展开摘要

The use of deep neural networks in reinforcement learning (RL) often suffers from performance degradation as model size increases. While soft mixtures of experts (SoftMoEs) have recently shown promise in mitigating this issue for online RL, the reasons behind their effectiveness remain largely unknown. In this work we provide an in-depth analysis identifying the key factors driving this performance gain. We discover the surprising result that tokenizing the encoder output, rather than the use of multiple experts, is what is behind the efficacy of SoftMoEs. Indeed, we demonstrate that even with an appropriately scaled single expert, we are able to maintain the performance gains, largely thanks to tokenization.

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Quality Measures for Dynamic Graph Generative Models

Ryien Hosseini, Filippo Simini, Venkatram Vishwanath, Rebecca Willett, Henry Hoffmann

展开摘要

Deep generative models have recently achieved significant success in modeling graph data, including dynamic graphs, where topology and features evolve over time. However, unlike in vision and natural language domains, evaluating generative models for dynamic graphs is challenging due to the difficulty of visualizing their output, making quantitative metrics essential. In this work, we develop a new quality metric for evaluating generative models of dynamic graphs. Current metrics for dynamic graphs typically involve discretizing the continuous-evolution of graphs into static snapshots and then applying conventional graph similarity measures. This approach has several limitations: (a) it models temporally related events as i.i.d. samples, failing to capture the non-uniform evolution of dynamic graphs; (b) it lacks a unified measure that is sensitive to both features and topology; (c) it fails to provide a scalar metric, requiring multiple metrics without clear superiority; and (d) it requires explicitly instantiating each static snapshot, leading to impractical runtime demands that hinder evaluation at scale. We propose a novel metric based on the Johnson-Lindenstrauss lemma, applying random projections directly to dynamic graph data. This results in an expressive, scalar, and application-agnostic measure of dynamic graph similarity that overcomes the limitations of traditional methods. We also provide a comprehensive empirical evaluation of metrics for continuous-time dynamic graphs, demonstrating the effectiveness of our approach compared to existing methods. Our implementation is available at https://github.com/ryienh/jl-metric.

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Direct Post-Training Preference Alignment for Multi-Agent Motion Generation Model Using Implicit Feedback from Pre-training Demonstrations

Thomas Tian, Kratarth Goel

展开摘要

Recent advancements in Large Language Models (LLMs) have revolutionized motion generation models in embodied applications such as autonomous driving and robotic manipulation. While LLM-type auto-regressive motion generation models benefit from training scalability, there remains a discrepancy between their token prediction objectives and human preferences. As a result, models pre-trained solely with token-prediction objectives often generate behaviors that deviate from what humans would prefer, making post-training preference alignment crucial for producing human-preferred motions. Unfortunately, post-training alignment requires extensive preference rankings of motions generated by the pre-trained model, which are costly and time-consuming to annotate, especially in multi-agent motion generation settings. Recently, there has been growing interest in leveraging expert demonstrations previously used during pre-training to scalably generate preference data for post-training alignment. However, these methods often adopt an adversarial assumption, treating all pre-trained model-generated samples as unpreferred examples and relying solely on pre-training expert demonstrations to construct preferred examples. This adversarial approach overlooks the valuable signal provided by preference rankings among the model's own generations, ultimately reducing alignment effectiveness and potentially leading to misaligned behaviors. In this work, instead of treating all generated samples as equally bad, we propose a principled approach that leverages implicit preferences encoded in pre-training expert demonstrations to construct preference rankings among the pre-trained model's generations, offering more nuanced preference alignment guidance with zero human cost. We apply our approach to large-scale traffic simulation (more than 100 agents) and demonstrate its effectiveness in improving the realism of pre-trained model's generated behaviors, making a lightweight 1M motion generation model comparable to state-of-the-art large imitation-based models by relying solely on implicit feedback from pre-training demonstrations, without requiring additional post-training human preference annotations or incurring high computational costs. Furthermore, we provide an in-depth analysis of preference data scaling laws and their effects on over-optimization, offering valuable insights for future studies.

Spotlight
Better Instruction-Following Through Minimum Bayes Risk

Ian Wu, Patrick Fernandes, Amanda Bertsch, Seungone Kim, Sina Khoshfetrat Pakazad, Graham Neubig

展开摘要

General-purpose LLM judges capable of human-level evaluation provide not only a scalable and accurate way of evaluating instruction-following LLMs but also new avenues for supervising and improving their performance. One promising way of leveraging LLM judges for supervision is through Minimum Bayes Risk (MBR) decoding, which uses a reference-based evaluator to select a high-quality output from amongst a set of candidate outputs. In the first part of this work, we explore using MBR decoding as a method for improving the test-time performance of instruction-following LLMs. We find that MBR decoding with reference-based LLM judges substantially improves over greedy decoding, best-of-N decoding with reference-free judges and MBR decoding with lexical and embedding-based metrics on AlpacaEval and MT-Bench. These gains are consistent across LLMs with up to 70B parameters, demonstrating that smaller LLM judges can be used to supervise much larger LLMs. Then, seeking to retain the improvements from MBR decoding while mitigating additional test-time costs, we explore iterative self-training on MBR-decoded outputs. We find that self-training using Direct Preference Optimisation leads to significant performance gains, such that the self-trained models with greedy decoding generally match and sometimes exceed the performance of their base models with MBR decoding.

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LiFT: Learning to Fine-Tune via Bayesian Parameter Efficient Meta Fine-Tuning

Minyoung Kim, Timothy Hospedales

展开摘要

We tackle the problem of parameter-efficient fine-tuning (PEFT) of a pre-trained large deep model on many different but related tasks. Instead of the simple but strong baseline strategy of task-wise independent fine-tuning, we aim to meta-learn the core shared information that can be used for unseen test tasks to improve the prediction performance further. That is, we propose a method for {\em learning-to-fine-tune} (LiFT). LiFT introduces a novel hierarchical Bayesian model that can be superior to both existing general meta learning algorithms like MAML and recent LoRA zoo mixing approaches such as LoRA-Retriever and model-based clustering. In our Bayesian model, the parameters of the task-specific LoRA modules are regarded as random variables where these task-wise LoRA modules are governed/regularized by higher-level latent random variables, which represents the prior of the LoRA modules that capture the shared information across all training tasks. To make the posterior inference feasible, we propose a novel SGLD-Gibbs sampling algorithm that is computationally efficient. To represent the posterior samples from the SGLD-Gibbs, we propose an online EM algorithm that maintains a Gaussian mixture representation for the posterior in an online manner in the course of iterative posterior sampling. We demonstrate the effectiveness of LiFT on NLP and vision multi-task meta learning benchmarks.

Spotlight
Theory on Mixture-of-Experts in Continual Learning

Hongbo Li, Sen Lin, Lingjie Duan, Yingbin Liang, Ness Shroff

展开摘要

Continual learning (CL) has garnered significant attention because of its ability to adapt to new tasks that arrive over time. Catastrophic forgetting (of old tasks) has been identified as a major issue in CL, as the model adapts to new tasks. The Mixture-of-Experts (MoE) model has recently been shown to effectively mitigate catastrophic forgetting in CL, by employing a gating network to sparsify and distribute diverse tasks among multiple experts. However, there is a lack of theoretical analysis of MoE and its impact on the learning performance in CL. This paper provides the first theoretical results to characterize the impact of MoE in CL via the lens of overparameterized linear regression tasks. We establish the benefit of MoE over a single expert by proving that the MoE model can diversify its experts to specialize in different tasks, while its router learns to select the right expert for each task and balance the loads across all experts. Our study further suggests an intriguing fact that the MoE in CL needs to terminate the update of the gating network after sufficient training rounds to attain system convergence, which is not needed in the existing MoE studies that do not consider the continual task arrival. Furthermore, we provide explicit expressions for the expected forgetting and overall generalization error to characterize the benefit of MoE in the learning performance in CL. Interestingly, adding more experts requires additional rounds before convergence, which may not enhance the learning performance. Finally, we conduct experiments on both synthetic and real datasets to extend these insights from linear models to deep neural networks (DNNs), which also shed light on the practical algorithm design for MoE in CL.

Spotlight
Simplifying Deep Temporal Difference Learning

Matteo Gallici, Mattie Fellows, Benjamin Ellis, Bartomeu Pou, Ivan Masmitja, Jakob Nicolaus Foerster, Mario Martin

展开摘要

$Q$-learning played a foundational role in the field reinforcement learning (RL). However, TD algorithms with off-policy data, such as $Q$-learning, or nonlinear function approximation like deep neural networks require several additional tricks to stabilise training, primarily a large replay buffer and target networks. Unfortunately, the delayed updating of frozen network parameters in the target network harms the sample efficiency and, similarly, the large replay buffer introduces memory and implementation overheads. In this paper, we investigate whether it is possible to accelerate and simplify off-policy TD training while maintaining its stability. Our key theoretical result demonstrates for the first time that regularisation techniques such as LayerNorm can yield provably convergent TD algorithms without the need for a target network or replay buffer, even with off-policy data. Empirically, we find that online, parallelised sampling enabled by vectorised environments stabilises training without the need for a large replay buffer. Motivated by these findings, we propose PQN, our simplified deep online $Q$-Learning algorithm. Surprisingly, this simple algorithm is competitive with more complex methods like: Rainbow in Atari, PPO-RNN in Craftax, QMix in Smax, and can be up to 50x faster than traditional DQN without sacrificing sample efficiency. In an era where PPO has become the go-to RL algorithm, PQN reestablishes off-policy $Q$-learning as a viable alternative.

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What Makes a Good Diffusion Planner for Decision Making?

Haofei Lu, Dongqi Han, Yifei Shen, Dongsheng Li

展开摘要

Diffusion models have recently shown significant potential in solving decision-making problems, particularly in generating behavior plans -- also known as diffusion planning. While numerous studies have demonstrated the impressive performance of diffusion planning, the mechanisms behind the key components of a good diffusion planner remain unclear and the design choices are highly inconsistent in existing studies. In this work, we address this issue through systematic empirical experiments on diffusion planning in an offline reinforcement learning (RL) setting, providing practical insights into the essential components of diffusion planning. We trained and evaluated over 6,000 diffusion models, identifying the critical components such as guided sampling, network architecture, action generation and planning strategy. We revealed that some design choices opposite to the common practice in previous work in diffusion planning actually lead to better performance, e.g., unconditional sampling with selection can be better than guided sampling and Transformer outperforms U-Net as denoising network. Based on these insights, we suggest a simple yet strong diffusion planning baseline that achieves state-of-the-art results on standard offline RL benchmarks. Code: https://github.com/Josh00-Lu/DiffusionVeteran.

Spotlight
Graph Sparsification via Mixture of Graphs

Guibin Zhang, Xiangguo Sun, Yanwei Yue, Chonghe Jiang, Kun Wang, Tianlong Chen, Shirui Pan

展开摘要

Graph Neural Networks (GNNs) have demonstrated superior performance across various graph learning tasks but face significant computational challenges when applied to large-scale graphs. One effective approach to mitigate these challenges is graph sparsification, which involves removing non-essential edges to reduce computational overhead. However, previous graph sparsification methods often rely on a single global sparsity setting and uniform pruning criteria, failing to provide customized sparsification schemes for each node's complex local context. In this paper, we introduce Mixture-of-Graphs (MoG), leveraging the concept of Mixture-of-Experts (MoE), to dynamically select tailored pruning solutions for each node. Specifically, MoG incorporates multiple sparsifier experts, each characterized by unique sparsity levels and pruning criteria, and selects the appropriate experts for each node. Subsequently, MoG performs a mixture of the sparse graphs produced by different experts on the Grassmann manifold to derive an optimal sparse graph. One notable property of MoG is its entirely local nature, as it depends on the specific circumstances of each individual node. Extensive experiments on four large-scale OGB datasets and two superpixel datasets, equipped with five GNN backbones, demonstrate that MoG (I) identifies subgraphs at higher sparsity levels ($8.67\\%\sim 50.85\\%$), with performance equal to or better than the dense graph, (II) achieves $1.47-2.62\times$ speedup in GNN inference with negligible performance drop, and (III) boosts ``top-student'' GNN performance ($1.02\\%\uparrow$ on RevGNN+\textsc{ogbn-proteins} and $1.74\\%\\uparrow$ on DeeperGCN+\textsc{ogbg-ppa}). The source code is available at \url{https://github.com/yanweiyue/MoG}.

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When Attention Sink Emerges in Language Models: An Empirical View

Xiangming Gu, Tianyu Pang, Chao Du, Qian Liu, Fengzhuo Zhang, Cunxiao Du, Ye Wang, Min Lin

展开摘要

Auto-regressive language Models (LMs) assign significant attention to the first token, even if it is not semantically important, which is known as **attention sink**. This phenomenon has been widely adopted in applications such as streaming/long context generation, KV cache optimization, inference acceleration, model quantization, and others. Despite its widespread use, a deep understanding of attention sink in LMs is still lacking. In this work, we first demonstrate that attention sinks exist universally in auto-regressive LMs with various inputs, even in small models. Furthermore, attention sink is observed to emerge during the LM pre-training, motivating us to investigate how *optimization*, *data distribution*, *loss function*, and *model architecture* in LM pre-training influence its emergence. We highlight that attention sink emerges after effective optimization on sufficient training data. The sink position is highly correlated with the loss function and data distribution. Most importantly, we find that attention sink acts more like key biases, *storing extra attention scores*, which could be non-informative and not contribute to the value computation. We also observe that this phenomenon (at least partially) stems from tokens' inner dependence on attention scores as a result of softmax normalization. After relaxing such dependence by replacing softmax attention with other attention operations, such as sigmoid attention without normalization, attention sinks do not emerge in LMs up to 1B parameters. The code is available at https://github.com/sail-sg/Attention-Sink.

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TabWak: A Watermark for Tabular Diffusion Models

Chaoyi Zhu, Jiayi Tang, Jeroen M. Galjaard, Pin-Yu Chen, Robert Birke, Cornelis Bos, Lydia Y. Chen

展开摘要

Synthetic data offers alternatives for data augmentation and sharing. Till date, it remains unknown how to use watermarking techniques to trace and audit synthetic tables generated by tabular diffusion models to mitigate potential misuses. In this paper, we design TabWak, the first watermarking method to embed invisible signatures that control the sampling of Gaussian latent codes used to synthesize table rows via the diffusion backbone. TabWak has two key features. Different from existing image watermarking techniques, TabWak uses self-cloning and shuffling to embed the secret key in positional information of random seeds that control the Gaussian latents, allowing to use different seeds at each row for high inter-row diversity and enabling row-wise detectability. To further boost the robustness of watermark detection against post-editing attacks, TabWak uses a valid-bit mechanism that focuses on the tail of the latent code distribution for superior noise resilience. We provide theoretical guarantees on the row diversity and effectiveness of detectability. We evaluate TabWak on five datasets against baselines to show that the quality of watermarked tables remains nearly indistinguishable from non-watermarked tables while achieving high detectability in the presence of strong post-editing attacks, with a 100% true positive rate at a 0.1% false positive rate on synthetic tables with fewer than 300 rows. Our code is available at the following anonymized repository https://github.com/chaoyitud/TabWak.

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Gap-Dependent Bounds for Q-Learning using Reference-Advantage Decomposition

Zhong Zheng, Haochen Zhang, Lingzhou Xue

展开摘要

We study the gap-dependent bounds of two important algorithms for on-policy $Q$-learning for finite-horizon episodic tabular Markov Decision Processes (MDPs): UCB-Advantage (Zhang et al. 2020) and Q-EarlySettled-Advantage (Li et al. 2021). UCB-Advantage and Q-EarlySettled-Advantage improve upon the results based on Hoeffding-type bonuses and achieve the {almost optimal} $\sqrt{T}$-type regret bound in the worst-case scenario, where $T$ is the total number of steps. However, the benign structures of the MDPs such as a strictly positive suboptimality gap can significantly improve the regret. While gap-dependent regret bounds have been obtained for $Q$-learning with Hoeffding-type bonuses, it remains an open question to establish gap-dependent regret bounds for $Q$-learning using variance estimators in their bonuses and reference-advantage decomposition for variance reduction. We develop a novel error decomposition framework to prove gap-dependent regret bounds of UCB-Advantage and Q-EarlySettled-Advantage that are logarithmic in $T$ and improve upon existing ones for $Q$-learning algorithms. Moreover, we establish the gap-dependent bound for the policy switching cost of UCB-Advantage and improve that under the worst-case MDPs. To our knowledge, this paper presents the first gap-dependent regret analysis for $Q$-learning using variance estimators and reference-advantage decomposition and also provides the first gap-dependent analysis on policy switching cost for $Q$-learning.

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MAD-TD: Model-Augmented Data stabilizes High Update Ratio RL

Claas A Voelcker, Marcel Hussing, ERIC EATON, Amir-massoud Farahmand, Igor Gilitschenski

展开摘要

Building deep reinforcement learning (RL) agents that find a good policy with few samples has proven notoriously challenging. To achieve sample efficiency, recent work has explored updating neural networks with large numbers of gradient steps for every new sample. While such high update-to-data (UTD) ratios have shown strong empirical performance, they also introduce instability to the training process. Previous approaches need to rely on periodic neural network parameter resets to address this instability, but restarting the training process is infeasible in many real-world applications and requires tuning the resetting interval. In this paper, we focus on one of the core difficulties of stable training with limited samples: the inability of learned value functions to generalize to unobserved on-policy actions. We mitigate this issue directly by augmenting the off-policy RL training process with a small amount of data generated from a learned world model. Our method, Model-Augmented Data for TD Learning (MAD-TD) uses small amounts of generated data to stabilize high UTD training and achieve competitive performance on the most challenging tasks in the DeepMind control suite. Our experiments further highlight the importance of employing a good model to generate data, MAD-TD's ability to combat value overestimation, and its practical stability gains for continued learning.

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Answer, Assemble, Ace: Understanding How LMs Answer Multiple Choice Questions

Sarah Wiegreffe, Oyvind Tafjord, Yonatan Belinkov, Hannaneh Hajishirzi, Ashish Sabharwal

展开摘要

Multiple-choice question answering (MCQA) is a key competence of performant transformer language models that is tested by mainstream benchmarks. However, recent evidence shows that models can have quite a range of performance, particularly when the task format is diversified slightly (such as by shuffling answer choice order). In this work we ask: how do successful models perform formatted MCQA? We employ vocabulary projection and activation patching methods to localize key hidden states that encode relevant information for predicting the correct answer. We find that prediction of a specific answer symbol is causally attributed to a few middle layers, and specifically their multi-head self-attention mechanisms. We show that subsequent layers increase the probability of the predicted answer symbol in vocabulary space, and that this probability increase is associated with a sparse set of attention heads with unique roles. We additionally uncover differences in how different models adjust to alternative symbols. Finally, we demonstrate that a synthetic task can disentangle sources of model error to pinpoint when a model has learned formatted MCQA, and show that logit differences between answer choice tokens continue to grow over the course of training.

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Scaling up the Banded Matrix Factorization Mechanism for Large Scale Differentially Private ML

Ryan McKenna

展开摘要

Correlated noise mechanisms such as DP Matrix Factorization (DP-MF) have proven to be effective alternatives to DP-SGD in large-epsilon few-epoch training regimes. Significant work has been done to find the best correlated noise strategies, and the current state-of-the-art approach is DP-BandMF , which optimally balances the benefits of privacy amplification and noise correlation. Despite it's utility advantages, severe scalability limitations prevent this mechanism from handling large-scale training scenarios where the number of training iterations may be more than $10^4$ and the number of model parameters may exceed $10^7$. In this work, we present techniques to scale up DP-BandMF along these two dimensions, significantly extending it's reach and enabling it to effectively handle settings with over $10^6$ training iterations and $10^9$ model parameters, with no utility degradation at smaller scales.

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BlendRL: A Framework for Merging Symbolic and Neural Policy Learning

Hikaru Shindo, Quentin Delfosse, Devendra Singh Dhami, Kristian Kersting

展开摘要

Humans can leverage both symbolic reasoning and intuitive responses. In contrast, reinforcement learning policies are typically encoded in either opaque systems like neural networks or symbolic systems that rely on predefined symbols and rules. This disjointed approach severely limits the agents’ capabilities, as they often lack either the flexible low-level reaction characteristic of neural agents or the interpretable reasoning of symbolic agents. To overcome this challenge, we introduce *BlendRL*, a neuro-symbolic RL framework that harmoniously integrates both paradigms. We empirically demonstrate that BlendRL agents outperform both neural and symbolic baselines in standard Atari environments, and showcase their robustness to environmental changes. Additionally, we analyze the interaction between neural and symbolic policies, illustrating how their hybrid use helps agents overcome each other's limitations.

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COPER: Correlation-based Permutations for Multi-View Clustering

Ran Eisenberg, Jonathan Svirsky, Ofir Lindenbaum

展开摘要

Combining data from different sources can improve data analysis tasks such as clustering. However, most of the current multi-view clustering methods are limited to specific domains or rely on a suboptimal and computationally intensive two-stage process of representation learning and clustering. We propose an end-to-end deep learning-based multi-view clustering framework for general data types (such as images and tables). Our approach involves generating meaningful fused representations using a novel permutation-based canonical correlation objective. We provide a theoretical analysis showing how the learned embeddings approximate those obtained by supervised linear discriminant analysis (LDA). Cluster assignments are learned by identifying consistent pseudo-labels across multiple views. Additionally, we establish a theoretical bound on the error caused by incorrect pseudo-labels in the unsupervised representations compared to LDA. Extensive experiments on ten multi-view clustering benchmark datasets provide empirical evidence for the effectiveness of the proposed model.

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