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The study of rigid protein-protein docking plays an essential role in a variety of tasks such as drug design and protein engineering. Recently, several learning-based methods have been proposed for the task, exhibiting much faster docking speed than those computational methods. In this paper, we propose a novel learning-based method called ElliDock, which predicts an elliptic paraboloid to represent the protein-protein docking interface. To be specific, our model estimates elliptic paraboloid interfaces for the two input proteins respectively, and obtains the roto-translation transformation for docking by making two interfaces coincide. By its design, ElliDock is independently equivariant with respect to arbitrary rotations/translations of the proteins, which is an indispensable property to ensure the generalization of the docking process. Experimental evaluations show that ElliDock achieves the fastest inference time among all compared methods, and outperforms state-of-the-art learning-based methods, like DiffDock-PP and Alphafold-Multimer, for particularly antibody-antigen docking.

Discussion and debate among Large Language Models (LLMs) have gained considerable attention due to their potential to enhance the reasoning ability of LLMs. Although natural language is an obvious choice for communication due to LLM's language understanding capability, the token sampling step needed when generating natural language poses a potential risk of information loss, as it uses only one token to represent the model's belief across the entire vocabulary. In this paper, we introduce a communication regime named CIPHER (Communicative Inter-Model Protocol Through Embedding Representation) to address this issue. Specifically, we remove the token sampling step from LLMs and let them communicate their beliefs across the vocabulary through the expectation of the raw transformer output embeddings. Remarkably, by deviating from natural language, CIPHER offers an advantage of encoding a broader spectrum of information without any modification to the model weights, outperforming the state-of-the-art LLM debate methods using natural language by 0.5-5.0% across five reasoning tasks and multiple open-source LLMs of varying sizes. This showcases the superiority and robustness of embeddings as an alternative "language" for communication among LLMs. We anticipate that CIPHER will inspire further exploration for the design of interactions within LLM agent systems, offering a new direction that could significantly influence future developments in the field.

In this work, we propose a novel link prediction model and further boost it by studying graph incompleteness. First, We introduce MPNN-then-SF, an innovative architecture leveraging structural feature (SF) to guide MPNN's representation pooling, with its implementation, namely Neural Common Neighbor (NCN). NCN exhibits superior expressiveness and scalability compared with existing models, which can be classified into two categories: SF-then-MPNN, augmenting MPNN's input with SF, and SF-and-MPNN, decoupling SF and MPNN. Second, we investigate the impact of graph incompleteness---the phenomenon that some links are unobserved in the input graph---on SF, like the common neighbor. Through dataset visualization, we observe that incompleteness reduces common neighbors and induces distribution shifts, significantly affecting model performance. To address this issue, we propose to use a link prediction model to complete the common neighbor structure. Combining this method with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins, and NCNC further surpasses state-of-the-art models in standard link prediction benchmarks.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals. Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression. To preserve the ordering of the continuous-output space, we design a new loss function and present necessary modifications to the CP classification techniques. Empirical results on many benchmarks show that this simple approach gives surprisingly good results on many practical problems.

Transductive node prediction has been a popular learning setting in Graph Neural Networks (GNNs). It has been widely observed that the shortage of information flow between the distant nodes and intra-batch nodes (for large-scale graphs) often hurt the generalization of GNNs which overwhelmingly adopt message-passing. Yet there is still no formal and direct theoretical results to quantitatively capture the underlying mechanism, despite the recent advance in both theoretical and empirical studies for GNN's generalization ability. In this paper, the $L$-hop interplay (i.e., message passing capability with training nodes) for a $L$-layer GNN is successfully incorporated in our derived PAC-Bayesian bound for GNNs in the semi-supervised transductive setting. In other words, we quantitatively show how the interplay between training and testing sets influence the generalization ability which also partly explains the effectiveness of some existing empirical methods for enhancing generalization. Based on this result, we further design a plug-and-play ***Graph** **G**lobal **W**orkspace* module for GNNs (InterpGNN-GW) to enhance the interplay, utilizing the key-value attention mechanism to summarize crucial nodes' embeddings into memory and broadcast the memory to all nodes, in contrast to the pairwise attention scheme in previous graph transformers. Extensive experiments on both small-scale and large-scale graph datasets validate the effectiveness of our theory and approaches.

In many text-generation problems, users may prefer not only a single response, but a diverse range of high-quality outputs from which to choose. Quality-diversity (QD) search algorithms aim at such outcomes, by continually improving and diversifying a population of candidates. However, the applicability of QD to qualitative domains, like creative writing, has been limited by the difficulty of algorithmically specifying measures of quality and diversity. Interestingly, recent developments in language models (LMs) have enabled guiding search through \emph{AI feedback}, wherein LMs are prompted in natural language to evaluate qualitative aspects of text. Leveraging this development, we introduce Quality-Diversity through AI Feedback (QDAIF), wherein an evolutionary algorithm applies LMs to both generate variation and evaluate the quality and diversity of candidate text. When assessed on creative writing domains, QDAIF covers more of a specified search space with high-quality samples than do non-QD controls. Further, human evaluation of QDAIF-generated creative texts validates reasonable agreement between AI and human evaluation. Our results thus highlight the potential of AI feedback to guide open-ended search for creative and original solutions, providing a recipe that seemingly generalizes to many domains and modalities. In this way, QDAIF is a step towards AI systems that can independently search, diversify, evaluate, and improve, which are among the core skills underlying human society's capacity for innovation.

Supervised learning methods have been found to exhibit inductive biases favoring simpler features. When such features are spuriously correlated with the label, this can result in suboptimal performance on minority subgroups. Despite the growing popularity of methods which learn from unlabeled data, the extent to which these representations rely on spurious features for prediction is unclear. In this work, we explore the impact of spurious features on Self-Supervised Learning (SSL) for visual representation learning. We first empirically show that commonly used augmentations in SSL can cause undesired invariances in the image space, and illustrate this with a simple example. We further show that classical approaches in combating spurious correlations, such as dataset re-sampling during SSL, do not consistently lead to invariant representations. Motivated by these findings, we propose LateTVG to remove spurious information from these representations during pre-training, by regularizing later layers of the encoder via pruning. We find that our method produces representations which outperform the baselines on several benchmarks, without the need for group or label information during SSL.

Transformers are ubiquitous in wide tasks. Interpreting their internals is a pivotal goal. Nevertheless, their particular components, feed-forward (FF) blocks, have typically been less analyzed despite their substantial parameter amounts. We analyze the input contextualization effects of FF blocks by rendering them in the attention maps as a human-friendly visualization scheme. Our experiments with both masked- and causal-language models reveal that FF networks modify the input contextualization to emphasize specific types of linguistic compositions. In addition, FF and its surrounding components tend to cancel out each other's effects, suggesting potential redundancy in the processing of the Transformer layer.

Equilibrium propagation (EP) is a compelling alternative to the back propagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to yield unbiased gradient estimates. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry contributes to bias is unknown because, in practice, its contribution may be masked by a finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that bias due to finite nudge can be avoided by estimating exact derivatives via a Cauchy integral. In contrast, weight asymmetry induces residual bias through poor alignment of EP's neuronal error vectors compared to BP resulting in low task performance. To mitigate the latter issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32$\times$32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Ampère equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.

Based on the theory of homogeneous spaces we derive *geometrically optimal edge attributes* to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions $\mathbb{R}^3$, position and orientations $\mathbb{R}^3 {\times} S^2$, and the group $SE(3)$ itself. Among these, $\mathbb{R}^3 {\times} S^2$ is an optimal choice due to the ability to represent directional information, which $\mathbb{R}^3$ methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full $SE(3)$ group. We support this claim with state-of-the-art results —in accuracy and speed— on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models. *Code available at [https://github.com/ebekkers/ponita](https://github.com/ebekkers/ponita)*

Aligning large language models (LLMs) with human values and intents critically involves the use of human or AI feedback. While dense feedback annotations are expensive to acquire and integrate, sparse feedback presents a structural design choice between ratings (e.g., score Response A on a scale of 1-7) and rankings (e.g., is Response A better than Response B?). In this work, we analyze the effect of this design choice for the alignment and evaluation of LLMs. We uncover an inconsistency problem wherein the preferences inferred from ratings and rankings significantly disagree 60% for both human and AI annotators. Our subsequent analysis identifies various facets of annotator biases that explain this phenomena such as human annotators would rate denser responses higher while preferring accuracy during pairwise judgments, for a particular comparison instance. To our surprise, we observe that the choice of feedback protocol has a significant effect on the evaluation of aligned LLMs. In particular, we find that LLMs that leverage rankings data for alignment (say model X) are preferred over those that leverage ratings data (say model Y), with a rank-based evaluation protocol (is X/Y's response better than reference response?) but not with a rating-based evaluation protocol (score Rank X/Y's response on a scale of 1-7). Our findings thus shed light on critical gaps in methods for evaluating the real-world utility of language models and their strong dependence on the feedback protocol used for alignment. Our code and data are available at \url{https://github.com/Hritikbansal/sparse_feedback}.

Most recent work in goal oriented visual navigation resorts to large-scale machine learning in simulated environments. The main challenge lies in learning compact representations generalizable to unseen environments and in learning high-capacity perception modules capable of reasoning on high-dimensional input. The latter is particularly difficult when the goal is not given as a category ("ObjectNav") but as an exemplar image ("ImageNav"), as the perception module needs to learn a comparison strategy requiring to solve an underlying visual correspondence problem. This has been shown to be difficult from reward alone or with standard auxiliary tasks. We address this problem through a sequence of two pretext tasks, which serve as a prior for what we argue is one of the main bottleneck in perception, extremely wide-baseline relative pose estimation and visibility prediction in complex scenes. The first pretext task, cross-view completion is a proxy for the underlying visual correspondence problem, while the second task addresses goal detection and finding directly. We propose a new dual encoder with a large-capacity binocular ViT model and show that correspondence solutions naturally emerge from the training signals. Experiments show significant improvements and SOTA performance on the two benchmarks, ImageNav and the Instance-ImageNav variant, where camera intrinsics and height differ between observation and goal.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies improve the overall GNNs' LP performance, none have explored their varying performance across different nodes and the underlying reasons. To this end, we demystify which nodes perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit worse LP performance, we surprisingly observe an inconsistent performance trend. This prompts us to propose a node-level metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC correlates with LP performance more than other node-level topological metrics, better identifying low-performing nodes than using degree. With TC, we discover a novel topological distribution shift issue in which nodes' newly joined neighbors tend to become less interactive with their existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and justify its efficacy in approximating TC with reduced computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

The transferability of deep neural networks (DNNs) has made significant progress in image and language processing. However, due to the heterogeneity among tables, such DNN bonus is still far from being well exploited on tabular data prediction (e.g., regression or classification tasks). Condensing knowledge from diverse domains, language models (LMs) possess the capability to comprehend feature names from various tables, potentially serving as versatile learners in transferring knowledge across distinct tables and diverse prediction tasks, but their discrete text representation space is inherently incompatible with numerical feature values in tables. In this paper, we present TP-BERTa, a specifically pre-trained LM for tabular data prediction. Concretely, a novel relative magnitude tokenization converts scalar numerical feature values to finely discrete, high-dimensional tokens, and an intra-feature attention approach integrates feature values with the corresponding feature names. Comprehensive experiments demonstrate that our pre-trained TP-BERTa leads the performance among tabular DNNs and is competitive with Gradient Boosted Decision Tree models in typical tabular data regime.

With the continuous advancement of neural network methodologies, time series prediction has attracted substantial interest over the past decades. Nonetheless, the interpretability of neural networks is insufficient and the utilization of deep learning techniques for prediction necessitates significant computational expenditures, rendering its application arduous in numerous scenarios. In order to tackle this challenge, an interpretable sparse system identification method which does not require a time-consuming training through back-propagation is proposed in this study. This method integrates advantages from both knowledge-based and data-driven approaches, and constructs dictionary functions by leveraging Fourier basis and taking into account both the long-term trends and the short-term fluctuations behind data. By using the $l_1$ norm for sparse optimization, prediction results can be gained with an explicit sparse expression function and an extremely high accuracy. The performance evaluation of the proposed method is conducted on comprehensive benchmark datasets, including ETT, Exchange, and ILI. Results reveal that our proposed method attains a significant overall improvement of more than 20\% in accordance with the most recent state-of-the-art deep learning methodologies. Additionally, our method demonstrates the efficient training capability on only CPUs. Therefore, this study may shed some light onto the realm of time series reconstruction and prediction.

Multitask Reinforcement Learning (MTRL) approaches have gained increasing attention for its wide applications in many important Reinforcement Learning (RL) tasks. However, while recent advancements in MTRL theory have focused on the improved statistical efficiency by assuming a shared structure across tasks, exploration--a crucial aspect of RL--has been largely overlooked. This paper addresses this gap by showing that when an agent is trained on a sufficiently diverse set of tasks, a generic policy-sharing algorithm with myopic exploration design like $\epsilon$-greedy that are inefficient in general can be sample-efficient for MTRL. To the best of our knowledge, this is the first theoretical demonstration of the "exploration benefits" of MTRL. It may also shed light on the enigmatic success of the wide applications of myopic exploration in practice. To validate the role of diversity, we conduct experiments on synthetic robotic control environments, where the diverse task set aligns with the task selection by automatic curriculum learning, which is empirically shown to improve sample-efficiency.

While Graph Neural Networks (GNNs) have achieved remarkable performance on various machine learning tasks on graph data, they also raised questions regarding their transparency and interpretability. Recently, there have been extensive research efforts to explain the decision-making process of GNNs. These efforts often focus on explaining why a certain prediction is made for a particular instance, or what discriminative features the GNNs try to detect for each class. However, to the best of our knowledge, there is no existing study on understanding the decision boundaries of GNNs, even though the decision-making process of GNNs is directly determined by the decision boundaries. To bridge this research gap, we propose a model-level explainability method called GNNBoundary, which attempts to gain deeper insights into the decision boundaries of graph classifiers. Specifically, we first develop an algorithm to identify the pairs of classes whose decision regions are adjacent. For an adjacent class pair, the near-boundary graphs between them are effectively generated by optimizing a novel objective function specifically designed for boundary graph generation. Thus, by analyzing the nearboundary graphs, the important characteristics of decision boundaries can be uncovered. To evaluate the efficacy of GNNBoundary, we conduct experiments on both synthetic and public real-world datasets. The results demonstrate that, via the analysis of faithful near-boundary graphs generated by GNNBoundary, we can thoroughly assess the robustness and generalizability of the explained GNNs. The official implementation can be found at https://github.com/yolandalalala/GNNBoundary.

Numerous explainability methods have been proposed to shed light on the inner workings of GNNs. Despite the inclusion of empirical evaluations in all the proposed algorithms, the interrogative aspects of these evaluations lack diversity. As a result, various facets of explainability pertaining to GNNs, such as a comparative analysis of counterfactual reasoners, their stability to variational factors such as different GNN architectures, noise, stochasticity in non-convex loss surfaces, feasibility amidst domain constraints, and so forth, have yet to be formally investigated. Motivated by this need, we present a benchmarking study on perturbation-based explainability methods for GNNs, aiming to systematically evaluate and compare a wide range of explainability techniques. Among the key findings of our study, we identify the Pareto-optimal methods that exhibit superior efficacy and stability in the presence of noise. Nonetheless, our study reveals that all algorithms are affected by stability issues when faced with noisy data. Furthermore, we have established that the current generation of counterfactual explainers often fails to provide feasible recourses due to violations of topological constraints encoded by domain-specific considerations. Overall, this benchmarking study empowers stakeholders in the field of GNNs with a comprehensive understanding of the state-of-the-art explainability methods, potential research problems for further enhancement, and the implications of their application in real-world scenarios.

Machine learning models are often used to decide who receives a loan, a job interview, or a public benefit. Models in such settings use features without considering their *actionability*. As a result, they can assign predictions that are \emph{fixed} -- meaning that individuals who are denied loans and interviews are, in fact, *precluded from access* to credit and employment. In this work, we introduce a procedure called *recourse verification* to test if a model assigns fixed predictions to its decision subjects. We propose a model-agnostic approach for verification with *reachable sets* -- i.e., the set of all points that a person can reach through their actions in feature space. We develop methods to construct reachable sets for discrete feature spaces, which can certify the responsiveness of *any model* by simply querying its predictions. We conduct a comprehensive empirical study on the infeasibility of recourse on datasets from consumer finance. Our results highlight how models can inadvertently preclude access by assigning fixed predictions and underscore the need to account for actionability in model development.