Learning (Approximately) Equivariant Networks via Constrained Optimization

Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects. Strictly equivariant models may struggle to fit the data, while unconstrained models lack a principled way to leverage partial symmetries. Even when the data is fully symmetric, enforcing equivariance can hurt training by limiting the model to a restricted region of the parameter space. Guided by homotopy principles, where an optimization problem is solved by gradually transforming a simpler problem into a complex one, we introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model and gradually reduces its deviation from equivariance. This gradual tightening smooths training early on and settles the model at a data-driven equilibrium, balancing between equivariance and non-equivariance. Across multiple architectures and tasks, our method consistently improves performance metrics, sample efficiency, and robustness to input perturbations compared with strictly equivariant models and heuristic equivariance relaxations.

CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics. However, performing these computations directly in the physical space often incurs significant computational costs. To address this issue, several neural surrogate models have been developed that operate in a compressed latent space to solve the PDE. While these approaches reduce computational complexity, they often use Transformer-based attention mechanisms to handle irregularly sampled domains, resulting in increased memory consumption. In contrast, convolutional neural networks allow memory-efficient encoding and decoding but are limited to regular discretizations. Motivated by these considerations, we propose CALM-PDE, a model class that efficiently solves arbitrarily discretized PDEs in a compressed latent space. We introduce a novel continuous convolution-based encoder-decoder architecture that uses an epsilon-neighborhood-constrained kernel and learns to apply the convolution operator to adaptive and optimized query points. We demonstrate the effectiveness of CALM-PDE on a diverse set of PDEs with both regularly and irregularly sampled spatial domains. CALM-PDE is competitive with or outperforms existing baseline methods while offering significant improvements in memory and inference time efficiency compared to Transformer-based methods.

LOGLO-FNO: Efficient Learning of Local and Global Features in Fourier Neural Operators

Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals due to swirling fluid motions caused by eddies and vortices. Faithfully modeling such signals using neural networks depends on accurately reconstructing moderate to high frequencies. However, it has been well known that deep neural nets exhibit the so-called spectral bias toward learning low-frequency components. Meanwhile, Fourier Neural Operators (FNOs) have emerged as a popular class of data-driven models in recent years for solving Partial Differential Equations (PDEs) and for surrogate modeling in general. Although impressive results have been achieved on several PDE benchmark problems, FNOs often perform poorly in learning non-dominant frequencies characterized by local features. This limitation stems from the spectral bias inherent in neural networks and the explicit exclusion of high-frequency modes in FNOs and their variants. Therefore, to mitigate these issues and improve FNO's spectral learning capabilities to represent a broad range of frequency components, we propose two key architectural enhancements: (i) a parallel branch performing local spectral convolutions (ii) a high-frequency propagation module. Moreover, we propose a novel frequency-sensitive loss term based on radially binned spectral errors. This introduction of a parallel branch for local convolutions reduces number of trainable parameters by up to 50% while achieving the accuracy of baseline FNO that relies solely on global convolutions. Experiments on three challenging PDE problems in fluid mechanics and biological pattern formation, and the qualitative and spectral analysis of predictions show the effectiveness of our method over the state-of-the-art neural operator baselines.

Preference-Based Gradient Estimation for ML-Based Approximate Combinatorial Optimization

Combinatorial optimization (CO) problems arise in a wide range of fields from medicine to logistics and manufacturing. While exact solutions are often not necessary, many applications require finding high-quality solutions quickly. For this purpose, we propose a data-driven approach to improve existing non-learned approximation algorithms for CO. We parameterize the approximation algorithm and train a graph neural network (GNN) to predict parameter values that lead to the best possible solutions. Our pipeline is trained end-to-end in a self-supervised fashion using gradient estimation, treating the approximation algorithm as a black box. We propose a novel gradient estimation scheme for this purpose, which we call preference-based gradient estimation. Our approach combines the benefits of the neural network and the non-learned approximation algorithm: The GNN leverages the information from the dataset to allow the approximation algorithm to find better solutions, while the approximation algorithm guarantees that the solution is feasible. We validate our approach on two well-known combinatorial optimization problems, the travelling salesman problem and the minimum k-cut problem, and show that our method is competitive with state of the art learned CO solvers.

Position: Graph Learning Will Lose Relevance Due To Poor Benchmarks

While machine learning on graphs has demonstrated promise in drug design and molecular property prediction, significant benchmarking challenges hinder its further progress and relevance. Current benchmarking practices often lack focus on transformative, real-world applications, favoring narrow domains like two-dimensional molecular graphs over broader, impactful areas such as combinatorial optimization, relational databases, or chip design. Additionally, many benchmark datasets poorly represent the underlying data, leading to inadequate abstractions and misaligned use cases. Fragmented evaluations and an excessive focus on accuracy further exacerbate these issues, incentivizing overfitting rather than fostering generalizable insights. These limitations have prevented the development of truly useful graph foundation models. This position paper calls for a paradigm shift toward more meaningful benchmarks, rigorous evaluation protocols, and stronger collaboration with domain experts to drive impactful and reliable advances in graph learning research, unlocking the potential of graph learning.

Tractable Transformers for Flexible Conditional Generation

Non-autoregressive (NAR) generative models are valuable because they can handle diverse conditional generation tasks in a more principled way than their autoregressive (AR) counterparts, which are constrained by sequential dependency requirements. Recent advancements in NAR models, such as diffusion language models, have demonstrated superior performance in unconditional generation compared to AR models (e.g., GPTs) of similar sizes. However, such improvements do not always lead to improved conditional generation performance. We show that a key reason for this gap is the difficulty in generalizing to conditional probability queries unseen during training. As a result, strong unconditional generation performance does not guarantee high-quality conditional generation. This paper proposes Tractable Transformers (Tracformer), a Transformer-based generative model that is more robust to different conditional generation tasks. Unlike existing models that rely solely on global contextual features derived from full inputs, Tracformers incorporate a sparse Transformer encoder to capture both local and global contextual information. This information is routed through a decoder for conditional generation. Empirical results demonstrate that Tracformers achieve state-of-the-art conditional generation performance on text modeling compared to recent diffusion and AR model baselines.

On Zero-Initialized Attention: Optimal Prompt and Gating Factor Estimation

The LLaMA-Adapter has recently emerged as an efficient fine-tuning technique for LLaMA models, leveraging zero-initialized attention to stabilize training and enhance performance. However, despite its empirical success, the theoretical foundations of zero-initialized attention remain largely unexplored. In this paper, we provide a rigorous theoretical analysis, establishing a connection between zero-initialized attention and mixture-of-expert models. We prove that both linear and non-linear prompts, along with gating functions, can be optimally estimated, with non-linear prompts offering greater flexibility for future applications. Empirically, we validate our findings on the open LLM benchmarks, demonstrating that non-linear prompts outperform linear ones. Notably, even with limited training data, both prompt types consistently surpass vanilla attention, highlighting the robustness and adaptability of zero-initialized attention.

Adaptive Width Neural Networks

For almost 70 years, researchers have mostly relied on hyper-parameter tuning to pick the width of neural networks' layers out of many possible choices. This paper challenges the status quo by introducing an easy-to-use technique to learn an unbounded width of a neural network's layer during training. The technique does not rely on alternate optimization nor hand-crafted gradient heuristics; rather, it jointly optimizes the width and the parameters of each layer via simple backpropagation. We apply the technique to a broad range of data domains such as tables, images, texts, and graphs, showing how the width adapts to the task's difficulty. By imposing a soft ordering of importance among neurons, it is possible to truncate the trained network at virtually zero cost, achieving a smooth trade-off between performance and compute resources in a structured way. Alternatively, one can dynamically compress the network with no performance degradation. In light of recent foundation models trained on large datasets, believed to require billions of parameters and where hyper-parameter tuning is unfeasible due to huge training costs, our approach stands as a viable alternative for width learning.

MolMix: A Simple Yet Effective Baseline for Multimodal Molecular Representation Learning

In this work, we propose a simple transformer-based baseline for multimodal molecular representation learning, integrating three distinct modalities: SMILES strings, 2D graph representations, and 3D conformers of molecules. A key aspect of our approach is the aggregation of 3D conformers, allowing the model to account for the fact that molecules can adopt multiple conformations-an important factor for accurate molecular representation. The tokens for each modality are extracted using modality-specific encoders: a transformer for SMILES strings, a message-passing neural network for 2D graphs, and an equivariant neural network for 3D conformers. The flexibility and modularity of this framework enable easy adaptation and replacement of these encoders, making the model highly versatile for different molecular tasks. The extracted tokens are then combined into a unified multimodal sequence, which is processed by a downstream transformer for prediction tasks. To efficiently scale our model for large multimodal datasets, we utilize Flash Attention 2 and bfloat16 precision. Despite its simplicity, our approach achieves state-of-the-art results across multiple datasets, demonstrating its effectiveness as a strong baseline for multimodal molecular representation learning.

LoGra-Med: Long Context Multi-Graph Alignment for Medical Vision-Language Model

State-of-the-art medical multi-modal large language models (med-MLLM), like LLaVA-Med or BioMedGPT, leverage instruction-following data in pre-training. However, those models primarily focus on scaling the model size and data volume to boost performance while mainly relying on the autoregressive learning objectives. Surprisingly, we reveal that such learning schemes might result in a weak alignment between vision and language modalities, making these models highly reliant on extensive pre-training datasets - a significant challenge in medical domains due to the expensive and time-consuming nature of curating high-quality instruction-following instances. We address this with LoGra-Med, a new multi-graph alignment algorithm that enforces triplet correlations across image modalities, conversation-based descriptions, and extended captions. This helps the model capture contextual meaning, handle linguistic variability, and build cross-modal associations between visuals and text. To scale our approach, we designed an efficient end-to-end learning scheme using black-box gradient estimation, enabling faster LLaMa 7B training. Our results show LoGra-Med matches LLAVA-Med performance on 600K image-text pairs for Medical VQA and significantly outperforms it when trained on 10% of the data. For example, on VQA-RAD, we exceed LLAVA-Med by 20.13% and nearly match the 100% pre-training score (72.52% vs. 72.64%). We also surpass SOTA methods like BiomedGPT on visual chatbots and RadFM on zero-shot image classification with VQA, highlighting the effectiveness of multi-graph alignment.