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Publications
All-in-one simulation-based inference
Manuel Gloeckler
Michael Deistler
Christian Dietrich Weilbach
Frank Wood
Jakob H. Macke
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
Autoformalization involves automatically translating informal math into formal theorems and proofs that are machine-verifiable. Euclidean ge… (see more)ometry provides an interesting and controllable domain for studying autoformalization. In this paper, we introduce a neuro-symbolic framework for autoformalizing Euclidean geometry, which combines domain knowledge, SMT solvers, and large language models (LLMs). One challenge in Euclidean geometry is that informal proofs rely on diagrams, leaving gaps in texts that are hard to formalize. To address this issue, we use theorem provers to fill in such diagrammatic information automatically, so that the LLM only needs to autoformalize the explicit textual steps, making it easier for the model. We also provide automatic semantic evaluation for autoformalized theorem statements. We construct LeanEuclid, an autoformalization benchmark consisting of problems from Euclid’s Elements and the UniGeo dataset formalized in the Lean proof assistant. Experiments with GPT-4 and GPT-4V show the capability and limitations of state-of-the-art LLMs on autoformalizing geometry problems. The data and code are available at https://github.com/loganrjmurphy/LeanEuclid.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a gene… (see more)ral convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and … (see more)the regularization of density paths (potential energy). These combinations yield different variational problems (Lagrangians), encompassing many variations of the optimal transport problem such as the Schr\"odinger bridge, unbalanced optimal transport, and optimal transport with physical constraints, among others. In general, the optimal density path is unknown, and solving these variational problems can be computationally challenging. We propose a novel deep learning based framework approaching all of these problems from a unified perspective. Leveraging the dual formulation of the Lagrangians, our method does not require simulating or backpropagating through the trajectories of the learned dynamics, and does not need access to optimal couplings. We showcase the versatility of the proposed framework by outperforming previous approaches for the single-cell trajectory inference, where incorporating prior knowledge into the dynamics is crucial for correct predictions.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problem… (see more)s are solved via their min-max Lagrangian formulations, which exhibit unstable oscillatory dynamics when optimized using gradient descent-ascent. The adoption of constrained optimization techniques in the machine learning community is currently limited by the lack of reliable, general-purpose update schemes for the Lagrange multipliers. This paper proposes the νPI algorithm and contributes an optimization perspective on Lagrange multiplier updates based on PI controllers, extending the work of Stooke, Achiam and Abbeel (2020). We provide theoretical and empirical insights explaining the inability of momentum methods to address the shortcomings of gradient descent-ascent, and contrast this with the empirical success of our proposed νPI controller. Moreover, we prove that νPI generalizes popular momentum methods for single-objective minimization. Our experiments demonstrate that νPI reliably stabilizes the multiplier dynamics and its hyperparameters enjoy robust and predictable behavior.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into mult… (see more)iple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete distributions when both the total population size and the category sizes are unknown. Here, we propose a novel solution using the hypergeometric likelihood to solve this estimation problem, even in the presence of severe under-sampling. Our approach accounts for a data generating process where the ground-truth is a mixture of distributions conditional on a continuous latent variable, as seen in collaborative filtering, using the variational autoencoder framework. Empirical data simulation demonstrates that our method outperforms other likelihood functions used to model count data, both in terms of accuracy of population size estimate and learning an informative latent space. We showcase our method’s versatility through applications in NLP, by inferring and estimating the complexity of latent vocabularies in reading passage excerpts, and in biology, by accurately recovering the true number of gene transcripts from sparse single-cell genomics data.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
Fine-tuning is a widespread technique that allows practitioners to transfer pre-trained capabilities, as recently showcased by the successfu… (see more)l applications of foundation models. However, fine-tuning reinforcement learning (RL) models remains a challenge. This work conceptualizes one specific cause of poor transfer, accentuated in the RL setting by the interplay between actions and observations: forgetting of pre-trained capabilities. Namely, a model deteriorates on the state subspace of the downstream task not visited in the initial phase of fine-tuning, on which the model behaved well due to pre-training. This way, we lose the anticipated transfer benefits. We identify conditions when this problem occurs, showing that it is common and, in many cases, catastrophic. Through a detailed empirical analysis of the challenging NetHack and Montezuma’s Revenge environments, we show that standard knowledge retention techniques mitigate the problem and thus allow us to take full advantage of the pre-trained capabilities. In particular, in NetHack, we achieve a new state-of-the-art for neural models, improving the previous best score from
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
Positional and structural encodings (PSE) enable better identifiability of nodes within a graph, as in general graphs lack a canonical node … (see more)ordering. This renders PSEs essential tools for empowering modern GNNs, and in particular graph Transformers. However, designing PSEs that work optimally for a variety of graph prediction tasks is a challenging and unsolved problem. Here, we present the graph positional and structural encoder (GPSE), a first-ever attempt to train a graph encoder that captures rich PSE representations for augmenting any GNN. GPSE can effectively learn a common latent representation for multiple PSEs, and is highly transferable. The encoder trained on a particular graph dataset can be used effectively on datasets drawn from significantly different distributions and even modalities. We show that across a wide range of benchmarks, GPSE-enhanced models can significantly improve the performance in certain tasks, while performing on par with those that employ explicitly computed PSEs in other cases. Our results pave the way for the development of large pre-trained models for extracting graph positional and structural information and highlight their potential as a viable alternative to explicitly computed PSEs as well as to existing self-supervised pre-training approaches.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
