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Risi Kondor

Risi Kondor appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine LearningArtificial Intelligencephysics.comp-phComputer Visioncond-mat.mtrl-scihep-exhep-phSocial and Information Networksastro-ph.IMBiological PhysicsBiomoleculesNumerical Analysisphysics.chem-phphysics.soc-ph

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Published work

14 published item(s)

preprint2026arXiv

Deep Minds and Shallow Probes

Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a representation should therefore be stable under the relevant representation symmetries rather than be tied to a particular basis. We study this group action in the tractable exact setting of the final readout layer, where equivalent realizations induce affine changes of hidden coordinates. The resulting symmetry principle singles out a unique hierarchy of shallow coordinate-stable probes, with linear probes as its degree-1 member. We also show that a natural object for cross-model probe transfer is a shared probe-visible quotient--the representation modulo directions invisible to the probe family--rather than the full hidden state. Experiments on synthetic and real-world tasks support both predictions, showing where degree-2 probes help beyond linear ones and how quotient-based transfer enables coverage-aware monitor portability across model families. These results point toward a broader geometric representation theory of neural probing, with coverage-aware monitor transfer as a concrete operational consequence.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

ATOM3D: Tasks On Molecules in Three Dimensions

Computational methods that operate on three-dimensional molecular structure have the potential to solve important questions in biology and chemistry. In particular, deep neural networks have gained significant attention, but their widespread adoption in the biomolecular domain has been limited by a lack of either systematic performance benchmarks or a unified toolkit for interacting with molecular data. To address this, we present ATOM3D, a collection of both novel and existing benchmark datasets spanning several key classes of biomolecules. We implement several classes of three-dimensional molecular learning methods for each of these tasks and show that they consistently improve performance relative to methods based on one- and two-dimensional representations. The specific choice of architecture proves to be critical for performance, with three-dimensional convolutional networks excelling at tasks involving complex geometries, graph networks performing well on systems requiring detailed positional information, and the more recently developed equivariant networks showing significant promise. Our results indicate that many molecular problems stand to gain from three-dimensional molecular learning, and that there is potential for improvement on many tasks which remain underexplored. To lower the barrier to entry and facilitate further developments in the field, we also provide a comprehensive suite of tools for dataset processing, model training, and evaluation in our open-source atom3d Python package. All datasets are available for download from https://www.atom3d.ai .

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Autobahn: Automorphism-based Graph Neural Nets

We introduce Automorphism-based graph neural networks (Autobahn), a new family of graph neural networks. In an Autobahn, we decompose the graph into a collection of subgraphs and apply local convolutions that are equivariant to each subgraph's automorphism group. Specific choices of local neighborhoods and subgraphs recover existing architectures such as message passing neural networks. Our formalism also encompasses novel architectures: as an example, we introduce a graph neural network that decomposes the graph into paths and cycles. The resulting convolutions reflect the natural way that parts of the graph can transform, preserving the intuitive meaning of convolution without sacrificing global permutation equivariance. We validate our approach by applying Autobahn to molecular graphs, where it achieves results competitive with state-of-the-art message passing algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multiresolution Equivariant Graph Variational Autoencoder

In this paper, we propose Multiresolution Equivariant Graph Variational Autoencoders (MGVAE), the first hierarchical generative model to learn and generate graphs in a multiresolution and equivariant manner. At each resolution level, MGVAE employs higher order message passing to encode the graph while learning to partition it into mutually exclusive clusters and coarsening into a lower resolution that eventually creates a hierarchy of latent distributions. MGVAE then constructs a hierarchical generative model to variationally decode into a hierarchy of coarsened graphs. Importantly, our proposed framework is end-to-end permutation equivariant with respect to node ordering. MGVAE achieves competitive results with several generative tasks including general graph generation, molecular generation, unsupervised molecular representation learning to predict molecular properties, link prediction on citation graphs, and graph-based image generation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Symmetry Group Equivariant Architectures for Physics

Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation or permutation invariance has driven impressive performance breakthroughs in computer vision, natural language processing, and other important applications. In this report, we argue that both the physics community and the broader machine learning community have much to understand and potentially to gain from a deeper investment in research concerning symmetry group equivariant machine learning architectures. For some applications, the introduction of symmetries into the fundamental structural design can yield models that are more economical (i.e. contain fewer, but more expressive, learned parameters), interpretable (i.e. more explainable or directly mappable to physical quantities), and/or trainable (i.e. more efficient in both data and computational requirements). We discuss various figures of merit for evaluating these models as well as some potential benefits and limitations of these methods for a variety of physics applications. Research and investment into these approaches will lay the foundation for future architectures that are potentially more robust under new computational paradigms and will provide a richer description of the physical systems to which they are applied.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Temporal Multiresolution Graph Neural Networks For Epidemic Prediction

In this paper, we introduce Temporal Multiresolution Graph Neural Networks (TMGNN), the first architecture that both learns to construct the multiscale and multiresolution graph structures and incorporates the time-series signals to capture the temporal changes of the dynamic graphs. We have applied our proposed model to the task of predicting future spreading of epidemic and pandemic based on the historical time-series data collected from the actual COVID-19 pandemic and chickenpox epidemic in several European countries, and have obtained competitive results in comparison to other previous state-of-the-art temporal architectures and graph learning algorithms. We have shown that capturing the multiscale and multiresolution structures of graphs is important to extract either local or global information that play a critical role in understanding the dynamic of a global pandemic such as COVID-19 which started from a local city and spread to the whole world. Our work brings a promising research direction in forecasting and mitigating future epidemics and pandemics.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Lorentz Group Equivariant Neural Network for Particle Physics

We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the finite-dimensional representations of the Lorentz group and the equivariant nonlinearity involves the tensor product. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters and are much more physically interpretable than leading approaches that use CNNs and point cloud approaches. The competitive performance of the network is demonstrated on a public classification dataset [27] for tagging top quark decays given energy-momenta of jet constituents produced in proton-proton collisions.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The general theory of permutation equivarant neural networks and higher order graph variational encoders

Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

The Multiscale Laplacian Graph Kernel

Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG kernels) that we define in this paper can account for structure at a range of different scales. At the heart of the MLG construction is another new graph kernel, called the Feature Space Laplacian Graph kernel (FLG kernel), which has the property that it can lift a base kernel defined on the vertices of two graphs to a kernel between the graphs. The MLG kernel applies such FLG kernels to subgraphs recursively. To make the MLG kernel computationally feasible, we also introduce a randomized projection procedure, similar to the Nyström method, but for RKHS operators.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Parallel MMF: a Multiresolution Approach to Matrix Computation

Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for sparse matrices. We argue that this makes pMMF a valuable new computational primitive in its own right, and present experiments on using pMMF for two distinct purposes: compressing matrices and preconditioning large sparse linear systems.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

On representing chemical environments

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms, and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether new approach, called Smooth Overlap of Atomic Positions (SOAP), that sidesteps these difficulties by directly defining the similarity between any two neighbourhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Incorporating Domain Knowledge in Matching Problems via Harmonic Analysis

Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in practice. Here, we investigate if this difficulty can be mitigated when some additional piece of information is available: (a) that all QAP instances of interest come from the same application, and (b) the correct solution for a set of such QAP instances is given. We propose a new approach to accelerate the solution of QAPs based on learning parameters for a modified objective function from prior QAP instances. A key feature of our approach is that it takes advantage of the algebraic structure of permutations, in conjunction with special methods for optimizing functions over the symmetric group Sn in Fourier space. Experiments show that in practical domains the new method can outperform existing approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons

We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a fixed functional form and hence is capable of modeling complex potential energy landscapes. It is systematically improvable with more data. We apply the method to bulk carbon, silicon and germanium and test it by calculating properties of the crystals at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.

0 citations0 reviewsNo code linkedOpen access
preprint2007arXiv

A novel set of rotationally and translationally invariant features for images based on the non-commutative bispectrum

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the original image than most existing systems of invariants. Our construction is based on the generalization of the concept of bispectrum to the three-dimensional rotation group SO(3), and a projection of the image onto the sphere.

0 citations0 reviewsNo code linkedOpen access