arXiv subjects

Risi Kondor

Publications and source records attributed to Risi Kondor.

At least 19 recordsLinked to original sources

arXiv2026

Probabilistic Modeling of Latent Agentic Substructures in Deep Neural Networks

We develop a theory of intelligent agency grounded in probabilistic modeling for neural models. Agents are represented as outcome distributions with epistemic utility given by log score, and compositions are defined through weighted logarithmic pooling that strictly improves every member's welfare. We prove that strict unanimity is impossible under linear pooling or in binary outcome spaces, but possible with three or more outcomes. Our framework admits recursive structure via cloning invariance, continuity, and openness, while tilt-based analysis rules out trivial duplication. Finally, we formalize an agentic alignment phenomenon in LLMs using our theory: eliciting a benevolent persona ("Luigi'") induces an antagonistic counterpart ("Waluigi"), while a manifest-then-suppress Waluigi strategy yields strictly larger first-order misalignment reduction than pure Luigi reinforcement alone. These results clarify how developing a principled mathematical framework for how subagents can coalesce into coherent higher-level entities provides novel implications for alignment in agentic AI systems.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

P-Tensors: a General Formalism for Constructing Higher Order Message Passing Networks

Several recent papers have proposed increasing the expressive power of graph neural networks by exploiting subgraphs or other topological structures. In parallel, researchers have investigated higher order permutation equivariant networks. In this paper we tie these two threads together by providing a general framework for higher order permutation equivariant message passing in subgraph neural networks. In this paper we introduce a new type of mathematical object called $P$-tensors, which provide a simple way to define the most general form of permutation equivariant message passing in both the above two categories of networks. We show that the P-Tensors paradigm can achieve state-of-the-art performance on benchmark molecular datasets.

stat.ML↗

arXiv2025

Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry

We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.

quant-ph↗

arXiv2025

Steerable Transformers for Volumetric Data

We introduce Steerable Transformers, an extension of the Vision Transformer mechanism that maintains equivariance to the special Euclidean group $\mathrm{SE}(d)$. We propose an equivariant attention mechanism that operates on features extracted by steerable convolutions. Operating in Fourier space, our network utilizes Fourier space non-linearities. Our experiments in both two and three dimensions show that adding steerable transformer layers to steerable convolutional networks enhances performance.

cs.CV↗

arXiv2025

A Geometric Approach to Steerable Convolutions

In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on geometric arguments and fundamental principles of pattern matching. We offer an intuitive explanation for the appearance of the Clebsch--Gordan decomposition and spherical harmonic basis functions. Furthermore, we suggest a novel way to construct steerable convolution layers using interpolation kernels that improve upon existing implementation, and offer greater robustness to noisy data.

cs.CV↗

arXiv2025

Graph Contrastive Learning versus Untrained Baselines: The Role of Dataset Size

Graph Contrastive Learning (GCL) has emerged as a leading paradigm for self-supervised learning on graphs, with strong performance reported on standardized datasets and growing applications ranging from genomics to drug discovery. We ask a basic question: does GCL actually outperform untrained baselines? We find that GCL's advantage depends strongly on dataset size and task difficulty. On standard datasets, untrained Graph Neural Networks (GNNs), simple multilayer perceptrons, and even handcrafted statistics can rival or exceed GCL. On the large molecular dataset ogbg-molhiv, we observe a crossover: GCL lags at small scales but pulls ahead beyond a few thousand graphs, though this gain eventually plateaus. On synthetic datasets, GCL accuracy approximately scales with the logarithm of the number of graphs and its performance gap (compared with untrained GNNs) varies with respect to task complexity. Moving forward, it is crucial to identify the role of dataset size in benchmarks and applications, as well as to design GCL algorithms that avoid performance plateaus.

cs.LG↗

arXiv2024

Learning to Solve Multiresolution Matrix Factorization by Manifold Optimization and Evolutionary Metaheuristics

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex multiscale or hierarchical strucutre. While MMF promises to yields a useful wavelet basis, finding the factorization itself is hard, and existing greedy methods tend to be brittle. In this paper, we propose a ``learnable'' version of MMF that carfully optimizes the factorization using metaheuristics, specifically evolutionary algorithms and directed evolution, along with Stiefel manifold optimization through backpropagating errors. We show that the resulting wavelet basis far outperforms prior MMF algorithms and gives comparable performance on standard learning tasks on graphs. Furthermore, we construct the wavelet neural networks (WNNs) learning graphs on the spectral domain with the wavelet basis produced by our MMF learning algorithm. Our wavelet networks are competitive against other state-of-the-art methods in molecular graphs classification and node classification on citation graphs. We release our implementation at https://github.com/HySonLab/LearnMMF

cs.LG↗

arXiv2024

Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU($2$)-symmetric quantum many-body problems, to design new equivariant components for equivariant neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term "fusion blocks," serve as universal approximators of any continuous equivariant function defined in the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.

cs.LG↗

arXiv2024

Sign Rank Limitations for Inner Product Graph Decoders

Inner product-based decoders are among the most influential frameworks used to extract meaningful data from latent embeddings. However, such decoders have shown limitations in representation capacity in numerous works within the literature, which have been particularly notable in graph reconstruction problems. In this paper, we provide the first theoretical elucidation of this pervasive phenomenon in graph data, and suggest straightforward modifications to circumvent this issue without deviating from the inner product framework.

cs.LG↗

arXiv2023

Fast Temporal Wavelet Graph Neural Networks

Spatio-temporal signals forecasting plays an important role in numerous domains, especially in neuroscience and transportation. The task is challenging due to the highly intricate spatial structure, as well as the non-linear temporal dynamics of the network. To facilitate reliable and timely forecast for the human brain and traffic networks, we propose the Fast Temporal Wavelet Graph Neural Networks (FTWGNN) that is both time- and memory-efficient for learning tasks on timeseries data with the underlying graph structure, thanks to the theories of multiresolution analysis and wavelet theory on discrete spaces. We employ Multiresolution Matrix Factorization (MMF) (Kondor et al., 2014) to factorize the highly dense graph structure and compute the corresponding sparse wavelet basis that allows us to construct fast wavelet convolution as the backbone of our novel architecture. Experimental results on real-world PEMS-BAY, METR-LA traffic datasets and AJILE12 ECoG dataset show that FTWGNN is competitive with the state-of-the-arts while maintaining a low computational footprint. Our PyTorch implementation is publicly available at https://github.com/HySonLab/TWGNN

cs.LG↗

arXiv2023

Transformers are efficient hierarchical chemical graph learners

Transformers, adapted from natural language processing, are emerging as a leading approach for graph representation learning. Contemporary graph transformers often treat nodes or edges as separate tokens. This approach leads to computational challenges for even moderately-sized graphs due to the quadratic scaling of self-attention complexity with token count. In this paper, we introduce SubFormer, a graph transformer that operates on subgraphs that aggregate information by a message-passing mechanism. This approach reduces the number of tokens and enhances learning long-range interactions. We demonstrate SubFormer on benchmarks for predicting molecular properties from chemical structures and show that it is competitive with state-of-the-art graph transformers at a fraction of the computational cost, with training times on the order of minutes on a consumer-grade graphics card. We interpret the attention weights in terms of chemical structures. We show that SubFormer exhibits limited over-smoothing and avoids over-squashing, which is prevalent in traditional graph neural networks.

cs.LG↗

arXiv2023

Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze

We develop a theoretical framework for $S_n$-equivariant convolutional quantum circuits with SU$(d)$-symmetry, building on and significantly generalizing Jordan's Permutational Quantum Computing (PQC) formalism based on Schur-Weyl duality connecting both SU$(d)$ and $S_n$ actions on qudits. In particular, we utilize the Okounkov-Vershik approach to prove Harrow's statement (Ph.D. Thesis 2005 p.160) on the equivalence between $\operatorname{SU}(d)$ and $S_n$ irrep bases and to establish the $S_n$-equivariant Convolutional Quantum Alternating Ansätze ($S_n$-CQA) using Young-Jucys-Murphy (YJM) elements. We prove that $S_n$-CQA is able to generate any unitary in any given $S_n$ irrep sector, which may serve as a universal model for a wide array of quantum machine learning problems with the presence of SU($d$) symmetry. Our method provides another way to prove the universality of Quantum Approximate Optimization Algorithm (QAOA) and verifies that 4-local SU($d$) symmetric unitaries are sufficient to build generic SU($d$) symmetric quantum circuits up to relative phase factors. We present numerical simulations to showcase the effectiveness of the ansätze to find the ground state energy of the $J_1$--$J_2$ antiferromagnetic Heisenberg model on the rectangular and Kagome lattices. Our work provides the first application of the celebrated Okounkov-Vershik's $S_n$ representation theory to quantum physics and machine learning, from which to propose quantum variational ansätze that strongly suggests to be classically intractable tailored towards a specific optimization problem.

quant-ph↗

arXiv2023

Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structures

Contemporary graph learning algorithms are not well-defined for large molecules since they do not consider the hierarchical interactions among the atoms, which are essential to determine the molecular properties of macromolecules. In this work, we propose Multiresolution Graph Transformers (MGT), the first graph transformer architecture that can learn to represent large molecules at multiple scales. MGT can learn to produce representations for the atoms and group them into meaningful functional groups or repeating units. We also introduce Wavelet Positional Encoding (WavePE), a new positional encoding method that can guarantee localization in both spectral and spatial domains. Our proposed model achieves competitive results on two macromolecule datasets consisting of polymers and peptides, and one drug-like molecule dataset. Importantly, our model outperforms other state-of-the-art methods and achieves chemical accuracy in estimating molecular properties (e.g., GAP, HOMO and LUMO) calculated by Density Functional Theory (DFT) in the polymers dataset. Furthermore, the visualizations, including clustering results on macromolecules and low-dimensional spaces of their representations, demonstrate the capability of our methodology in learning to represent long-range and hierarchical structures. Our PyTorch implementation is publicly available at https://github.com/HySonLab/Multires-Graph-Transformer

cs.LG↗

arXiv2023

Modeling Polypharmacy and Predicting Drug-Drug Interactions using Deep Generative Models on Multimodal Graphs

Latent representations of drugs and their targets produced by contemporary graph autoencoder models have proved useful in predicting many types of node-pair interactions on large networks, including drug-drug, drug-target, and target-target interactions. However, most existing approaches model either the node's latent spaces in which node distributions are rigid or do not effectively capture the interrelations between drugs; these limitations hinder the methods from accurately predicting drug-pair interactions. In this paper, we present the effectiveness of variational graph autoencoders (VGAE) in modeling latent node representations on multimodal networks. Our approach can produce flexible latent spaces for each node type of the multimodal graph; the embeddings are used later for predicting links among node pairs under different edge types. To further enhance the models' performance, we suggest a new method that concatenates Morgan fingerprints, which capture the molecular structures of each drug, with their latent embeddings before preceding them to the decoding stage for link prediction. Our proposed model shows competitive results on three multimodal networks: (1) a multimodal graph consisting of drug and protein nodes, (2) a multimodal graph constructed from a subset of the DrugBank database involving drug nodes under different interaction types, and (3) a multimodal graph consisting of drug and cell line nodes. Our source code is publicly available at https://github.com/HySonLab/drug-interactions.

cs.LG↗

arXiv2022

Predicting Drug-Drug Interactions using Deep Generative Models on Graphs

Latent representations of drugs and their targets produced by contemporary graph autoencoder-based models have proved useful in predicting many types of node-pair interactions on large networks, including drug-drug, drug-target, and target-target interactions. However, most existing approaches model the node's latent spaces in which node distributions are rigid and disjoint; these limitations hinder the methods from generating new links among pairs of nodes. In this paper, we present the effectiveness of variational graph autoencoders (VGAE) in modeling latent node representations on multimodal networks. Our approach can produce flexible latent spaces for each node type of the multimodal graph; the embeddings are used later for predicting links among node pairs under different edge types. To further enhance the models' performance, we suggest a new method that concatenates Morgan fingerprints, which capture the molecular structures of each drug, with their latent embeddings before preceding them to the decoding stage for link prediction. Our proposed model shows competitive results on two multimodal networks: (1) a multi-graph consisting of drug and protein nodes, and (2) a multi-graph consisting of drug and cell line nodes. Our source code is publicly available at https://github.com/HySonLab/drug-interactions.

q-bio.BM↗

arXiv2022

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.

cs.LG↗

arXiv2022

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.

cs.LG↗