arXiv subjects

Geoffrey J. Gordon

Publications and source records attributed to Geoffrey J. Gordon.

At least 19 recordsLinked to original sources

arXiv2026

Text Has Curvature

Does natural language text have an intrinsic curvature? Language is increasingly modeled in curved geometries - hyperbolic spaces for hierarchy, mixed-curvature manifolds for compositional structure - yet a basic scientific question remains unresolved: what does curvature mean for text itself, in a way that is native to language rather than an artifact of the embedding space we choose? We argue that text does indeed have curvature, and show how to detect it, define it, and use it. To this end, we propose Texture, a text-native, word-level discrete curvature signal, and make three contributions. (a) Existence: We provide empirical and theoretical certificates that semantic inference in natural corpora is non-flat. (b) Definition: We define Texture as a signed two-axis curvature of the word-in-context belief field - the differential of reconciliation between prefix and suffix - measuring, via a debiased Schr\"odinger transport divergence, whether adding context from one side contracts the semantic effect of context from the other side (focus, positive) or expands it into competing continuations (fan-out, negative). (c) Utility: Texture is actionable: it serves as a general-purpose measurement and control primitive enabling geometry without geometric training; we instantiate it on two representative tasks, improving long-context inference through curvature-guided compression and retrieval-augmented generation through curvature-guided routing. Together, our results establish a text-native curvature paradigm, making Texture practically useful.

cs.LG↗

arXiv2025

CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection

Does the intrinsic curvature of complex networks hold the key to unveiling graph anomalies that conventional approaches overlook? Reconstruction-based graph anomaly detection (GAD) methods overlook such geometric outliers, focusing only on structural and attribute-level anomalies. To this end, we propose CurvGAD - a mixed-curvature graph autoencoder that introduces the notion of curvature-based geometric anomalies. CurvGAD introduces two parallel pipelines for enhanced anomaly interpretability: (1) Curvature-equivariant geometry reconstruction, which focuses exclusively on reconstructing the edge curvatures using a mixed-curvature, Riemannian encoder and Gaussian kernel-based decoder; and (2) Curvature-invariant structure and attribute reconstruction, which decouples structural and attribute anomalies from geometric irregularities by regularizing graph curvature under discrete Ollivier-Ricci flow, thereby isolating the non-geometric anomalies. By leveraging curvature, CurvGAD refines the existing anomaly classifications and identifies new curvature-driven anomalies. Extensive experimentation over 10 real-world datasets (both homophilic and heterophilic) demonstrates an improvement of up to 6.5% over state-of-the-art GAD methods. The code is available at: https://github.com/karish-grover/curvgad.

cs.LG↗

arXiv2025

LICORICE: Label-Efficient Concept-Based Interpretable Reinforcement Learning

Recent advances in reinforcement learning (RL) have predominantly leveraged neural network policies for decision-making, yet these models often lack interpretability, posing challenges for stakeholder comprehension and trust. Concept bottleneck models offer an interpretable alternative by integrating human-understandable concepts into policies. However, prior work assumes that concept annotations are readily available during training. For RL, this requirement poses a significant limitation: it necessitates continuous real-time concept annotation, which either places an impractical burden on human annotators or incurs substantial costs in API queries and inference time when employing automated labeling methods. To overcome this limitation, we introduce a novel training scheme that enables RL agents to efficiently learn a concept-based policy by only querying annotators to label a small set of data. Our algorithm, LICORICE, involves three main contributions: interleaving concept learning and RL training, using an ensemble to actively select informative data points for labeling, and decorrelating the concept data. We show how LICORICE reduces human labeling efforts to 500 or fewer concept labels in three environments, and 5000 or fewer in two more complex environments, all at no cost to performance. We also explore the use of VLMs as automated concept annotators, finding them effective in some cases but imperfect in others. Our work significantly reduces the annotation burden for interpretable RL, making it more practical for real-world applications that necessitate transparency.

cs.LG↗

arXiv2024

Meta-Analysis with Untrusted Data

[See paper for full abstract] Meta-analysis is a crucial tool for answering scientific questions. It is usually conducted on a relatively small amount of ``trusted'' data -- ideally from randomized, controlled trials -- which allow causal effects to be reliably estimated with minimal assumptions. We show how to answer causal questions much more precisely by making two changes. First, we incorporate untrusted data drawn from large observational databases, related scientific literature and practical experience -- without sacrificing rigor or introducing strong assumptions. Second, we train richer models capable of handling heterogeneous trials, addressing a long-standing challenge in meta-analysis. Our approach is based on conformal prediction, which fundamentally produces rigorous prediction intervals, but doesn't handle indirect observations: in meta-analysis, we observe only noisy effects due to the limited number of participants in each trial. To handle noise, we develop a simple, efficient version of fully-conformal kernel ridge regression, based on a novel condition called idiocentricity. We introduce noise-correcting terms in the residuals and analyze their interaction with a ``variance shaving'' technique. In multiple experiments on healthcare datasets, our algorithms deliver tighter, sounder intervals than traditional ones. This paper charts a new course for meta-analysis and evidence-based medicine, where heterogeneity and untrusted data are embraced for more nuanced and precise predictions.

stat.ML↗

arXiv2022

Fundamental Limits and Tradeoffs in Invariant Representation Learning

A wide range of machine learning applications such as privacy-preserving learning, algorithmic fairness, and domain adaptation/generalization among others, involve learning invariant representations of the data that aim to achieve two competing goals: (a) maximize information or accuracy with respect to a target response, and (b) maximize invariance or independence with respect to a set of protected features (e.g., for fairness, privacy, etc). Despite their wide applicability, theoretical understanding of the optimal tradeoffs -- with respect to accuracy, and invariance -- achievable by invariant representations is still severely lacking. In this paper, we provide an information theoretic analysis of such tradeoffs under both classification and regression settings. More precisely, we provide a geometric characterization of the accuracy and invariance achievable by any representation of the data; we term this feasible region the information plane. We provide an inner bound for this feasible region for the classification case, and an exact characterization for the regression case, which allows us to either bound or exactly characterize the Pareto optimal frontier between accuracy and invariance. Although our contributions are mainly theoretical, a key practical application of our results is in certifying the potential sub-optimality of any given representation learning algorithm for either classification or regression tasks. Our results shed new light on the fundamental interplay between accuracy and invariance, and may be useful in guiding the design of future representation learning algorithms.

cs.LG↗

arXiv2022

Inherent Tradeoffs in Learning Fair Representations

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy is not entirely clear, even for the basic paradigm of classification problems. In this paper, we characterize an inherent tradeoff between statistical parity and accuracy in the classification setting by providing a lower bound on the sum of group-wise errors of any fair classifiers. Our impossibility theorem could be interpreted as a certain uncertainty principle in fairness: if the base rates differ among groups, then any fair classifier satisfying statistical parity has to incur a large error on at least one of the groups. We further extend this result to give a lower bound on the joint error of any (approximately) fair classifiers, from the perspective of learning fair representations. To show that our lower bound is tight, assuming oracle access to Bayes (potentially unfair) classifiers, we also construct an algorithm that returns a randomized classifier that is both optimal (in terms of accuracy) and fair. Interestingly, when the protected attribute can take more than two values, an extension of this lower bound does not admit an analytic solution. Nevertheless, in this case, we show that the lower bound can be efficiently computed by solving a linear program, which we term as the TV-Barycenter problem, a barycenter problem under the TV-distance. On the upside, we prove that if the group-wise Bayes optimal classifiers are close, then learning fair representations leads to an alternative notion of fairness, known as the accuracy parity, which states that the error rates are close between groups. Finally, we also conduct experiments on real-world datasets to confirm our theoretical findings.

cs.LG↗

arXiv2021

Understanding and Mitigating Accuracy Disparity in Regression

With the widespread deployment of large-scale prediction systems in high-stakes domains, e.g., face recognition, criminal justice, etc., disparity in prediction accuracy between different demographic subgroups has called for fundamental understanding on the source of such disparity and algorithmic intervention to mitigate it. In this paper, we study the accuracy disparity problem in regression. To begin with, we first propose an error decomposition theorem, which decomposes the accuracy disparity into the distance between marginal label distributions and the distance between conditional representations, to help explain why such accuracy disparity appears in practice. Motivated by this error decomposition and the general idea of distribution alignment with statistical distances, we then propose an algorithm to reduce this disparity, and analyze its game-theoretic optima of the proposed objective functions. To corroborate our theoretical findings, we also conduct experiments on five benchmark datasets. The experimental results suggest that our proposed algorithms can effectively mitigate accuracy disparity while maintaining the predictive power of the regression models.

cs.LG↗

arXiv2021

Successor Feature Sets: Generalizing Successor Representations Across Policies

Successor-style representations have many advantages for reinforcement learning: for example, they can help an agent generalize from past experience to new goals, and they have been proposed as explanations of behavioral and neural data from human and animal learners. They also form a natural bridge between model-based and model-free RL methods: like the former they make predictions about future experiences, and like the latter they allow efficient prediction of total discounted rewards. However, successor-style representations are not optimized to generalize across policies: typically, we maintain a limited-length list of policies, and share information among them by representation learning or GPI. Successor-style representations also typically make no provision for gathering information or reasoning about latent variables. To address these limitations, we bring together ideas from predictive state representations, belief space value iteration, successor features, and convex analysis: we develop a new, general successor-style representation, together with a Bellman equation that connects multiple sources of information within this representation, including different latent states, policies, and reward functions. The new representation is highly expressive: for example, it lets us efficiently read off an optimal policy for a new reward function, or a policy that imitates a new demonstration. For this paper, we focus on exact computation of the new representation in small, known environments, since even this restricted setting offers plenty of interesting questions. Our implementation does not scale to large, unknown environments -- nor would we expect it to, since it generalizes POMDP value iteration, which is difficult to scale. However, we believe that future work will allow us to extend our ideas to approximate reasoning in large, unknown environments.

cs.LG↗

arXiv2020

Trade-offs and Guarantees of Adversarial Representation Learning for Information Obfuscation

Crowdsourced data used in machine learning services might carry sensitive information about attributes that users do not want to share. Various methods have been proposed to minimize the potential information leakage of sensitive attributes while maximizing the task accuracy. However, little is known about the theory behind these methods. In light of this gap, we develop a novel theoretical framework for attribute obfuscation. Under our framework, we propose a minimax optimization formulation to protect the given attribute and analyze its inference guarantees against worst-case adversaries. Meanwhile, it is clear that in general there is a tension between minimizing information leakage and maximizing task accuracy. To understand this, we prove an information-theoretic lower bound to precisely characterize the fundamental trade-off between accuracy and information leakage. We conduct experiments on two real-world datasets to corroborate the inference guarantees and validate this trade-off. Our results indicate that, among several alternatives, the adversarial learning approach achieves the best trade-off in terms of attribute obfuscation and accuracy maximization.

cs.LG↗

arXiv2020

An Empirical Investigation of Beam-Aware Training in Supertagging

Structured prediction is often approached by training a locally normalized model with maximum likelihood and decoding approximately with beam search. This approach leads to mismatches as, during training, the model is not exposed to its mistakes and does not use beam search. Beam-aware training aims to address these problems, but unfortunately, it is not yet widely used due to a lack of understanding about how it impacts performance, when it is most useful, and whether it is stable. Recently, Negrinho et al. (2018) proposed a meta-algorithm that captures beam-aware training algorithms and suggests new ones, but unfortunately did not provide empirical results. In this paper, we begin an empirical investigation: we train the supertagging model of Vaswani et al. (2016) and a simpler model with instantiations of the meta-algorithm. We explore the influence of various design choices and make recommendations for choosing them. We observe that beam-aware training improves performance for both models, with large improvements for the simpler model which must effectively manage uncertainty during decoding. Our results suggest that a model must be learned with search to maximize its effectiveness.

cs.CL↗

arXiv2020

Conditional Learning of Fair Representations

We propose a novel algorithm for learning fair representations that can simultaneously mitigate two notions of disparity among different demographic subgroups in the classification setting. Two key components underpinning the design of our algorithm are balanced error rate and conditional alignment of representations. We show how these two components contribute to ensuring accuracy parity and equalized false-positive and false-negative rates across groups without impacting demographic parity. Furthermore, we also demonstrate both in theory and on two real-world experiments that the proposed algorithm leads to a better utility-fairness trade-off on balanced datasets compared with existing algorithms on learning fair representations for classification.

cs.LG↗

arXiv2019

An Empirical Study of Example Forgetting during Deep Neural Network Learning

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

cs.LG↗

arXiv2019

Learning Neural Networks with Adaptive Regularization

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing an adaptive and data-dependent regularization motivated by the empirical Bayes method. Specifically, we propose to construct a matrix-variate normal prior (on weights) whose covariance matrix has a Kronecker product structure. This structure is designed to capture the correlations in neurons through backpropagation. Under the assumption of this Kronecker factorization, the prior encourages neurons to borrow statistical strength from one another. Hence, it leads to an adaptive and data-dependent regularization when training networks on small datasets. To optimize the model, we present an efficient block coordinate descent algorithm with analytical solutions. Empirically, we demonstrate that the proposed method helps networks converge to local optima with smaller stable ranks and spectral norms. These properties suggest better generalizations and we present empirical results to support this expectation. We also verify the effectiveness of the approach on multiclass classification and multitask regression problems with various network structures.

cs.LG↗

arXiv2019

Learning Beam Search Policies via Imitation Learning

Beam search is widely used for approximate decoding in structured prediction problems. Models often use a beam at test time but ignore its existence at train time, and therefore do not explicitly learn how to use the beam. We develop an unifying meta-algorithm for learning beam search policies using imitation learning. In our setting, the beam is part of the model, and not just an artifact of approximate decoding. Our meta-algorithm captures existing learning algorithms and suggests new ones. It also lets us show novel no-regret guarantees for learning beam search policies.

stat.ML↗

arXiv2019

On Learning Invariant Representation for Domain Adaptation

Due to the ability of deep neural nets to learn rich representations, recent advances in unsupervised domain adaptation have focused on learning domain-invariant features that achieve a small error on the source domain. The hope is that the learnt representation, together with the hypothesis learnt from the source domain, can generalize to the target domain. In this paper, we first construct a simple counterexample showing that, contrary to common belief, the above conditions are not sufficient to guarantee successful domain adaptation. In particular, the counterexample exhibits \emph{conditional shift}: the class-conditional distributions of input features change between source and target domains. To give a sufficient condition for domain adaptation, we propose a natural and interpretable generalization upper bound that explicitly takes into account the aforementioned shift. Moreover, we shed new light on the problem by proving an information-theoretic lower bound on the joint error of \emph{any} domain adaptation method that attempts to learn invariant representations. Our result characterizes a fundamental tradeoff between learning invariant representations and achieving small joint error on both domains when the marginal label distributions differ from source to target. Finally, we conduct experiments on real-world datasets that corroborate our theoretical findings. We believe these insights are helpful in guiding the future design of domain adaptation and representation learning algorithms.

cs.LG↗

arXiv2019

Dual Policy Iteration

Recently, a novel class of Approximate Policy Iteration (API) algorithms have demonstrated impressive practical performance (e.g., ExIt from [2], AlphaGo-Zero from [27]). This new family of algorithms maintains, and alternately optimizes, two policies: a fast, reactive policy (e.g., a deep neural network) deployed at test time, and a slow, non-reactive policy (e.g., Tree Search), that can plan multiple steps ahead. The reactive policy is updated under supervision from the non-reactive policy, while the non-reactive policy is improved with guidance from the reactive policy. In this work we study this Dual Policy Iteration (DPI) strategy in an alternating optimization framework and provide a convergence analysis that extends existing API theory. We also develop a special instance of this framework which reduces the update of non-reactive policies to model-based optimal control using learned local models, and provides a theoretically sound way of unifying model-free and model-based RL approaches with unknown dynamics. We demonstrate the efficacy of our approach on various continuous control Markov Decision Processes.

cs.LG↗

arXiv2018

A Density Functional Tight Binding Layer for Deep Learning of Chemical Hamiltonians

Current neural networks for predictions of molecular properties use quantum chemistry only as a source of training data. This paper explores models that use quantum chemistry as an integral part of the prediction process. This is done by implementing self-consistent-charge Density-Functional-Tight-Binding (DFTB) theory as a layer for use in deep learning models. The DFTB layer takes, as input, Hamiltonian matrix elements generated from earlier layers and produces, as output, electronic properties from self-consistent field solutions of the corresponding DFTB Hamiltonian. Backpropagation enables efficient training of the model to target electronic properties. Two types of input to the DFTB layer are explored, splines and feed-forward neural networks. Because overfitting can cause models trained on smaller molecules to perform poorly on larger molecules, regularizations are applied that penalize non-monotonic behavior and deviation of the Hamiltonian matrix elements from those of the published DFTB model used to initialize the model. The approach is evaluated on 15,700 hydrocarbons by comparing the root mean square error in energy and dipole moment, on test molecules with 8 heavy atoms, to the error from the initial DFTB model. When trained on molecules with up to 7 heavy atoms, the spline model reduces the test error in energy by 60% and in dipole moments by 42%. The neural network model performs somewhat better, with error reductions of 67% and 59% respectively. Training on molecules with up to 4 heavy atoms reduces performance, with both the spline and neural net models reducing the test error in energy by about 53% and in dipole by about 25%.

physics.chem-ph↗

arXiv2018

Tuning the Molecular Weight Distribution from Atom Transfer Radical Polymerization Using Deep Reinforcement Learning

We devise a novel technique to control the shape of polymer molecular weight distributions (MWDs) in atom transfer radical polymerization (ATRP). This technique makes use of recent advances in both simulation-based, model-free reinforcement learning (RL) and the numerical simulation of ATRP. A simulation of ATRP is built that allows an RL controller to add chemical reagents throughout the course of the reaction. The RL controller incorporates fully-connected and convolutional neural network architectures and bases its decision upon the current status of the ATRP reaction. The initial, untrained, controller leads to ending MWDs with large variability, allowing the RL algorithm to explore a large search space. When trained using an actor-critic algorithm, the RL controller is able to discover and optimize control policies that lead to a variety of target MWDs. The target MWDs include Gaussians of various width, and more diverse shapes such as bimodal distributions. The learned control policies are robust and transfer to similar but not identical ATRP reaction settings, even under the presence of simulated noise. We believe this work is a proof-of-concept for employing modern artificial intelligence techniques in the synthesis of new functional polymer materials.

physics.chem-ph↗