arXiv subjects

Michael Murray

Publications and source records attributed to Michael Murray.

At least 19 recordsLinked to original sources

arXiv2026

Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm

Sharpness-Aware Minimization (SAM) aims to improve generalization by encouraging insensitivity to small, worst-case parameter perturbations. However, the notion of a "small" perturbation is inherently geometry-dependent: while existing SAM variants have explored a wide range of choices, a clear perspective on which geometries are most effective in practice remains elusive. Recent work on matrix-aware optimization, particularly the Muon optimizer, suggests that respecting the matrix structure of hidden-layer weights can lead to strong empirical performance. Motivated by this, we study matrix-aware geometry in both stages of SAM: we introduce a layerwise spectral inner perturbation for matrix-valued hidden-layer parameters and combine it with either AdamW/SGDW or Muon in the outer update. Across ImageNet-1K experiments on ViT-Small/16 and ResNet-50, we find that the combination of a spectral inner step with a Muon outer step performs consistently strongly, achieving the best validation accuracy on both models among the evaluated methods.

cs.LG↗

arXiv2026

A Few Words Go a Long Way: Language Guided Robot Policy Synthesis

While vision-language-action models have demonstrated impressive zero-shot manipulation capabilities, they remain fundamentally black box policies that are difficult to interpret, adapt, or correct when they inevitably fail. In this work, we propose ARCHITECT, a framework that treats robot policy acquisition as an interactive program synthesis task. ARCHITECT leverages the reasoning capabilities of LLM coding agents to synthesize modular robot programs that utilize a suite of perception and control tools. Unlike end-to-end models where distribution shift leads to unpredictable, cascading failures, our modular architecture allows users to isolate failures and localize feedback at the level of abstraction required. We introduce an iterative process where a human supervisor provides natural language corrections to steer the policy. These corrections are grounded in the policy code by program execution traces and distilled into a persistent skill library, a form of long-term in-context learning which enables the agent to accumulate a repertoire of reusable, interpretable behaviors. In a benchmark evaluation on a Franka Panda robot, ARCHITECT outperforms state-of-the-art VLA models and program synthesis baselines on complex, long-horizon tasks, including articulated object manipulation and cloth folding. Our results demonstrate that the synthesized skill library enables the system to transfer to novel tasks with decreasing human intervention, providing a steerable and data-efficient alternative to black-box robot learning. Website: https://robo-architect.github.io/

cs.RO↗

arXiv2026

FlowDAgger: Human-in-the-Loop Adaptation of Generative Robot Policies in Latent Space

Pretrained generative robot policies based on flow matching and diffusion have achieved impressive results across a wide range of manipulation tasks. Yet real-world deployments routinely expose failure modes outside the pretraining distribution. Closing these gaps typically requires large-scale data collection or online reinforcement learning on physical hardware, which is impractical for rapid and safe adaptation. We present FlowDAgger, a sample- and compute-efficient method for adapting frozen generative robot policies from human interventions in latent space. Our key idea is action inversion: each human expert action is mapped to the noise that would have produced it under the frozen base policy, using reverse-time integration followed by local refinement. The resulting inverted noise provides supervision for a lightweight latent policy that steers the base model at deployment time, enabling rapid skill acquisition while preserving its behavioral priors. We evaluate FlowDAgger in simulation and on real-world bimanual and single-arm manipulation, adapting both action-head VLAs and world-action models from a handful of interventions. FlowDAgger outperforms supervised fine-tuning and latent-space RL baselines and preserves pretrained skills on held-out tasks, offering a practical path for adapting robot foundation models in the real world. Website: https://microsoft.github.io/FlowDAgger

cs.RO↗

arXiv2026

Benchmarking Affordance Generalization with BusyBox

Vision-Language-Action (VLA) models have been attracting the attention of researchers and practitioners thanks to their promise of generalization. Although single-task policies still offer competitive performance, VLAs are increasingly able to handle commands and environments unseen in their training set. While generalization in vision and language space is undoubtedly important for robust versatile behaviors, a key meta-skill VLAs need to possess is affordance generalization -- the ability to manipulate new objects with familiar physical features. In this work, we present BusyBox, a physical benchmark for systematic semi-automatic evaluation of VLAs' affordance generalization. BusyBox consists of 6 modules with switches, sliders, wires, buttons, a display, and a dial. The modules can be swapped and rotated to create a multitude of BusyBox variations with different visual appearances but the same set of affordances. We empirically demonstrate that generalization across BusyBox variants is highly challenging even for strong open-weights VLAs such as $\pi_{0.5}$ and GR00T-N1.6. To encourage the research community to evaluate their own VLAs on BusyBox and to propose new affordance generalization experiments, we have designed BusyBox to be easy to build in most robotics labs. We release the full set of CAD files for 3D-printing its parts as well as a bill of materials for (optionally) assembling its electronics. We also publish a dataset of language-annotated demonstrations that we collected using the common bimanual Mobile Aloha robot on the canonical BusyBox configuration. All of the released materials are available at https://microsoft.github.io/BusyBox.

cs.RO↗

arXiv2025

Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits

Many learning problems are organized by group symmetries. While invariance is often imposed through architectures or group averaging, we ask when it can emerge from training on a finite random subset of an orbit. We study this question in classical Hopfield networks, where strict memorization can be expressed as a linear margin problem. Reparameterizing minimization of energy flow (MEF) as an exponential loss connects gradient descent to the corresponding minimum-norm hard-margin memorizer. Our main result shows that, for independent uniform samples from any finite permutation orbit, the exact sample hard-margin support vector machine (HSVM) concentrates exponentially around the invariant full-orbit HSVM. Consequently, an orbit-size-independent polynomial number of samples suffices both for approximate parameter invariance and for simultaneous memorization of every orbit element; directional convergence transfers this conclusion asymptotically to MEF gradient descent. For graph-isomorphism orbits, we characterize the invariant parameters as a three-dimensional subspace and show that every such orbit is memorizable. For cliques of fixed linear density, additional symmetry sharpens the uniform memorization bound to $O(v^4\log(1/\delta))$, exponentially smaller than the orbit size. Together with experiments across several learning rules, these results give a finite-sample account of how optimization bias can recover symmetry from partial group-structured data.

cs.LG↗

arXiv2025

Guarding Against Malicious Biased Threats (GAMBiT): Experimental Design of Cognitive Sensors and Triggers with Behavioral Impact Analysis

This paper introduces GAMBiT (Guarding Against Malicious Biased Threats), a cognitive-informed cyber defense framework that leverages deviations from human rationality as a new defensive surface. Conventional cyber defenses assume rational, utility-maximizing attackers, yet real-world adversaries exhibit cognitive constraints and biases that shape their interactions with complex digital systems. GAMBiT embeds insights from cognitive science into cyber environments through cognitive triggers, which activate biases such as loss aversion, base-rate neglect, and sunk-cost fallacy, and through newly developed cognitive sensors that infer attackers' cognitive states from behavioral and network data. Three rounds of human-subject experiments (total n=61) in a simulated small business network demonstrate that these manipulations significantly disrupt attacker performance, reducing mission progress, diverting actions off the true attack path, and increasing detectability. These results demonstrate that cognitive biases can be systematically triggered to degrade the attacker's efficiency and enhance the defender's advantage. GAMBiT establishes a new paradigm in which the attacker's mind becomes part of the battlefield and cognitive manipulation becomes a proactive vector for cyber defense.

cs.CR↗

arXiv2025

Low Rank Gradients and Where to Find Them

This paper investigates low-rank structure in the gradients of the training loss for two-layer neural networks while relaxing the usual isotropy assumptions on the training data and parameters. We consider a spiked data model in which the bulk can be anisotropic and ill-conditioned, we do not require independent data and weight matrices and we also analyze both the mean-field and neural-tangent-kernel scalings. We show that the gradient with respect to the input weights is approximately low rank and is dominated by two rank-one terms: one aligned with the bulk data-residue , and another aligned with the rank one spike in the input data. We characterize how properties of the training data, the scaling regime and the activation function govern the balance between these two components. Additionally, we also demonstrate that standard regularizers, such as weight decay, input noise and Jacobian penalties, also selectively modulate these components. Experiments on synthetic and real data corroborate our theoretical predictions.

cs.LG↗

arXiv2024

Bounds for the smallest eigenvalue of the NTK for arbitrary spherical data of arbitrary dimension

Bounds on the smallest eigenvalue of the neural tangent kernel (NTK) are a key ingredient in the analysis of neural network optimization and memorization. However, existing results require distributional assumptions on the data and are limited to a high-dimensional setting, where the input dimension $d_0$ scales at least logarithmically in the number of samples $n$. In this work we remove both of these requirements and instead provide bounds in terms of a measure of the collinearity of the data: notably these bounds hold with high probability even when $d_0$ is held constant versus $n$. We prove our results through a novel application of the hemisphere transform.

stat.ML↗

arXiv2024

Benign overfitting in leaky ReLU networks with moderate input dimension

The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two-layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data that can be decomposed into the sum of a common signal and a random noise component, that lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign (or harmful) overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non-benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension $d$ and training sample size $n$, while results in prior work require $d = \Omega(n^2 \log n)$, here we require only $d = \Omega\left(n\right)$.

cs.LG↗

arXiv2023

Training shallow ReLU networks on noisy data using hinge loss: when do we overfit and is it benign?

We study benign overfitting in two-layer ReLU networks trained using gradient descent and hinge loss on noisy data for binary classification. In particular, we consider linearly separable data for which a relatively small proportion of labels are corrupted or flipped. We identify conditions on the margin of the clean data that give rise to three distinct training outcomes: benign overfitting, in which zero loss is achieved and with high probability test data is classified correctly; overfitting, in which zero loss is achieved but test data is misclassified with probability lower bounded by a constant; and non-overfitting, in which clean points, but not corrupt points, achieve zero loss and again with high probability test data is classified correctly. Our analysis provides a fine-grained description of the dynamics of neurons throughout training and reveals two distinct phases: in the first phase clean points achieve close to zero loss, in the second phase clean points oscillate on the boundary of zero loss while corrupt points either converge towards zero loss or are eventually zeroed by the network. We prove these results using a combinatorial approach that involves bounding the number of clean versus corrupt updates across these phases of training.

cs.LG↗

arXiv2023

Mildly Overparameterized ReLU Networks Have a Favorable Loss Landscape

We study the loss landscape of both shallow and deep, mildly overparameterized ReLU neural networks on a generic finite input dataset for the squared error loss. We show both by count and volume that most activation patterns correspond to parameter regions with no bad local minima. Furthermore, for one-dimensional input data, we show most activation regions realizable by the network contain a high dimensional set of global minima and no bad local minima. We experimentally confirm these results by finding a phase transition from most regions having full rank Jacobian to many regions having deficient rank depending on the amount of overparameterization.

cs.LG↗

arXiv2022

Characterizing the Spectrum of the NTK via a Power Series Expansion

Under mild conditions on the network initialization we derive a power series expansion for the Neural Tangent Kernel (NTK) of arbitrarily deep feedforward networks in the infinite width limit. We provide expressions for the coefficients of this power series which depend on both the Hermite coefficients of the activation function as well as the depth of the network. We observe faster decay of the Hermite coefficients leads to faster decay in the NTK coefficients and explore the role of depth. Using this series, first we relate the effective rank of the NTK to the effective rank of the input-data Gram. Second, for data drawn uniformly on the sphere we study the eigenvalues of the NTK, analyzing the impact of the choice of activation function. Finally, for generic data and activation functions with sufficiently fast Hermite coefficient decay, we derive an asymptotic upper bound on the spectrum of the NTK.

cs.LG↗

arXiv2021

Activation function design for deep networks: linearity and effective initialisation

The activation function deployed in a deep neural network has great influence on the performance of the network at initialisation, which in turn has implications for training. In this paper we study how to avoid two problems at initialisation identified in prior works: rapid convergence of pairwise input correlations, and vanishing and exploding gradients. We prove that both these problems can be avoided by choosing an activation function possessing a sufficiently large linear region around the origin, relative to the bias variance $\sigma_b^2$ of the network's random initialisation. We demonstrate empirically that using such activation functions leads to tangible benefits in practice, both in terms test and training accuracy as well as training time. Furthermore, we observe that the shape of the nonlinear activation outside the linear region appears to have a relatively limited impact on training. Finally, our results also allow us to train networks in a new hyperparameter regime, with a much larger bias variance than has previously been possible.

cs.LG↗

arXiv2020

Non associative magnetic translations from parallel transport in projective Hilbert bundles

The non-associativity of translations in a quantum system with magnetic field background has received renewed interest in association with topologically trivial gerbes over $\mathbb{R}^n.$ The non-associativity is described by a 3-cocycle of the group $\mathbb{R}^n$ with values in the unit circle $S^1.$ The gerbes over a space $M$ are topologically classified by the Dixmier-Douady class which is an element of $\mathrm{H}^3(M,\mathbb{Z}).$ However, there is a finer description in terms of local differential forms of degrees $d=0,1,2,3$ and the case of the magnetic translations for $n=3$ the 2-form part is the magnetic field $B$ with non zero divergence. In this paper we study a quantum field theoretic construction in terms of $n$-component fermions on a circle. The non associativity arises when trying to lift the translation group action on the 1-particle system to the second quantized system.

math-ph↗

arXiv2020

Representation Learning for High-Dimensional Data Collection under Local Differential Privacy

The collection of individuals' data has become commonplace in many industries. Local differential privacy (LDP) offers a rigorous approach to preserving privacy whereby the individual privatises their data locally, allowing only their perturbed datum to leave their possession. LDP thus provides a provable privacy guarantee to the individual against both adversaries and database administrators. Existing LDP mechanisms have successfully been applied to low-dimensional data, but in high dimensions the privacy-inducing noise largely destroys the utility of the data. In this work, our contributions are two-fold: first, by adapting state-of-the-art techniques from representation learning, we introduce a novel approach to learning LDP mechanisms. These mechanisms add noise to powerful representations on the low-dimensional manifold underlying the data, thereby overcoming the prohibitive noise requirements of LDP in high dimensions. Second, we introduce a novel denoising approach for downstream model learning. The training of performant machine learning models using collected LDP data is a common goal for data collectors, and downstream model performance forms a proxy for the LDP data utility. Our approach significantly outperforms current state-of-the-art LDP mechanisms.

cs.LG↗

arXiv2020

New opportunities at the photon energy frontier

Ultra-peripheral collisions (UPCs) involving heavy ions and protons are the energy frontier for photon-mediated interactions. UPC photons can be used for many purposes, including probing low-$x$ gluons via photoproduction of dijets and vector mesons, probes of beyond-standard-model processes, such as those enabled by light-by-light scattering, and studies of two-photon production of the Higgs.

hep-ph↗

arXiv2020

Encoder blind combinatorial compressed sensing

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has access to the encoder matrix, which in the combinatorial case is sparse and binary. In this paper we consider the problem of designing a decoder to recover a set of sparse codes from their linear measurements alone, that is without access to encoder matrix. To this end we study the matrix factorisation task of recovering both the encoder and sparse coding matrices from the associated linear measurement matrix. The contribution of this paper is a computationally efficient decoding algorithm, Decoder-Expander Based Factorisation, with strong performance guarantees. In particular, under mild assumptions on the sparse coding matrix and by deploying a novel random encoder matrix, we prove that Decoder-Expander Based Factorisation recovers both the encoder and sparse coding matrix at the optimal measurement rate with high probability and from a near optimal number of measurement vectors. In addition, our experiments demonstrate the efficacy and computational efficiency of our algorithm in practice. Beyond compressed sensing our results may be of interest for researchers working in areas such as linear sketching, coding theory and matrix compression.

cs.LG↗

arXiv2019

Vision-and-Dialog Navigation

Robots navigating in human environments should use language to ask for assistance and be able to understand human responses. To study this challenge, we introduce Cooperative Vision-and-Dialog Navigation, a dataset of over 2k embodied, human-human dialogs situated in simulated, photorealistic home environments. The Navigator asks questions to their partner, the Oracle, who has privileged access to the best next steps the Navigator should take according to a shortest path planner. To train agents that search an environment for a goal location, we define the Navigation from Dialog History task. An agent, given a target object and a dialog history between humans cooperating to find that object, must infer navigation actions towards the goal in unexplored environments. We establish an initial, multi-modal sequence-to-sequence model and demonstrate that looking farther back in the dialog history improves performance. Sourcecode and a live interface demo can be found at https://cvdn.dev/

cs.CL↗