arXiv subjects

Thomas Walker

Publications and source records attributed to Thomas Walker.

At least 19 recordsLinked to original sources

arXiv2026

Scute: Exact Batched Serving for PEFT Adapters Beyond LoRA

Existing serving systems for large language models batch requests for many different LoRA adapters on one GPU. However, these systems reject adapters from other parameter-efficient fine-tuning (PEFT) methods such as DoRA, (IA), VeRA and OFT. One solution to this is to convert these adapters to LoRA, but this induces a significant memory and accuracy cost. Instead, we show that, under some modifications, a batched LoRA kernel can serve all of these methods exactly and efficiently. We achieve this by writing each method in one normal form, a LoRA computation with six slots for an adapter's own vectors and matrices. Some slots can merge into an adapter's weights at load time; the others remain live and induce a cost. We give ways to efficiently pay this cost and predict it from a zero-parameter byte model. We package this system, Scute, and build it on top of vLLM. Scute serves all five methods, coming as checkpoints from the Hugging Face PEFT library, in one batch, and it matches that library with a mean error of at most 1.5% of each adapter's effect. Under a burst of requests on an RTX A6000, a mix of these methods takes 5-17% more decode time than the same number of LoRA adapters. Furthermore, using Scute, the same GPU can serve 64 to 1024 (IA) and VeRA adapters at 1.5x to at least 2.5x the request rate of their LoRA conversions.

cs.LG↗

arXiv2026

Improving Generative Model Self-Training with Geometrically Modified Outputs

Self-training generative models - the continued improvement of a model using its own outputs - is becoming increasingly important as high-quality training data becomes scarce. However, naively finetuning on model-generated samples leads to degradation through model collapse and the model autophagy disorder. Negative-guidance self-training methods turn this degradation into a useful signal, using a model finetuned on its own outputs to guide the original model toward improved generation. Existing methods, however, take the negative signal in standard model outputs as given. We instead ask whether this signal can be explicitly strengthened. We introduce Geometrically Modified Outputs (GMOs), which reweight the singular values of the generator's input-output Jacobian to increase the influence of its leading singular directions. This geometric modification amplifies the mode-seeking behavior and distortions of standard outputs, providing a stronger and more targeted negative signal for self-training. Across a range of one-step generative models, GMOs consistently improve the performance of negative-guidance methods, including Neon and SIMS, compared with using standard model outputs.

cs.LG↗

arXiv2026

Behavioral Monitoring of JEPA World Models with Jacobian Centroids

Detecting failures in World Model (WM)-based planning requires monitoring whether the model is behaviorally aligned with the current task, which in turn requires studying its internal representations. Here, we show that centroids---sub-component Jacobian row-sums---effectively identify the behavioral properties of WMs, complementing traditional activation-based knowledge signals. The centroids of a model are easily computed through Jacobian vector products and characterize how the model organizes the geometry of its input space, yielding an efficient perspective on internal representations, including the generation of task-relevant saliency maps. Evaluated on continuous control tasks using JEPA WMs, this behavioral view reveals a structural dissociation, where the encoder correctly represents the goal while the predictor remains behaviorally unresponsive. This failure mode directly predicts planning failure before any action is taken, allowing for goal resampling to recapture out-of-distribution success. Moreover, centroid-based methods outperform baseline methods as distribution-shift detectors. Together, these tools yield a behavioral monitoring stack that is operational and consequential under distribution shifts.

cs.LG↗

arXiv2026

A Computational Tropical Geometry Framework for Neural Networks

We propose a computational tropical geometry framework for the symbolic analysis of neural networks with tropical activations. The number of linear regions of a neural network has been actively studied as a measure of the expressivity of a given architecture. To study these, we work in the setting of tropical geometry---a combinatorial and polyhedral variant of algebraic geometry---where there are known connections between tropical rational maps and feedforward neural networks. We expand this connection by developing concrete computational tools for studying the linear regions of neural networks. We present an algorithm, together with a proof of correctness, which computes the linear regions of a neural network as explicit unions of polyhedra. We further relate the computation of the number of linear regions of a tropical expression to the number of monomials that appear in it, and show how tropical expressions can often be pruned to remove redundant monomials. We introduce the Hoffman constant of a neural network's tropical expression, a geometric quantity that controls the distance from any point in the input space to the farthest linear region. We provide the open source Julia library TropicalNN.jl, which is built on top of the OSCAR computer algebra system and implements the algorithms mentioned above to analyze neural networks symbolically using their tropical representations. We present a set of proof-of-concept computational examples to demonstrate how our tropical geometric theory can be applied to reveal insights on the expressivity of a network architecture.

cs.LG↗

arXiv2026

Beyond Pixel Histories: World Models with Persistent 3D State

Interactive world models continually generate video by responding to a user's actions, enabling open-ended generation capabilities. However, existing models typically lack a 3D representation of the environment, meaning 3D consistency must be implicitly learned from data, and spatial memory is restricted to limited temporal context windows. This results in an unrealistic user experience and presents significant obstacles to downstream tasks such as training agents. To address this, we present PERSIST, a new paradigm of world model which simulates the evolution of a latent 3D scene: environment, camera, and renderer. This allows us to synthesise new frames with persistent spatial memory and consistent geometry. Both quantitative metrics and a qualitative user study show substantial improvements in spatial memory, 3D consistency, and long-horizon stability over existing methods, enabling coherent, evolving 3D worlds. We further demonstrate novel capabilities, including synthesising diverse 3D environments from a single image, as well as enabling fine-grained, geometry-aware control over generated experiences by supporting environment editing and specification directly in 3D space. Project page: https://francelico.github.io/persist.github.io

cs.CV↗

arXiv2026

Semantic Foam: Unifying Spatial and Semantic Scene Decomposition

Modern scene reconstruction methods, such as 3D Gaussian Splatting, deliver photo-realistic novel view synthesis at real-time speeds, yet their adoption in interactive graphics applications has been limited. A major bottleneck is the difficulty of interacting with these representations compared to traditional, human-authored 3D assets. While previous research has attempted to impose semantic decomposition on these models, significant challenges remain regarding segmentation quality and consistency. To address this, we introduce Semantic Foam, extending the recently proposed Radiant Foam representations to semantic decomposition tasks. Our approach integrates the natural spatial volumetric decomposition of Radiant Foam's Voronoi mesh with an explicit semantic feature field parameterized at the cell level. This explicit structure enables direct spatial regularization, which prevents artifacts caused by occlusion or inconsistent supervision across views - common pitfalls for other point-based representations. Experimental results show that our method achieves comparable or superior object-level segmentation performance compared to state-of-the-art methods like Gaussian Grouping and SAGA.

cs.CV↗

arXiv2026

The Geometric Structure of Models Learning Sparse Data

The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the training data provides a sufficiently dense sample of the underlying low-dimensional data manifold, or where such a low-dimensional manifold is conceivably present. We describe the regimes where the MH is not applicable as sparse. In this paper, we demonstrate that models succeed in the sparse regime by exploiting a highly structured local geometry, a property we formalize as normal alignment. We prove that normal-aligned classifiers -- whose input-output Jacobians are rank-one and align perfectly with the training data -- minimize the training objective under norm constraints and achieve maximal local robustness under a non-zero Jacobian constraint. For continuous piecewise-affine deep networks, normal alignment manifests geometrically as centroid alignment within the network's induced power diagram partition and results from the feature-learning regime. Motivated by these theoretical insights, we introduce GrokAlign, a regularization strategy that actively induces normal alignment. We demonstrate that GrokAlign significantly accelerates the training dynamics of deep networks relevant to the grokking phenomenon. Furthermore, we apply the principle of normal alignment to Recursive Feature Machines (RFMs) to introduce Recursive Feature Alignment Machines (RFAMs). We show that RFAMs exhibit greater adversarial robustness compared to RFMs when trained on tabular data.

cs.LG↗

arXiv2026

The Linear Centroids Hypothesis: Features as Directions Learned by Local Experts

The Linear Representation Hypothesis (LRH) identifies features of a trained deep network (DN) as linear directions in the activation spaces, i.e., output spaces of intermediate layers. This characterization decouples the input-output maps learned by a DN from the organization of feature directions in its activation spaces. We introduce the Linear Centroids Hypothesis (LCH), which instead identifies features with linear directions among a DN's centroid spaces -- where any vector denotes a centroid or summary of a local affine expert characterizing the learned input-output maps of the DN exactly (e.g., for piecewise-affine DNs) or approximately (e.g., for smooth DNs like transformers). We show that replacing intermediate activations with centroids yields a functional drop-in alternative for standard interpretability tools. Empirically, this change yields sparser, more downstream-useful feature dictionaries on DINO ViTs, suppresses spurious directions on a controlled task, recovers interpretable circuits in GPT2-Large, and produces faithful gradient-based saliency maps. LCH unifies dictionaries, probing, circuits, and saliency maps into a single geometric object grounded in the network's input-output map -- making interpretability mechanistic by construction rather than post hoc. Code to study the LCH https://github.com/ThomasWalker1/LinearCentroidsHypothesis .

cs.LG↗

arXiv2026

A High-Flux Source of Cold Strontium with a Loading Rate of $4 \times 10^{10}$ atoms/s for Open Release

We present a high-flux source of cold strontium atoms based on a two-dimensional magneto-optical trap (2D MOT) and a Zeeman slower. We use the source to load a 3D MOT in a separate science chamber, observing a loading rate of $4 \times 10^{10}$ atoms/s -- to our knowledge, the highest reported loading flux for strontium. To characterise the vacuum pressure in the science chamber, we load the atoms into a magnetic trap and measure a lifetime of between 8 and 24 seconds, depending on oven temperature. Finally, we characterise the atom flux and velocity distributions from the oven and from the 2D MOT source, finding reasonable agreement with models in the free molecular flow regime. Our results show it is possible to readily produce a cold strontium flux at comparable levels to alkali species, at oven temperatures compatible with long-term operation, and at vacuum pressures suitable for state-of-the-art quantum experiments. We make our design available at no cost, to benefit researchers in the quantum community.

cond-mat.quant-gas↗

arXiv2025

GrokAlign: Geometric Characterisation and Acceleration of Grokking

A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustness to input perturbations, also known as grokking. Prior work has associated phenomena like delayed generalisation with the transition of a deep network from a linear to a feature learning regime, and emergent robustness with changes to the network's functional geometry, in particular the arrangement of the so-called linear regions in deep networks employing continuous piecewise affine nonlinearities. Here, we explain how grokking is realised in the Jacobian of a deep network and demonstrate that aligning a network's Jacobians with the training data (in the sense of cosine similarity) ensures grokking under a low-rank Jacobian assumption. Our results provide a strong theoretical motivation for the use of Jacobian regularisation in optimizing deep networks -- a method we introduce as GrokAlign -- which we show empirically to induce grokking much sooner than more conventional regularizers like weight decay. Moreover, we introduce centroid alignment as a tractable and interpretable simplification of Jacobian alignment that effectively identifies and tracks the stages of deep network training dynamics. Accompanying webpage (https://thomaswalker1.github.io/blog/grokalign.html) and code (https://github.com/ThomasWalker1/grokalign).

cs.LG↗

arXiv2025

Magnetic Feshbach resonances in Ba$^+$+Li collisions due to strong spin-orbit coupling

We report a pronounced dependence of magnetic Feshbach resonance spectra on the initial hyperfine-Zeeman state of Li in ultracold $^{138}$Ba$^+$+$^6$Li collisions. The measured number and distribution of resonances differ significantly between the two lowest states despite their similar electron spin character. We address this puzzle by developing a comprehensive yet generic computational model calibrated against key statistical features in the experimental spectrum. We confirm that strong spin-orbit coupling induces essential changes in the distribution of resonances, leading to an increase in the number of resolvable resonances. Our model reproduces the statistics of the spectrum with the lowest Li state but struggles with the second-lowest state, where a significantly smaller number of resonances is experimentally observed.

physics.atom-ph↗

arXiv2025

CrossSDF: 3D Reconstruction of Thin Structures From Cross-Sections

Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due to the data sparsity between slicing planes, while current bespoke methods struggle to reconstruct thin geometric structures and preserve topological continuity. This is important for medical applications where thin vessel structures are present in CT and MRI scans. This paper introduces CrossSDF, a novel approach for extracting a 3D signed distance field from 2D signed distances generated from planar contours. Our approach makes the training of neural SDFs contour-aware by using losses designed for the case where geometry is known within 2D slices. Our results demonstrate a significant improvement over existing methods, effectively reconstructing thin structures and producing accurate 3D models without the interpolation artifacts or over-smoothing of prior approaches.

cs.CV↗

arXiv2025

Exploring atom-ion Feshbach resonances below the s-wave limit

Revealing the quantum properties of matter requires a high degree of experimental control accompanied by a profound theoretical understanding. At ultracold temperatures, quantities that appear continuous in everyday life, such as the motional angular momentum of two colliding particles, become quantized, leaving a measurable imprint on experimental results. Embedding a single particle within a larger quantum bath at lowest temperatures can result in resonant partial-wave dependent interaction, whose strength near zero energy is dictated by universal threshold scaling laws. Hybrid atom-ion systems have emerged as a novel platform in which a single charged atom in an ultracold bath serves as a well-controlled impurity of variable energy. However, entering the low-energy s-wave regime and exploring the role of higher-partial-wave scattering within has remained an open challenge. Here, we immerse a Barium ion in a cloud of ultracold spin-polarized Lithium atoms, realize tunable collision energies below the s-wave limit and explore resonant higher-partial-wave scattering by studying the energy dependence of Feshbach resonances. Utilizing precise electric field control, we tune the collision energy over four orders of magnitude, reaching from the many-parital-wave to the s-wave regime. At the lowest energies, we probe the energy dependence of an isolated s-wave Feshbach resonance and introduce a theoretical model that allows to distinguish it from higher-partial-wave resonances. Additionally, at energies around the p-wave barrier, we find and identify an open-channel f-wave resonance, consistent with threshold laws. Our findings highlight and benchmark the importance of higher-partial-wave scattering well within the s-wave regime and offer control over chemical reactions and complex many-body dynamics in atom-ion ensembles - on the level of individual angular momentum quanta.

physics.atom-ph↗

arXiv2024

Concept Boundary Vectors

Machine learning models are trained with relatively simple objectives, such as next token prediction. However, on deployment, they appear to capture a more fundamental representation of their input data. It is of interest to understand the nature of these representations to help interpret the model's outputs and to identify ways to improve the salience of these representations. Concept vectors are constructions aimed at attributing concepts in the input data to directions, represented by vectors, in the model's latent space. In this work, we introduce concept boundary vectors as a concept vector construction derived from the boundary between the latent representations of concepts. Empirically we demonstrate that concept boundary vectors capture a concept's semantic meaning, and we compare their effectiveness against concept activation vectors.

cs.LG↗

arXiv2024

Spatially-Adaptive Hash Encodings For Neural Surface Reconstruction

Positional encodings are a common component of neural scene reconstruction methods, and provide a way to bias the learning of neural fields towards coarser or finer representations. Current neural surface reconstruction methods use a "one-size-fits-all" approach to encoding, choosing a fixed set of encoding functions, and therefore bias, across all scenes. Current state-of-the-art surface reconstruction approaches leverage grid-based multi-resolution hash encoding in order to recover high-detail geometry. We propose a learned approach which allows the network to choose its encoding basis as a function of space, by masking the contribution of features stored at separate grid resolutions. The resulting spatially adaptive approach allows the network to fit a wider range of frequencies without introducing noise. We test our approach on standard benchmark surface reconstruction datasets and achieve state-of-the-art performance on two benchmark datasets.

cs.CV↗

arXiv2024

Tightening the Evaluation of PAC Bounds Using Formal Verification Results

Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity. However, current state-of-the-art results are loose in approximating the generalisation capacity of deployed machine learning models. Consequently, while PAC bounds are theoretically useful, their applicability for evaluating a model's generalisation property in a given operational design domain is limited. The underlying classical theory is supported by the idea that bounds can be tightened when the number of test points available to the user to evaluate the model increases. Yet, in the case of neural networks, the number of test points required to obtain bounds of interest is often impractical even for small problems. In this paper, we take the novel approach of using the formal verification of neural systems to inform the evaluation of PAC bounds. Rather than using pointwise information obtained from repeated tests, we use verification results on regions around test points. We show that conditioning existing bounds on verification results leads to a tightening proportional to the underlying probability mass of the verified region.

cs.LG↗

arXiv2023

Explicit Neural Surfaces: Learning Continuous Geometry With Deformation Fields

We introduce Explicit Neural Surfaces (ENS), an efficient smooth surface representation that directly encodes topology with a deformation field from a known base domain. We apply this representation to reconstruct explicit surfaces from multiple views, where we use a series of neural deformation fields to progressively transform the base domain into a target shape. By using meshes as discrete surface proxies, we train the deformation fields through efficient differentiable rasterization. Using a fixed base domain allows us to have Laplace-Beltrami eigenfunctions as an intrinsic positional encoding alongside standard extrinsic Fourier features, with which our approach can capture fine surface details. Compared to implicit surfaces, ENS trains faster and has several orders of magnitude faster inference times. The explicit nature of our approach also allows higher-quality mesh extraction whilst maintaining competitive surface reconstruction performance and real-time capabilities.

cs.CV↗

arXiv2023

Spherical Feature Pyramid Networks For Semantic Segmentation

Semantic segmentation for spherical data is a challenging problem in machine learning since conventional planar approaches require projecting the spherical image to the Euclidean plane. Representing the signal on a fundamentally different topology introduces edges and distortions which impact network performance. Recently, graph-based approaches have bypassed these challenges to attain significant improvements by representing the signal on a spherical mesh. Current approaches to spherical segmentation exclusively use variants of the UNet architecture, meaning more successful planar architectures remain unexplored. Inspired by the success of feature pyramid networks (FPNs) in planar image segmentation, we leverage the pyramidal hierarchy of graph-based spherical CNNs to design spherical FPNs. Our spherical FPN models show consistent improvements over spherical UNets, whilst using fewer parameters. On the Stanford 2D-3D-S dataset, our models achieve state-of-the-art performance with an mIOU of 48.75, an improvement of 3.75 IoU points over the previous best spherical CNN.

cs.CV↗