arXiv subjects

Simon Lucey

Publications and source records attributed to Simon Lucey.

At least 19 recordsLinked to original sources

arXiv2026

Language Models Can Benefit from Domain-Specific Inductive Biases

Language models are typically trained with a single choice of architecture on diverse domains and data sources. Modern transformers have been extensively refined for such general-purpose learning, but are they equally effective across different subsets of the pretraining data? We investigate this question by training small language models from scratch on representative subsets of pretraining data such as web text, code, and mathematics. We introduce variants of transformers in which standard activation functions are replaced with learned splines tuned on specific datasets, providing a simple way to modify their inductive biases. Using a mix-and-match of architectures and datasets, we evaluate cross-domain transfer, i.e. how well does an architecture tuned for one domain perform on data from another? We find that the tuned transformer variants improve training efficiency or generalization on all seven of our tested datasets, but the gains are often domain-specific. For example, architectures tuned on a natural language dataset such as FineWeb perform well on TinyStories, whereas those tuned on mathematics perform poorly on natural language. We identify several mechanisms underlying these improvements, including wider loss basins and more abundant "lottery tickets". Our results show that different subsets of pretraining data can benefit from different learning mechanisms, highlighting a limitation of the prevailing trend towards a small set of general-purpose architectures and optimizers. This points to an opportunity to improve data efficiency by developing domain-specific learning strategies that retain the ability to train general-purpose models.

cs.LG↗

arXiv2026

Making Transformers Logical

Transformers do not merely lack data on some Boolean extrapolation tasks; they generalize in a systematically wrong way. Recent work on generalization on the unseen has shown that, despite fitting the observed domain, Transformers often extrapolate according to a simpler minimum-degree interpolator rather than the true target function. These Boolean tasks are not practical applications, but controlled stress tests for understanding Transformer inductive bias. We ask whether this failure mode can be corrected by injecting explicit structural priors into attention. Existing structured-initialization methods alter Transformer inductive bias indirectly, by choosing query and key projections whose similarity scores approximate a desired attention pattern. However, we find that when applied to Boolean extrapolation, these QK-based priors can be rapidly overwritten during training and fail to change the learned extrapolation rule. We propose a simpler alternative: initialize the additive attention mask directly. Unlike standard hard masks used for causality or locality attention, our mask is a finite, learnable attention-logit bias initialized from task-level interaction structure. This separates the structural prior from content-dependent attention scores, allowing it to persist throughout optimization. On Boolean reasoning tasks, mask-based initialization achieves near-perfect extrapolation where vanilla and QK-initialized Transformers remain trapped by the default inductive bias. The same mechanism also improves low-data arithmetic performance and remains competitive on vision and language benchmarks. These results show that attention masks can serve not only as architectural constraints, but as a simple substrate for encoding persistent inductive bias in Transformers.

cs.AI↗

arXiv2026

Should We Skip Diffusion?

Diffusion models learn semantic representations while generating images. In the Decoupled Diffusion Transformer (DDT), a condition encoder provides features that guide a velocity decoder in denoising. To enable effective denoising at all noise levels, these features must capture both high-level abstract structures and low-level details. However, skip/residual connections in the encoder allow shallow features to bypass successive transformations, which may limit progressive abstraction, or at least make it difficult to disentangle different levels of abstraction. We propose DDT-RFE, which removes the residual connections around the Self-Attention and MLP operations in each encoder block while maintaining stable training. To retain the information that abstraction discards but that the decoder still needs, we fuse the input patch embedding with intermediate and final encoder features to form the encoder output. The decoder thus has access to information from multiple encoder depths, while each encoder block is able to learn more abstract representations. DDT-RFE achieves overall improvements over DDT across visual understanding tasks, including image classification, semantic segmentation, object discovery, and semantic correspondence, while using fewer encoder blocks. It also achieves a lower FID for image generation on ImageNet.

cs.LG↗

arXiv2026

Optimizer Geometry Sets the Pace: Spectral Learning Dynamics in Matrix Factorization

Recent successes of matrix- and curvature-based optimizers have renewed interest in how update geometry shapes learning. These methods normalize or precondition updates, changing how different components progress during training. In deep matrix factorization, the geometry that slows gradient descent (GD) favors low-rank solutions by delaying the emergence of small singular modes. This raises the question of what remains of that spectral bias when normalization or curvature correction weakens or removes the slowdown. We study how optimizer geometry and depth jointly govern this behavior through a common framework for singular mode dynamics. Under explicit balance and alignment assumptions, we derive birth, saturation, and decay laws for Euclidean GD, coordinate-wise updates of SignGD and an instantaneous Adam approximation, spectral updates of Muon and cumulative Shampoo, and a block curvature model of K-FAC. The resulting picture is not a simple ordering from stronger to weaker low-rank bias. To highlight, SignGD and ideal Muon eliminate the divergent birth barrier and drive unsupported modes to zero in finite time. Cumulative Shampoo initially retains GD's depth-dependent barrier, then accumulated gradients produce a catch-up phase while making previously active modes increasingly persistent. Undamped K-FAC cancels the factorization-induced slowdown while preserving the ordering of the target singular values, whereas positive damping introduces a spectral threshold below which the slow GD phase laws reappear. These results give normalization, accumulated state, damping, and depth a direct interpretation as controls determining when modes emerge, persist, and disappear during training.

cs.LG↗

arXiv2026

Conditioned Initialization for Attention

Transformers are a dominant architecture in modern machine learning, powering applications across vision, language, and beyond. At the core of their success lies the attention layer, where the query, key, and value matrices determine how token dependencies are captured. While considerable work has focused on scaling and optimizing Transformers, comparatively little attention has been paid to how the weights of the queries, keys and values are initialized. Common practice relies on random initialization or alternatives such as mimetic initialization, which imitates weight patterns from converged models, and weight selection, which transfers weights from a teacher model. In this paper, we argue that initialization can introduce an optimization bias that fundamentally shapes training dynamics. We propose conditioned initialization, a principled scheme that initializes attention weights to improve the spectral properties of the attention layer. Theoretically, we show that conditioned initialization can potentially reduce the condition number of the attention Jacobian, leading to more stable optimization. Empirically, it accelerates convergence and improves generalization across diverse applications, highlighting conditioning as a critical yet underexplored area for advancing Transformer performance. Importantly, conditioned initialization is simple to apply and integrates seamlessly into a wide range of Transformer architectures.

cs.LG↗

arXiv2026

Memory Efficient Tabular Foundation Models

Tabular Foundation Models, such as TabPFN, have received a large amount of recent attention due to their performance on in-context tabular machine learning tasks, which often exceeds classical baselines. However, practical deployment considerations of these models has received less attention. In this paper we investigate the memory requirements for these models. We demonstrate that employing model compression approaches can enable memory reductions of up to 7.6 with similar levels of performance, reducing deployment requirements by nearly 87%. Our work provides insight to practitioners seeking efficient deployment of these models in practical settings.

cs.LG↗

arXiv2026

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks

Transformers are remarkably versatile and their design is largely consistent across a variety of applications. But are they optimal for any given task or dataset? The answer may be key for pushing AI beyond merely scaling current designs. *Method.* We present a method to optimize a transformer architecture for a given dataset, which we use as a tool to study optimal task-specific inductive biases. This method replaces the most important non-linearities (GeLUs,;softmax) with functions learned on held-out data. We then train the resulting architectures on other datasets, as a way to evaluate the compatibility between pairs of tasks. Findings. On algorithmic toy tasks, we identify new architectures with dramatic improvements in learning speed, in- and out-of-distribution generalization, and stability across seeds. The new designs prove very task-specific however, and indicate that these tasks require inductive biases very different from those of standard transformers. On code and language modeling datasets, we also find architectures with consistent, yet smaller improvements. These designs transfer much better across datasets and domains (English & computer code). Implications. Our results show that standard transformers are rarely a local optimum in the space of architectures. Simple alternatives can perform much better but sacrifice universality. This suggests that there may be room for improved architectures that better support multiple capabilities simultaneously, such as fluency and robust reasoning.

cs.LG↗

arXiv2026

G3Splat: Geometrically Consistent Generalizable Gaussian Splatting

3D Gaussians have become a powerful scene representation for real-time splatting and high-quality novel-view synthesis. This has motivated generalizable splatting -- methods that adapt feed-forward geometry prediction networks to produce per-pixel Gaussians from a set of images. However, most generalizable splatting pipelines are supervised primarily through a view-synthesis loss to predict Gaussian orientation, anisotropic scale, opacity, and appearance in addition to their locations. We show that this learning objective is under-constrained. Models trained with view synthesis alone produce splats whose orientations and scales have no geometric connotation. The result is that, while producing decent view-synthesis performance, nearly all generalizable splatting methods produce geometrically inaccurate and misaligned Gaussians. We introduce G3Splat, a geometry-consistent generalizable splatting framework that addresses these degeneracies through differentiable geometric priors on the predicted 3D Gaussians, making the learning problem well-posed. These priors encourage the per-pixel splats to remain on their viewing rays and to orient themselves in accordance with local surfaces. Our priors are architecture-agnostic and can be incorporated into any previously studied geometric backbone for generalizable splatting, as well as different scene representations. We test G3Splat with both DUSt3R-style and VGGT-style backbones to predict pixel-aligned full-rank 3DGS as well as surfel-like 2DGS. Trained on RE10K, G3Splat produces Gaussian splats with significantly higher geometric fidelity than baselines, providing state-of-the-art novel-view depth, mesh reconstruction, and relative pose estimation performance while preserving novel-view synthesis quality, as evaluated on datasets such as ACID and ScanNet. Code and pretrained models are released on our project page.

cs.CV↗

arXiv2026

Parameter-Efficient Fine-Tuning with Learnable Rank

Low-Rank Adaptation (LoRA) is a popular parameter-efficient fine-tuning (PEFT) method that restricts weight updates to low-rank adapters, introducing a fixed low-rank inductive bias by optimizing in a low-dimensional subspace. In this work, we question whether a fixed-rank constraint is the most effective inductive bias for parameter-efficient fine-tuning. We introduce *Learnable Rank LoRA (LR-LoRA)*, a PEFT method in which the adapter rank is learned during the training process. Instead of prescribing a uniform rank for all adapter layers, LR-LoRA allows the optimizer to determine the appropriate rank for each layer. Using this approach, we find substantial layer-wise variation in the learned ranks, with the attention and MLP layers in the transformer models exhibiting systematically different rank preferences. Across a range of language understanding and commonsense reasoning benchmarks, LR-LoRA achieves state-of-the-art performance in most settings and consistently outperforms strong PEFT baselines, demonstrating that a learnable rank provides a more flexible and effective inductive bias than fixed-rank adaptations.

cs.CL↗

arXiv2026

Mask the Target: A Plug-and-Play Regularizer Against LoRA Forgetting

Low-Rank Adaptation (LoRA) has become one of the most widely used fine-tuning mechanisms for adapting large language models to new domains, tasks, and users. Yet adaptation performance alone can obscure an important failure mode: LoRA updates may improve performance on the target distribution while degrading prior capabilities learned during pretraining and alignment. We show that this forgetting becomes especially severe when the adaptation distribution differs substantially from the models original training or alignment distributions. The challenge is amplified in practical settings, where the original training and alignment data are typically unavailable. Motivated by this constraint, we study how LoRA based adaptation balances new learning against forgetting in a replay-free setting, and introduce a simple output space regularizer that can be added directly to existing training pipelines. Our method removes the ground-truth token from both the base and adapted model distributions, renormalizes the remaining probabilities, and applies KL regularization only over the non-target vocabulary. This preserves the base models relative preferences among alternative tokens without directly opposing the cross-entropy signal required for adaptation. As the regularizer acts only at the loss level, it requires no replay data, architectural changes, adapter redesign, or inference-time overhead, and can be applied directly to existing LoRA variants. Across all LoRA variants tested and across various backbones, our method improves the frontier between new learning and forgetting when the adaptation distribution differs substantially from the base models original training or alignment distributions, suggesting a broadly applicable route toward more reliable LLM updating.

cs.CL↗

arXiv2026

The Quantization Benefits of Residual-Free Transformers

Large-scale transformer training and deployment are increasingly constrained by the transfer of activations, gradients, and optimizer states across accelerators. Low-bit quantization offers a natural remedy, but transformer activations are often heavy-tailed and outlier-dominated, making simple quantization highly lossy. We show that this difficulty is not only a property of the quantizer, but also of the architecture. Specifically, residual connections can drive transformer activations away from Gaussianity during training. Using controlled comparisons between residual and residual-free transformers, we demonstrate that this effect leads to substantially higher quantization error and accuracy degradation at low precision in residual models. We explain the phenomenon through an excess kurtosis analysis, showing that residual mixing can amplify non-Gaussianity, whereas dense mixing in residual-free contracts non-Gaussianity. We then show that residual-free transformers can be made trainable using orthogonal initialization, spectral or second-order optimization, and depth-aware scaling of attention temperature. In language tasks, while there is a small drop in full precision performance, these models retain near-Gaussian activations and exhibit significantly improved robustness to low-bit quantization. Our results identify an accuracy--compressibility trade-off in transformer design and motivate architecture-level approaches to quantization-friendly foundation models.

cs.LG↗

arXiv2026

Stable Forgetting: Bounded Parameter-Efficient Unlearning in Foundation Models

Machine unlearning in foundation models (e.g., language and vision transformers) is essential for privacy and safety; however, existing approaches are unstable and unreliable. A widely used strategy, the gradient difference method, applies gradient descent to retained data while performing gradient ascent on forgotten data. When combined with cross-entropy, this procedure can trigger the unbounded growth of weights and gradients, degrading both forgetting and retention. We provide a theoretical framework that explains this failure by showing how ascent destabilizes optimization in transformer feedforward MLP layers. Guided by this insight, we propose *Bounded Parameter-Efficient Unlearning*, which stabilizes LoRA-based fine-tuning by applying bounded functions to MLP adapters. This controls the weight dynamics during ascent and enables reliable convergence. We validate the approach on Vision Transformer class deletion on CIFAR-100, where GD+Sine is the only evaluated method to achieve both high forget quality and model utility across ViT-B/16, ViT-L/14, and DeiT-S architectures, and demonstrate generality on language-model benchmarks (TOFU, TDEC, MUSE) across architectures from 22M to 8B parameters, achieving improved forgetting while preserving utility.

cs.LG↗

arXiv2026

SineProject: Machine Unlearning for Stable Vision Language Alignment

Multimodal Large Language Models (MLLMs) increasingly need to forget specific knowledge such as unsafe or private information without requiring full retraining. However, existing unlearning methods often disrupt vision language alignment, causing models to reject both harmful and benign queries. We trace this failure to the projector network during unlearning, its Jacobian becomes severely illconditioned, leading to unstable optimization and drift in cross modal embeddings. We introduce SineProject, a simple method that augments the frozen projector with sinusoidally modulated trainable parameters, improving the Jacobian's spectral conditioning and stabilizing alignment throughout unlearning. Across standard safety and privacy unlearning benchmarks using LLaVA v1.5 7B and 13B, SineProject reduces benign query refusals while achieving complete forgetting of targeted information, yielding state of the art forget retain trade offs with negligible computational overhead.

cs.CV↗

arXiv2026

3D-LFM: Lifting Foundation Model

The lifting of 3D structure and camera from 2D landmarks is at the cornerstone of the entire discipline of computer vision. Traditional methods have been confined to specific rigid objects, such as those in Perspective-n-Point (PnP) problems, but deep learning has expanded our capability to reconstruct a wide range of object classes (e.g. C3DPO and PAUL) with resilience to noise, occlusions, and perspective distortions. All these techniques, however, have been limited by the fundamental need to establish correspondences across the 3D training data -- significantly limiting their utility to applications where one has an abundance of "in-correspondence" 3D data. Our approach harnesses the inherent permutation equivariance of transformers to manage varying number of points per 3D data instance, withstands occlusions, and generalizes to unseen categories. We demonstrate state of the art performance across 2D-3D lifting task benchmarks. Since our approach can be trained across such a broad class of structures we refer to it simply as a 3D Lifting Foundation Model (3D-LFM) -- the first of its kind.

cs.CV↗

arXiv2026

Trading Positional Complexity vs. Deepness in Coordinate Networks

It is well noted that coordinate-based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been mainly studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. In addition, we argue that employing a more complex positional encoding -- that scales exponentially with the number of modes -- requires only a linear (rather than deep) coordinate function to achieve comparable performance. Counter-intuitively, we demonstrate that trading positional embedding complexity for network deepness is orders of magnitude faster than current state-of-the-art; despite the additional embedding complexity. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice.

cs.CV↗

arXiv2026

From Activation to Initialization: Scaling Insights for Optimizing Neural Fields

In the realm of computer vision, Neural Fields have gained prominence as a contemporary tool harnessing neural networks for signal representation. Despite the remarkable progress in adapting these networks to solve a variety of problems, the field still lacks a comprehensive theoretical framework. This article aims to address this gap by delving into the intricate interplay between initialization and activation, providing a foundational basis for the robust optimization of Neural Fields. Our theoretical insights reveal a deep-seated connection among network initialization, architectural choices, and the optimization process, emphasizing the need for a holistic approach when designing cutting-edge Neural Fields.

cs.CV↗

arXiv2026

Weight Conditioning for Smooth Optimization of Neural Networks

In this article, we introduce a novel normalization technique for neural network weight matrices, which we term weight conditioning. This approach aims to narrow the gap between the smallest and largest singular values of the weight matrices, resulting in better-conditioned matrices. The inspiration for this technique partially derives from numerical linear algebra, where well-conditioned matrices are known to facilitate stronger convergence results for iterative solvers. We provide a theoretical foundation demonstrating that our normalization technique smoothens the loss landscape, thereby enhancing convergence of stochastic gradient descent algorithms. Empirically, we validate our normalization across various neural network architectures, including Convolutional Neural Networks (CNNs), Vision Transformers (ViT), Neural Radiance Fields (NeRF), and 3D shape modeling. Our findings indicate that our normalization method is not only competitive but also outperforms existing weight normalization techniques from the literature.

cs.CV↗

arXiv2026

Rethinking Attention: Polynomial Alternatives to Softmax in Transformers

This paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the Frobenius norm of the attention matrix, which stabilizes training. Motivated by this, we explore alternative activations, specifically polynomials, that achieve a similar regularization effect. Our theoretical analysis shows that certain polynomials can serve as effective substitutes for softmax, achieving strong performance across transformer applications despite violating softmax's typical properties of positivity, normalization, and sparsity. Extensive experiments support these findings, offering a new perspective on attention mechanisms.

cs.LG↗