arXiv subjects

Hemanth Saratchandran

Publications and source records attributed to Hemanth Saratchandran.

At least 37 records · Page 2Linked to original sources

arXiv2025

Structured Initialization for Vision Transformers

Convolutional Neural Networks (CNNs) inherently encode strong inductive biases, enabling effective generalization on small-scale datasets. In this paper, we propose integrating this inductive bias into ViTs, not through an architectural intervention but solely through initialization. The motivation here is to have a ViT that can enjoy strong CNN-like performance when data assets are small, but can still scale to ViT-like performance as the data expands. Our approach is motivated by our empirical results that random impulse filters can achieve commensurate performance to learned filters within a CNN. We improve upon current ViT initialization strategies, which typically rely on empirical heuristics such as using attention weights from pretrained models or focusing on the distribution of attention weights without enforcing structures. Empirical results demonstrate that our method significantly outperforms standard ViT initialization across numerous small and medium-scale benchmarks, including Food-101, CIFAR-10, CIFAR-100, STL-10, Flowers, and Pets, while maintaining comparative performance on large-scale datasets such as ImageNet-1K. Moreover, our initialization strategy can be easily integrated into various transformer-based architectures such as Swin Transformer and MLP-Mixer with consistent improvements in performance.

cs.CV↗

arXiv2025

From Tables to Signals: Revealing Spectral Adaptivity in TabPFN

Task-agnostic tabular foundation models such as TabPFN have achieved impressive performance on tabular learning tasks, yet the origins of their inductive biases remain poorly understood. In this work, we study TabPFN through the lens of signal reconstruction and provide the first frequency-based analysis of its in-context learning behavior. We show that TabPFN possesses a broader effective frequency capacity than standard ReLU-MLPs, even without hyperparameter tuning. Moreover, unlike MLPs whose spectra evolve primarily over training epochs, we find that TabPFN's spectral capacity adapts directly to the number of samples provided in-context, a phenomenon we term Spectral Adaptivity. We further demonstrate that positional encoding modulates TabPFN's frequency response, mirroring classical results in implicit neural representations. Finally, we show that these properties enable TabPFN to perform training-free and hyperparameter-free image denoising, illustrating its potential as a task-agnostic implicit model. Our analysis provides new insight into the structure and inductive biases of tabular foundation models and highlights their promise for broader signal reconstruction tasks.

cs.LG↗

arXiv2025

SineLoRA$Δ$: Sine-Activated Delta Compression

Resource-constrained weight deployment is a task of immense practical importance. Recently, there has been interest in the specific task of \textit{Delta Compression}, where parties each hold a common base model and only communicate compressed weight updates. However, popular parameter efficient updates such as Low Rank Adaptation (LoRA) face inherent representation limitations - which are especially pronounced when combined with aggressive quantization. To overcome this, we build on recent work that improves LoRA representation capacity by using fixed-frequency sinusoidal functions to increase stable rank without adding additional parameters. We extend this to the quantized setting and present the first theoretical analysis showing how stable rank evolves under quantization. From this, we introduce SineLoRA$Δ$, a principled and effective method for delta compression that improves the expressivity of quantized low-rank adapters by applying a sinusoidal activation. We validate SineLoRA$Δ$ across a diverse variety of domains - including language modeling, vision-language tasks, and text-to-image generation - achieving up to 66% memory reduction with similar performance. We additionally provide a novel application of the canonical Bjøntegaard Delta metric to consistently compare adapter compression changes across the rate-distortion curve.

cs.LG↗

arXiv2025

Enhancing Transformers Through Conditioned Embedded Tokens

Transformers have transformed modern machine learning, driving breakthroughs in computer vision, natural language processing, and robotics. At the core of their success lies the attention mechanism, which enables the modeling of global dependencies among input tokens. However, we reveal that the attention block in transformers suffers from inherent ill-conditioning, which hampers gradient-based optimization and leads to inefficient training. To address this, we develop a theoretical framework that establishes a direct relationship between the conditioning of the attention block and that of the embedded tokenized data. Building on this insight, we introduce conditioned embedded tokens, a method that systematically modifies the embedded tokens to improve the conditioning of the attention mechanism. Our analysis demonstrates that this approach significantly mitigates ill-conditioning, leading to more stable and efficient training. We validate our methodology across various transformer architectures, achieving consistent improvements in image classification, object detection, instance segmentation, and natural language processing, highlighting its broad applicability and effectiveness.

cs.CV↗

arXiv2025

Cutting the Skip: Training Residual-Free Transformers

Transformers have achieved remarkable success across a wide range of applications, a feat often attributed to their scalability. Yet training them without skip (residual) connections remains notoriously difficult. While skips stabilize optimization, they also disrupt the hierarchical structure of representations, raising the long-standing question of whether transformers can be trained efficiently without them. In this work, we address this problem by analyzing the Jacobian of a skipless transformer block, showing why skips improve conditioning and revealing that their stabilization benefits can be recovered through a principled initialization strategy. Building on this insight, we introduce the first method that enables stable and efficient training of skipless transformers without altering the standard architecture. We validate our approach on Vision Transformers (ViTs) in both supervised and self-supervised settings, demonstrating that skipless ViTs trained with our initialization overcome the usual optimization barriers, learn richer hierarchical representations, and outperform strong baselines, that incorporate skip connections, on dense prediction benchmarks. These results show that skip connections are not a fundamental requirement for training ViTs and open new avenues for hierarchical representation learning in vision models.

cs.LG↗

arXiv2025

Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems

Data-driven modeling of nonlinear dynamical systems is often hampered by measurement noise. We propose a denoising framework, called Runge-Kutta and Total Variation Based Implicit Neural Representation (RKTV-INR), that represents the state trajectory with an implicit neural representation (INR) fitted directly to noisy observations. Runge-Kutta integration and total variation are imposed as constraints to ensure that the reconstructed state is a trajectory of a dynamical system that remains close to the original data. The trained INR yields a clean, continuous trajectory and provides accurate first-order derivatives via automatic differentiation. These denoised states and derivatives are then supplied to Sparse Identification of Nonlinear Dynamics (SINDy) to recover the governing equations. Experiments demonstrate effective noise suppression, precise derivative estimation, and reliable system identification.

cs.LG↗

arXiv2025

Always Skip Attention

We highlight a curious empirical result within modern Vision Transformers (ViTs). Specifically, self-attention catastrophically fails to train unless it is used in conjunction with a skip connection. This is in contrast to other elements of a ViT that continue to exhibit good performance (albeit suboptimal) when skip connections are removed. Further, we show that this critical dependence on skip connections is a relatively new phenomenon, with previous deep architectures (\eg, CNNs) exhibiting good performance in their absence. In this paper, we theoretically characterize that the self-attention mechanism is fundamentally ill-conditioned and is, therefore, uniquely dependent on skip connections for regularization. Additionally, we propose Token Graying -- a simple yet effective complement (to skip connections) that further improves the condition of input tokens. We validate our approach in both supervised and self-supervised training methods.

cs.LG↗

arXiv2025

Towards Higher Effective Rank in Parameter-efficient Fine-tuning using Khatri--Rao Product

Parameter-efficient fine-tuning (PEFT) has become a standard approach for adapting large pre-trained models. Amongst PEFT methods, low-rank adaptation (LoRA) has achieved notable success. However, recent studies have highlighted its limitations compared against full-rank alternatives, particularly when applied to multimodal and large language models. In this work, we present a quantitative comparison amongst full-rank and low-rank PEFT methods using a synthetic matrix approximation benchmark with controlled spectral properties. Our results confirm that LoRA struggles to approximate matrices with relatively flat spectrums or high frequency components -- signs of high effective ranks. To this end, we introduce KRAdapter, a novel PEFT algorithm that leverages the Khatri-Rao product to produce weight updates, which, by construction, tends to produce matrix product with a high effective rank. We demonstrate performance gains with KRAdapter on vision-language models up to 1B parameters and on large language models up to 8B parameters, particularly on unseen common-sense reasoning tasks. In addition, KRAdapter maintains the memory and compute efficiency of LoRA, making it a practical and robust alternative to fine-tune billion-scale parameter models.

cs.LG↗

arXiv2025

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning

Pretraining on large, semantically rich datasets is key for developing language models. Surprisingly, recent studies have shown that even synthetic data, generated procedurally through simple semantic-free algorithms, can yield some of the same benefits as natural language pretraining. It is unclear what specific capabilities such simple synthetic data instils in a model, where these capabilities reside in the architecture, and how they manifest within its weights. In this short paper, we identify several beneficial forms of procedural data, together with specific algorithmic reasoning skills that improve in small transformers. Our core finding is that different procedural rules instil distinct but complementary inductive structures in the model. With extensive ablations and partial-transfer experiments, we discover that these structures reside in different parts of the model. Attention layers often carry the most transferable information, but some pretraining rules impart useful structure to MLP blocks instead. Most interestingly, the structures induced by multiple rules can be composed to jointly reinforce multiple capabilities. These results suggest an exciting possibility of disentangling the acquisition of knowledge from reasoning in language models, with the goal of improving their robustness and data efficiency.

cs.LG↗

arXiv2025

Leaner Transformers: More Heads, Less Depth

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means better", leading to ever-increasing model sizes. This paper challenge this ideology by showing that many existing transformers might be unnecessarily oversized. We discover a theoretical principle that redefines the role of multi-head attention. An important benefit of the multiple heads is in improving the conditioning of the attention block. We exploit this theoretical insight and redesign popular architectures with an increased number of heads. The improvement in the conditioning proves so significant in practice that model depth can be decreased, reducing the parameter count by up to 30-50% while maintaining accuracy. We obtain consistent benefits across a variety of transformer-based architectures of various scales, on tasks in computer vision (ImageNet-1k) as well as language and sequence modeling (GLUE benchmark, TinyStories, and the Long-Range Arena benchmark).

cs.LG↗

arXiv2025

Preconditioners for the Stochastic Training of Neural Fields

Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvature-aware diagonal preconditioners, demonstrating their effectiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF).

cs.CV↗

arXiv2025

Efficient Learning With Sine-Activated Low-rank Matrices

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of parameters, striking a balance between compactness and performance. However, a common challenge has been the compromise between parameter efficiency and the accuracy of the model, where reduced parameters often lead to diminished accuracy compared to their full-rank counterparts. In this work, we propose a novel theoretical framework that integrates a sinusoidal function within the low-rank decomposition process. This approach not only preserves the benefits of the parameter efficiency characteristic of low-rank methods but also increases the decomposition's rank, thereby enhancing model performance. Our method proves to be a plug in enhancement for existing low-rank models, as evidenced by its successful application in Vision Transformers (ViT), Large Language Models (LLMs), Neural Radiance Fields (NeRF) and 3D shape modelling.

cs.LG↗

arXiv2025

RandLoRA: Full-rank parameter-efficient fine-tuning of large models

Low-Rank Adaptation (LoRA) and its variants have shown impressive results in reducing the number of trainable parameters and memory requirements of large transformer networks while maintaining fine-tuning performance. The low-rank nature of the weight update inherently limits the representation power of fine-tuned models, however, thus potentially compromising performance on complex tasks. This raises a critical question: when a performance gap between LoRA and standard fine-tuning is observed, is it due to the reduced number of trainable parameters or the rank deficiency? This paper aims to answer this question by introducing RandLoRA, a parameter-efficient method that performs full-rank updates using a learned linear combinations of low-rank, non-trainable random matrices. Our method limits the number of trainable parameters by restricting optimization to diagonal scaling matrices applied to the fixed random matrices. This allows us to effectively overcome the low-rank limitations while maintaining parameter and memory efficiency during training. Through extensive experimentation across vision, language, and vision-language benchmarks, we systematically evaluate the limitations of LoRA and existing random basis methods. Our findings reveal that full-rank updates are beneficial across vision and language tasks individually, and even more so for vision-language tasks, where RandLoRA significantly reduces -- and sometimes eliminates -- the performance gap between standard fine-tuning and LoRA, demonstrating its efficacy.

cs.CL↗

arXiv2025

A Ruelle dynamical zeta function for equivariant flows

For proper group actions on smooth manifolds, with compact quotients, we define an equivariant version of the Ruelle dynamical $ζ$-function for equivariant flows satisfying a nondegeneracy condition. The construction is based on an equivariant generalisation of Guillemin's trace formula, obtained in a companion paper. This formula implies several properties of the equivariant Ruelle $ζ$-function. We ask the question in what situations an equivariant generalisation of Fried's conjecture holds, relating the equivariant Ruelle $ζ$-function to equivariant analytic torsion. We compute the equivariant Ruelle $ζ$-function in several examples, including examples where the classical Ruelle $ζ$-function is not defined. The equivariant Fried conjecture holds in the examples where the condition of the conjecture (vanishing of the kernel of the Laplacian) is satisfied.

math.DG↗

arXiv2025

An equivariant Guillemin trace formula

Guillemin's trace formula is an expression for the distributional trace of an operator defined by pulling back functions along a flow on a compact manifold. We obtain an equivariant generalisation of this formula, for proper, cocompact group actions. This is motivated by the construction of an equivariant version of the Ruelle dynamical $ζ$-function in another paper by the same authors, which is based on the equivariant Guillemin trace formula. To obtain this formula, we first develop an equivariant version of the distributional trace that appears in Guillemin's formula and other places.

math.DG↗

arXiv2024

D'OH: Decoder-Only Random Hypernetworks for Implicit Neural Representations

Deep implicit functions have been found to be an effective tool for efficiently encoding all manner of natural signals. Their attractiveness stems from their ability to compactly represent signals with little to no offline training data. Instead, they leverage the implicit bias of deep networks to decouple hidden redundancies within the signal. In this paper, we explore the hypothesis that additional compression can be achieved by leveraging redundancies that exist between layers. We propose to use a novel runtime decoder-only hypernetwork - that uses no offline training data - to better exploit cross-layer parameter redundancy. Previous applications of hypernetworks with deep implicit functions have employed feed-forward encoder/decoder frameworks that rely on large offline datasets that do not generalize beyond the signals they were trained on. We instead present a strategy for the optimization of runtime deep implicit functions for single-instance signals through a Decoder-Only randomly projected Hypernetwork (D'OH). By directly changing the latent code dimension, we provide a natural way to vary the memory footprint of neural representations without the costly need for neural architecture search on a space of alternative low-rate structures.

cs.LG↗

arXiv2024

Invertible Neural Warp for NeRF

This paper tackles the simultaneous optimization of pose and Neural Radiance Fields (NeRF). Departing from the conventional practice of using explicit global representations for camera pose, we propose a novel overparameterized representation that models camera poses as learnable rigid warp functions. We establish that modeling the rigid warps must be tightly coupled with constraints and regularization imposed. Specifically, we highlight the critical importance of enforcing invertibility when learning rigid warp functions via neural network and propose the use of an Invertible Neural Network (INN) coupled with a geometry-informed constraint for this purpose. We present results on synthetic and real-world datasets, and demonstrate that our approach outperforms existing baselines in terms of pose estimation and high-fidelity reconstruction due to enhanced optimization convergence.

cs.CV↗

arXiv2024

A Sampling Theory Perspective on Activations for Implicit Neural Representations

Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. While commonly using techniques like Fourier positional encodings or non-traditional activation functions (e.g., Gaussian, sinusoid, or wavelets) to capture high-frequency content, their properties lack exploration within a unified theoretical framework. Addressing this gap, we conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that sinc activations, previously unused in conjunction with INRs, are theoretically optimal for signal encoding. Additionally, we establish a connection between dynamical systems and INRs, leveraging sampling theory to bridge these two paradigms.

cs.LG↗