Gautham Govind Anil

Sahil Goyal, Swayam Agrawal, Gautham Govind Anil et al.

We introduce Elastic Looped Transformers (ELT), a highly parameter-efficient class of visual generative models based on a recurrent transformer architecture. While conventional generative models rely on deep stacks of unique transformer layers, our approach employs iterative, weight-shared transformer blocks to drastically reduce parameter counts while maintaining high synthesis quality. To effectively train these models for image and video generation, we propose the idea of Intra-Loop Self Distillation (ILSD), where student configurations (intermediate loops) are distilled from the teacher configuration (maximum training loops) to ensure consistency across the model's depth in a single training step. Our framework yields a family of elastic models from a single training run, enabling Any-Time inference capability with dynamic trade-offs between computational cost and generation quality, with the same parameter count. ELT significantly shifts the efficiency frontier for visual synthesis. With $4\times$ reduction in parameter count under iso-inference-compute settings, ELT achieves a competitive FID of $2.0$ on class-conditional ImageNet $256 \times 256$ and FVD of $72.8$ on class-conditional UCF-101.

Maximilian Fleissner, Gautham Govind Anil, Debarghya Ghoshdastidar

The NTK is a widely used tool in the theoretical analysis of deep learning, allowing us to look at supervised deep neural networks through the lenses of kernel regression. Recently, several works have investigated kernel models for self-supervised learning, hypothesizing that these also shed light on the behavior of wide neural networks by virtue of the NTK. However, it remains an open question to what extent this connection is mathematically sound -- it is a commonly encountered misbelief that the kernel behavior of wide neural networks emerges irrespective of the loss function it is trained on. In this paper, we bridge the gap between the NTK and self-supervised learning, focusing on two-layer neural networks trained under the Barlow Twins loss. We prove that the NTK of Barlow Twins indeed becomes constant as the width of the network approaches infinity. Our analysis technique is a bit different from previous works on the NTK and may be of independent interest. Overall, our work provides a first justification for the use of classic kernel theory to understand self-supervised learning of wide neural networks. Building on this result, we derive generalization error bounds for kernelized Barlow Twins and connect them to neural networks of finite width.

Gautham Govind Anil, Pascal Esser, Debarghya Ghoshdastidar

Contrastive learning is a paradigm for learning representations from unlabelled data that has been highly successful for image and text data. Several recent works have examined contrastive losses to claim that contrastive models effectively learn spectral embeddings, while few works show relations between (wide) contrastive models and kernel principal component analysis (PCA). However, it is not known if trained contrastive models indeed correspond to kernel methods or PCA. In this work, we analyze the training dynamics of two-layer contrastive models, with non-linear activation, and answer when these models are close to PCA or kernel methods. It is well known in the supervised setting that neural networks are equivalent to neural tangent kernel (NTK) machines, and that the NTK of infinitely wide networks remains constant during training. We provide the first convergence results of NTK for contrastive losses, and present a nuanced picture: NTK of wide networks remains almost constant for cosine similarity based contrastive losses, but not for losses based on dot product similarity. We further study the training dynamics of contrastive models with orthogonality constraints on output layer, which is implicitly assumed in works relating contrastive learning to spectral embedding. Our deviation bounds suggest that representations learned by contrastive models are close to the principal components of a certain matrix computed from random features. We empirically show that our theoretical results possibly hold beyond two-layer networks.

Gautham Govind Anil, Shaan Ul Haque, Nithish Kannen et al.

Diffusion models are widely used for generative tasks across domains. While pre-trained diffusion models effectively capture the training data distribution, it is often desirable to shape these distributions using reward functions to align with downstream applications. Policy gradient methods, such as Proximal Policy Optimization (PPO), are widely used in the context of autoregressive generation. However, the marginal likelihoods required for such methods are intractable for diffusion models, leading to alternative proposals and relaxations. In this context, we unify variants of Rejection sAmpling based Fine-Tuning (RAFT) as GRAFT, and show that this implicitly performs PPO with reshaped rewards. We then introduce P-GRAFT to shape distributions at intermediate noise levels and demonstrate empirically that this can lead to more effective fine-tuning. We mathematically explain this via a bias-variance tradeoff. Motivated by this, we propose inverse noise correction to improve flow models without leveraging explicit rewards. We empirically evaluate our methods on text-to-image(T2I) generation, layout generation, molecule generation and unconditional image generation. Notably, our framework, applied to Stable Diffusion 2, improves over policy gradient methods on popular T2I benchmarks in terms of VQAScore and shows an $8.81\%$ relative improvement over the base model. For unconditional image generation, inverse noise correction improves FID of generated images at lower FLOPs/image.

Gautham Govind Anil, Sachin Yadav, Dheeraj Nagaraj et al.

We introduce Interleaved Gibbs Diffusion (IGD), a novel generative modeling framework for discrete-continuous data, focusing on problems with important, implicit and unspecified constraints in the data. Most prior works on discrete and discrete-continuous diffusion assume a factorized denoising distribution, which can hinder the modeling of strong dependencies between random variables in such problems. We empirically demonstrate a significant improvement in 3-SAT performance out of the box by switching to a Gibbs-sampling style discrete diffusion model which does not assume factorizability. Motivated by this, we introduce IGD which generalizes discrete time Gibbs sampling type Markov chain for the case of discrete-continuous generation. IGD allows for seamless integration between discrete and continuous denoisers while theoretically guaranteeing exact reversal of a suitable forward process. Further, it provides flexibility in the choice of denoisers, allows conditional generation via state-space doubling and inference time refinement. Empirical evaluations on three challenging generation tasks - molecule structures, layouts and tabular data - demonstrate state-of-the-art performance. Notably, IGD achieves state-of-the-art results without relying on domain-specific inductive biases like equivariant diffusion or auxiliary losses. We explore a wide range of modeling, and interleaving strategies along with hyperparameters in each of these problems.