Chris De

Satyen Kale, Jason D. Lee, Chris De Sa et al.

Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the convergence of Gradient Flow (GF) on the population loss, partly due to the simplicity that a continuous-time analysis buys us. An overarching theme of our paper is providing general conditions under which SGD converges, assuming that GF on the population loss converges. Our main tool to establish this connection is a general converse Lyapunov like theorem, which implies the existence of a Lyapunov potential under mild assumptions on the rates of convergence of GF. In fact, using these potentials, we show a one-to-one correspondence between rates of convergence of GF and geometrical properties of the underlying objective. When these potentials further satisfy certain self-bounding properties, we show that they can be used to provide a convergence guarantee for Gradient Descent (GD) and SGD (even when the paths of GF and GD/SGD are quite far apart). It turns out that these self-bounding assumptions are in a sense also necessary for GD/SGD to work. Using our framework, we provide a unified analysis for GD/SGD not only for classical settings like convex losses, or objectives that satisfy PL / KL properties, but also for more complex problems including Phase Retrieval and Matrix sq-root, and extending the results in the recent work of Chatterjee 2022.

Albert Tseng, Christopher De Sa

Modern sparse language models typically achieve sparsity through Mixture-of-Experts (MoE) layers, which dynamically route tokens to dense MLP "experts." However, dynamic hard routing has a number of drawbacks, such as potentially poor hardware efficiency and needing auxiliary losses for stable training. In contrast, the tokenizer embedding table, which is natively sparse, largely avoids these issues by selecting a single embedding per token at the cost of not having contextual information. In this work, we introduce the Large Lookup Layer (L$^3$), which unlocks a new axis of sparsity by generalizing embedding tables to model decoder layers. L$^3$ layers use static token-based routing to aggregate a set of learned embeddings per token in a context-dependent way, allowing the model to efficiently balance memory and compute by caching information in embeddings. L$^3$ has two main components: (1) a systems-friendly architecture that allows for fast training and CPU-offloaded inference with no overhead, and (2) an information-theoretic embedding allocation algorithm that effectively balances speed and quality. We empirically test L$^3$ by training transformers with up to 2.6B active parameters and find that L$^3$ strongly outperforms both dense models and iso-sparse MoEs in both language modeling and downstream tasks.

Subham Sekhar Sahoo, Aaron Gokaslan, Chris De Sa et al.

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect performance. In this paper, we explore whether the diffusion process can be learned from data. Our work is grounded in Bayesian inference and seeks to improve log-likelihood estimation by casting the learned diffusion process as an approximate variational posterior that yields a tighter lower bound (ELBO) on the likelihood. A widely held assumption is that the ELBO is invariant to the noise process: our work dispels this assumption and proposes multivariate learned adaptive noise (MULAN), a learned diffusion process that applies noise at different rates across an image. Specifically, our method relies on a multivariate noise schedule that is a function of the data to ensure that the ELBO is no longer invariant to the choice of the noise schedule as in previous works. Empirically, MULAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet and reduces the number of training steps by 50%. We provide the code, along with a blog post and video tutorial on the project page: https://s-sahoo.com/MuLAN

Jessica Zosa Forde, A. Feder Cooper, Kweku Kwegyir-Aggrey et al.

Algorithmic fairness has emphasized the role of biased data in automated decision outcomes. Recently, there has been a shift in attention to sources of bias that implicate fairness in other stages in the ML pipeline. We contend that one source of such bias, human preferences in model selection, remains under-explored in terms of its role in disparate impact across demographic groups. Using a deep learning model trained on real-world medical imaging data, we verify our claim empirically and argue that choice of metric for model comparison, especially those that do not take variability into account, can significantly bias model selection outcomes.