Foundation models have made significant strides in understanding the genomic language of DNA sequences. However, previous models typically adopt the tokenization methods designed for natural language, which are unsuitable for DNA sequences due to their unique characteristics. In addition, the optimal approach to tokenize DNA remains largely under-explored, and may not be intuitively understood by humans even if discovered. To address these challenges, we introduce MxDNA, a novel framework where the model autonomously learns an effective DNA tokenization strategy through gradient decent. MxDNA employs a sparse Mixture of Convolution Experts coupled with a deformable convolution to model the tokenization process, with the discontinuous, overlapping, and ambiguous nature of meaningful genomic segments explicitly considered. On Nucleotide Transformer Benchmarks and Genomic Benchmarks, MxDNA demonstrates superior performance to existing methods with less pretraining data and time, highlighting its effectiveness. Finally, we show that MxDNA learns unique tokenization strategy distinct to those of previous methods and captures genomic functionalities at a token level during self-supervised pretraining. Our MxDNA aims to provide a new perspective on DNA tokenization, potentially offering broad applications in various domains and yielding profound insights.

The scalability of Distributed Stochastic Gradient Descent (SGD) is today limited by communication bottlenecks. We propose a novel SGD variant: Communicationefficient SGD with Error Reset, or CSER. The key idea in CSER is first a new technique called "error reset" that adapts arbitrary compressors for SGD, producing bifurcated local models with periodic reset of resulting local residual errors. Second we introduce partial synchronization for both the gradients and the models, leveraging advantages from them. We prove the convergence of CSER for smooth non-convex problems. Empirical results show that when combined with highly aggressive compressors, the CSER algorithms accelerate the distributed training by nearly 10 for CIFAR-100, and by 4.5 for ImageNet.

The scalability of Distributed Stochastic Gradient Descent (SGD) is today limited by communication bottlenecks. We propose a novel SGD variant: Communicationefficient SGD with Error Reset, or CSER. The key idea in CSER is first a new technique called "error reset" that adapts arbitrary compressors for SGD, producing bifurcated local models with periodic reset of resulting local residual errors. Second we introduce partial synchronization for both the gradients and the models, leveraging advantages from them. We prove the convergence of CSER for smooth non-convex problems. Empirical results show that when combined with highly aggressive compressors, the CSER algorithms accelerate the distributed training by nearly 10 for CIFAR-100, and by 4.5 for ImageNet.

"limited tweak relative to previous work" The contributions of CSER put it beyond merely a "tweak". "results not very surprising" Our work is the first to push the compression ratio to 1024 for both worker-to-server and Our GRBS compressor (Section 3.3) reduces "No accuracy loss" is conditional. We will revise the claim by adding context. "is it using NCCL" All the algorithms use the same communication library: Horovod with NCCL. "How is the experimental setup chosen" Multiple nodes connected by 10Gb/s Ethernet is a typical setup used in In this work, we aim to show that we can significantly reduce the heavy inter-node communication.

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new strings from the language that don't already appear in the training data. Here we ask what we can conclude about language generation using only this specification, without further assumptions. In particular, suppose that an adversary enumerates the strings of an unknown target language L that is known only to come from one of a possibly infinite list of candidates. A computational agent is trying to learn to generate from this language; we say that the agent generates from L in the limit if after some finite point in the enumeration of L, the agent is able to produce new elements that come exclusively from L and that have not yet been presented by the adversary. Our main result is that there is an agent that is able to generate in the limit for every countable list of candidate languages. This contrasts dramatically with negative results due to Gold and Angluin in a well-studied model of language learning where the goal is to identify an unknown language from samples; the difference between these results suggests that identifying a language is a fundamentally different problem than generating from it.

Large neural networks can be pruned to a small fraction of their original size, with little loss in accuracy, by following a time-consuming "train, prune, re-train" approach. Frankle & Carbin [9] conjecture that we can avoid this by training lottery tickets, i.e., special sparse subnetworks found at initialization, that can be trained to high accuracy. However, a subsequent line of work [11, 41] presents concrete evidence that current algorithms for finding trainable networks at initialization, fail simple baseline comparisons, e.g., against training random sparse subnetworks. Finding lottery tickets that train to better accuracy compared to simple baselines remains an open problem.

Large neural networks can be pruned to a small fraction of their original size, with little loss in accuracy, by following a time-consuming "train, prune, re-train" approach. Frankle & Carbin [9] conjecture that we can avoid this by training lottery tickets, i.e., special sparse subnetworks found at initialization, that can be trained to high accuracy. However, a subsequent line of work [11, 41] presents concrete evidence that current algorithms for finding trainable networks at initialization, fail simple baseline comparisons, e.g., against training random sparse subnetworks. Finding lottery tickets that train to better accuracy compared to simple baselines remains an open problem.

Fine-tuning foundation models often compromises their robustness to distribution shifts. To remedy this, most robust fine-tuning methods aim to preserve the pretrained features. However, not all pre-trained features are robust and those methods are largely indifferent to which ones to preserve. We propose dual risk minimization (DRM), which combines empirical risk minimization with worst-case risk minimization, to better preserve the core features of downstream tasks. In particular, we utilize core-feature descriptions generated by LLMs to induce core-based zero-shot predictions which then serve as proxies to estimate the worst-case risk. DRM balances two crucial aspects of model robustness: expected performance and worst-case performance, establishing a new state of the art on various real-world benchmarks. DRM significantly improves the out-of-distribution performance of CLIP ViT-L/14@336 on ImageNet (75.9 77.1), WILDS-iWildCam (47.1 51.8), and WILDS-FMoW (50.7 53.1); opening up new avenues for robust fine-tuning. Our code is available at https://github.com/vaynexie/DRM.

Given a sufficiently large amount of labeled data, the non-convex low-rank matrix recovery problem contains no spurious local minima, so a local optimization algorithm is guaranteed to converge to a global minimum starting from any initial guess. However, the actual amount of data needed by this theoretical guarantee is very pessimistic, as it must prevent spurious local minima from existing anywhere, including at adversarial locations. In contrast, prior work based on good initial guesses have more realistic data requirements, because they allow spurious local minima to exist outside of a neighborhood of the solution. In this paper, we quantify the relationship between the quality of the initial guess and the corresponding reduction in data requirements. Using the restricted isometry constant as a surrogate for sample complexity, we compute a sharp "threshold" number of samples needed to prevent each specific point on the optimization landscape from becoming a spurious local minimum. Optimizing the threshold over regions of the landscape, we see that for initial points around the ground truth, a linear improvement in the quality of the initial guess amounts to a constant factor improvement in the sample complexity.

Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest and most studied algorithm. LMC can suffer from slow convergence - requiring a large number of steps of small step-size to obtain good quality samples. This becomes stark in the case of diffusion models where a large number of steps gives the best samples, but the quality degrades rapidly with smaller number of steps. Randomized Midpoint Method has been recently proposed as a better discretization of Langevin dynamics for sampling from strongly log-concave distributions. However, important applications such as diffusion models involve non-log concave densities and contain time varying drift. We propose its variant, the Poisson Midpoint Method, which approximates a small step-size LMC with large step-sizes. We prove that this can obtain a quadratic speed up of LMC under very weak assumptions. We apply our method to diffusion models for image generation and show that it maintains the quality of DDPM with 1000 neural network calls with just 50-80 neural network calls and outperforms ODE based methods with similar compute.