Scaling laws provide important insights that can guide the design of large language models (LLMs). Existing work has primarily focused on studying scaling laws for pretraining (upstream) loss. However, in transfer learning settings, in which LLMs are pretrained on an unsupervised dataset and then finetuned on a downstream task, we often also care about the downstream performance. In this work, we study the scaling behavior in a transfer learning setting, where LLMs are finetuned for machine translation tasks. Specifically, we investigate how the choice of the pretraining data and its size affect downstream performance (translation quality) as judged by: downstream cross-entropy and translation quality metrics such as BLEU and COMET scores. Our experiments indicate that the size of the finetuning dataset and the distribution alignment between the pretraining and downstream data significantly influence the scaling behavior. With sufficient alignment, both downstream cross-entropy and translation quality scores improve monotonically with more pretraining data. In such cases, we show that it is possible to predict the downstream translation quality metrics with good accuracy using a log-law. However, there are cases where moderate misalignment causes the downstream translation scores to fluctuate or get worse with more pretraining, whereas downstream cross-entropy monotonically improves. By analyzing these, we provide new practical insights for choosing appropriate pretraining data.

We present a principled, per-instance approach to quantifying the difficulty of unlearning via fine-tuning. We begin by sharpening an analysis of noisy gradient descent for unlearning (Chien et al., 2024), obtaining a better utility–unlearning trade-off by replacing worst-case privacy loss bounds with per-instance privacy losses (Thudi et al., 2024), each of which bounds the (R ´enyi) divergence to retraining without an individual datapoint. To demonstrate the practical applicability of our theory, we present empirical results showing that our theoretical predictions are born out both for Stochastic Gradient Langevin Dynamics (SGLD) as well as for standard fine-tuning without explicit noise. We further demonstrate that per-instance privacy losses correlate well with several existing data difficulty metrics, while also identifying harder groups of data points, and introduce novel evaluation methods based on loss barriers. All together, our findings provide a foundation for more efficient and adaptive unlearning strategies tailored to the unique properties of individual data points.

The high communication cost of sending model updates from the clients to the server is a significant bottleneck for scalable federated learning (FL). Among existing approaches, state-of-the-art bitrate-accuracy tradeoffs have been achieved using stochastic compression methods – in which the client n sends a sample from a client-only probability distribution $q_{\phi^{(n)}}$, and the server estimates the mean of the clients’ distributions using these samples. However, such methods do not take full advantage of the FL setup where the server, throughout the training process, has side information in the form of a global distribution $p_{\theta}$ that is close to the client-only distribution $q_{\phi^{(n)}}$ in Kullback-Leibler (KL) divergence. In this work, we exploit this \emph{closeness} between the clients’ distributions $q_{\phi^{(n)}}$’s and the side information $p_{\theta}$ at the server, and propose a framework that requires approximately $D_{KL}(q_{\phi^{(n)}}|| p_{\theta})$ bits of communication. We show that our method can be integrated into many existing stochastic compression frameworks to attain the same (and often higher) test accuracy with up to 82 times smaller bitrate than the prior work – corresponding to 2,650 times overall compression.

We study $L_2$ mean estimation under central differential privacy and communication constraints, and address two key challenges: firstly, existing mean estimation schemes that simultaneously handle both constraints are usually optimized for $L_\infty$ geometry and rely on random rotation or Kashin’s representation to adapt to $L_2$ geometry, resulting in suboptimal leading constants in mean square errors (MSEs); secondly, schemes achieving order-optimal communication-privacy trade-offs do not extend seamlessly to streaming differential privacy (DP) settings (e.g., tree aggregation or matrix factorization), rendering them incompatible with DP-FTRL type optimizers. In this work, we tackle these issues by introducing a novel privacy accounting method for the sparsified Gaussian mechanism that incorporates the randomness inherent in sparsification into the DP noise. Unlike previous approaches, our accounting algorithm directly operates in $L_2$ geometry, yielding MSEs that fast converge to those of the uncompressed Gaussian mechanism. Additionally, we extend the sparsification scheme to the matrix factorization framework under streaming DP and provide a precise accountant tailored for DP-FTRL type optimizers. Empirically, our method demonstrates at least a 100x improvement of compression for DP-SGD across various FL tasks.

The high communication cost between the server and the clients is a significant bottleneck in scaling distributed learning for overparametrized deep models. One popular approach for reducing this communication overhead is randomized sketching. However, existing theoretical analyses for sketching-based distributed learning (sketch-DL) either incur a prohibitive dependence on the ambient dimension or need additional restrictive assumptions such as heavy-hitters. Nevertheless, despite existing pessimistic analyses, empirical evidence suggests that sketch-DL is competitive with its uncompressed counterpart, thus motivating a sharper analysis. In this work, we introduce a sharper ambient dimension-independent convergence analysis for sketch-DL using the second-order geometry specified by the loss Hessian. Our results imply ambient dimension-independent communication complexity for sketch-DL. We present empirical results both on the loss Hessian and overall accuracy of sketch-DL supporting our theoretical results. Taken together, our results provide theoretical justification for the observed empirical success of sketch-DL.

We consider the mutual information between a uniformly-random input and the corresponding output through the deletion channel. We prove an upper bound that’s within approximately 0.1 of the best-known lower bounds for all values of the deletion probabilityd, and much closer for small and larged. We give simulation results which suggest that our upper bound is within 0.05 of the exact value for alld, and within 0.01 ford> 0.75. Despite our upper bounds, based on simulations, we conjecture that the mutual information is positive for all deletion probabilities less than 1. Our results imply impossibility results for the (equivalent) problem of compression of i.i.d. sources correlated via the deletion channel, a relevant model for DNA storage.

We propose sandwiched video compression – a video compression system that wraps neural networks around a standard video codec. The sandwich framework consists of a neural pre- and post-processor with a standard video codec between them. The networks are trained jointly to optimize a rate-distortion loss function with the goal of significantly improving over the standard codec in various compression scenarios. End-to-end training in this setting requires a differentiable proxy for the standard video codec, which incorporates temporal processing with motion compensation, inter/intra mode decisions, and in-loop filtering. We propose differentiable approximations to key video codec components and demonstrate that, in addition to providing meaningful compression improvements over the standard codec, the neural codes of the sandwich lead to significantly better rate-distortion performance in two important scenarios. When transporting high-resolution video via low-resolution HEVC, the sandwich system obtains 6.5 dB improvements over standard HEVC. More importantly, using the well-known perceptual similarity metric, LPIPS, we observe 30% improvements in rate at the same quality over HEVC. Last but not least, we show that pre- and post-processors formed by very modestly-parameterized, light-weight networks can closely approximate these results.

We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed order-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits), exact optimality (in the non-asymptotic setting) still has not been achieved. In this work, we take a step towards characterizing the exact-optimal approach in the presence of shared randomness (a random variable shared between the server and the user) and identify several conditions for exact optimality. We prove that one of the conditions is to utilize a rotationally symmetric shared random codebook. Based on this, we propose a randomization mechanism where the codebook is a randomly rotated simplex -- satisfying the properties of the exact-optimal codebook. The proposed mechanism is based on a $k$-closest encoding which we prove to be exact-optimal for the randomly rotated simplex codebook.

Compression and efficient storage of neural network (NN) parameters is critical for applications that run on resource-constrained devices. Despite the significant progress in NN model compression, there has been considerably less investigation in the actual physical storage of NN parameters. Conventionally, model compression and physical storage are decoupled, as digital storage media with error-correcting codes (ECCs) provide robust error-free storage. However, this decoupled approach is inefficient as it ignores the overparameterization present in most NNs and forces the memory device to allocate the same amount of resources to every bit of information regardless of its importance. In this work, we investigate analog memory devices as an alternative to digital media – one that naturally provides a way to add more protection for significant bits unlike its counterpart, but is noisy and may compromise the stored model’s performance if used naively. We develop a variety of robust coding strategies for NN weight storage on analog devices, and propose an approach to jointly optimize model compression and memory resource allocation. We then demonstrate the efficacy of our approach on models trained on MNIST, CIFAR-10, and ImageNet datasets for existing compression techniques. Compared to conventional error-free digital storage, our method reduces the memory footprint by up to one order of magnitude, without significantly compromising the stored model’s accuracy.

We study the neural network (NN) compression problem, viewing the tension between the compression ratio and NN performance through the lens of rate-distortion theory. We choose a distortion metric that reflects the effect of NN compression on the model output and then derive the tradeoff between rate (compression ratio) and distortion. In addition to characterizing theoretical limits of NN compression, this formulation shows that pruning, implicitly or explicitly, must be a part of a good compression algorithm. This observation bridges a gap between parts of the literature pertaining to NN and data compression, respectively, providing insight into the empirical success of pruning for NN compression. Finally, we propose a novel pruning strategy derived from our information-theoretic formulation and show that it outperforms the relevant baselines on CIFAR-10 and ImageNet datasets.

Storage-efficient privacy-guaranteed learning is crucial due to enormous amounts of sensitive user data required for increasingly many learning tasks. We propose a framework for reducing the storage cost while at the same time providing privacy guarantees, without essential loss in the utility of the data for learning. Our method comprises noise injection followed by lossy compression. We show that, when appropriately matching the lossy compression to the distribution of the added noise, the compressed examples converge, in distribution, to that of the noise-free training data. In this sense, the utility of the data for learning is essentially maintained, while reducing storage and privacy leakage by quantifiable amounts. We present experimental results on the CelebA dataset for gender classification and find that our suggested pipeline delivers in practice on the promise of the theory: the individuals in the images are unrecognizable (or less recognizable, depending on the noise level), overall storage of the data is substantially reduced, with no essential loss of the classification accuracy. As an added bonus, our experiments suggest that our method yields a substantial boost to robustness in the face of adversarial test data.