Deep Neural Networks (DNNs) have been a large driver for AI breakthroughs in recent years, ranging from self-driving cars to intelligent assistants. However, these models have been getting increasingly large as they become more accurate and safe. This means that their training becomes increasingly costly and time-consuming, and typically yields a single model to fit all targets. To mitigate this, various techniques have been proposed in the literature, including pruning, sparsification or quantization of the model weights and updates. While achieving high compression rates, they often incur significant computational overheads at training or lead to non-negligible accuracy penalty. Alternatively, factorization methods have been leveraged for low-rank compression of DNNs. Similarly, such techniques (e.g., SVD) frequently rely on heavy iterative decompositions of layers and are potentially sub-optimal for non-linear models, such as DNNs. We take a further step in designing efficient low-rank models and propose Maestro, a framework for trainable low-rank layers. Instead of iteratively applying a priori decompositions, the low-rank structure is baked into the training process through LoD, a low-rank ordered decomposition. Not only is this the first time importance ordering via sampling is applied on the decomposed DNN structure, but it also allows selecting ranks at a layer granularity. Our theoretical analysis demonstrates that LoD recovers the SVD decomposition of linear mapping on uniformly distributed data and PCA for linear autoencoders. Applied to DNNs, Maestro enables the extraction of lower footprint models that preserve performance. Simultaneously, it enables the graceful tradeoff between accuracy-latency for deployment to even more constrained devices, without retraining.

Feature normalization transforms such as Batch and Layer-Normalization have become indispensable ingredients of state-of-the-art deep neural networks. Recent studies on fine-tuning large pretrained models indicate that just tuning the parameters of these affine transforms can achieve high accuracy for downstream tasks. These findings open the questions about the expressive power of tuning the normalization layers of frozen networks. In this work, we take the first step towards this question and show that for random ReLU networks, finetuning only its normalization layers can reconstruct any target network that is $O(\sqrt{\text{width}})$ times smaller. We show that this holds even for randomly sparsified networks, under sufficient overparameterization, in agreement with prior empirical work.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including lexicographic operations, non-linear functions, function calls, program counters, and conditional branches. Using this framework, we emulate a computer using a simple instruction-set architecture, which allows us to map iterative algorithms to programs that can be executed by a constant depth looped transformer network. We show how a single frozen transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and even a full backpropagation, in-context learning algorithm. Our findings reveal the potential of transformer networks as programmable compute units and offer insight into the mechanics of attention.

Modern recommender systems perform large-scale retrieval by embedding queries and item candidates in the same unified space, followed by approximate nearest neighbor search to select top candidates given a query embedding. In this paper, we propose a novel generative retrieval approach, where the retrieval model autoregressively decodes the identifiers of the target candidates. To that end, we create semantically meaningful tuple of codewords to serve as a Semantic ID for each item. Given Semantic IDs for items in a user session, a Transformer-based sequence-to-sequence model is trained to predict the Semantic ID of the next item that the user will interact with. We show that recommender systems trained with the proposed paradigm significantly outperform the current SOTA models on various datasets. In addition, we show that incorporating Semantic IDs into the sequence-to-sequence model enhances its ability to generalize, as evidenced by the improved retrieval performance observed for items with no prior interaction history.

A recent work by Ramanujan et al. (2020) provides significant empirical evidence that sufficiently overparameterized, random neural networks contain untrained subnetworks that achieve state-of-the-art accuracy on several predictive tasks. A follow-up line of theoretical work provides justification of these findings by proving that slightly overparameterized neural networks, with commonly used continuous-valued random initializations can indeed be pruned to approximate any target network. In this work, we show that the amplitude of those random weights does not even matter. We prove that any target network of width $d$ and depth $l$ can be approximated up to arbitrary accuracy $\varepsilon$ by simply pruning a random network of binary $\{\pm1\}$ weights that is wider and deeper than the target network only by a polylogarithmic factor of $d, l$ and $\varepsilon$.

Fine-tuning pretrained language models (LMs) without making any architectural changes has become a norm for learning various language downstream tasks. However, for non-language downstream tasks, a common practice is to employ task-specific designs for input, output layers, and loss functions. For instance, it is possible to fine-tune an LM into an MNIST classifier by replacing the word embedding layer with an image patch embedding layer, the word token output layer with a 10-way output layer, and the word prediction loss with a 10-way classification loss, respectively. A natural question arises: Can LM fine-tuning solve non-language downstream tasks without changing the model architecture or loss function? To answer this, we propose Language-Interfaced Fine-Tuning (LIFT) and study its efficacy and limitations by conducting an extensive empirical study on a suite of non-language classification and regression tasks. LIFT does not make any changes to the model architecture or loss function, and it solely relies on the natural language interface, enabling "no-code machine learning with LMs." We find that LIFT performs comparably well across a wide range of low-dimensional classification and regression tasks, matching the performances of the best baselines in many cases, especially for the classification tasks. We also report experimental results on the fundamental properties of LIFT, including inductive bias, robustness, and sample complexity. We also analyze the effect of pretraining on LIFT and a few properties/techniques specific to LIFT, e.g., context-aware learning via appropriate prompting, calibrated predictions, data generation, and two-stage fine-tuning. Our code is available at https://github.com/UW-Madison-Lee-Lab/LanguageInterfacedFineTuning.

It is well known that modern deep neural networks are powerful enough to memorize datasets even when the labels have been randomized. Recently, Vershynin(2020) settled a long standing question by Baum(1988), proving that deep threshold networks can memorize $n$ points in $d$ dimensions using $\widetilde{\mathcal{O}}(e^{1/\delta^2}+\sqrt{n})$ neurons and $\widetilde{\mathcal{O}}(e^{1/\delta^2}(d+\sqrt{n})+n)$ weights, where $\delta$ is the minimum distance between the points. In this work, we improve the dependence on $\delta$ from exponential to almost linear, proving that $\widetilde{\mathcal{O}}(\frac{1}{\delta}+\sqrt{n})$ neurons and $\widetilde{\mathcal{O}}(\frac{d}{\delta}+n)$ weights are sufficient. Our construction uses Gaussian random weights only in the first layer, while all the subsequent layers use binary or integer weights. We also prove new lower bounds by connecting memorization in neural networks to the purely geometric problem of separating $n$ points on a sphere using hyperplanes.

Stochastic gradient descent without replacement sampling is widely used in practice for model training. However, the vast majority of SGD analyses assumes data is sampled with replacement, and when the function minimized is strongly convex, an $\mathcal{O}\left(\frac{1}{T}\right)$ rate can be established when SGD is run for $T$ iterations. A recent line of breakthrough works on SGD without replacement (SGDo) established an $\mathcal{O}\left(\frac{n}{T^2}\right)$ convergence rate when the function minimized is strongly convex and is a sum of $n$ smooth functions, and an $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^3}{T^3}\right)$ rate for sums of quadratics. On the other hand, the tightest known lower bound postulates an $\Omega\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ rate, leaving open the possibility of better SGDo convergence rates in the general case. In this paper, we close this gap and show that SGD without replacement achieves a rate of $\mathcal{O}\left(\frac{1}{T^2}+\frac{n^2}{T^3}\right)$ when the sum of the functions is a quadratic, and offer a new lower bound of $\Omega\left(\frac{n}{T^2}\right)$ for strongly convex functions that are sums of smooth functions.

The strong lottery ticket hypothesis (LTH) postulates that one can approximate any target neural network by only pruning the weights of a sufficiently over-parameterized random network. A recent work by Malach et al. [MYSS20] establishes the first theoretical analysis for the strong LTH: one can provably approximate a neural network of width $d$ and depth $l$, by pruning a random one that is a factor $O(d^4 l^2)$ wider and twice as deep. This polynomial over-parameterization requirement is at odds with recent experimental research that achieves good approximation with networks that are a small factor wider than the target. In this work, we close the gap and offer an exponential improvement to the over-parameterization requirement for the existence of lottery tickets. We show that any target network of width $d$ and depth $l$ can be approximated by pruning a random network that is a factor $O(log(dl))$ wider and twice as deep. Our analysis heavily relies on connecting pruning random ReLU networks to random instances of the Subset Sum problem. We then show that this logarithmic over-parameterization is essentially optimal for constant depth networks. Finally, we verify several of our theoretical insights with experiments.

Due to its decentralized nature, Federated Learning (FL) lends itself to adversarial attacks in the form of backdoors during training. The goal of a backdoor is to corrupt the performance of the trained model on specific sub-tasks (e.g., by classifying green cars as frogs). A range of FL backdoor attacks have been introduced in the literature, but also methods to defend against them, and it is currently an open question whether FL systems can be tailored to be robust against backdoors. In this work, we provide evidence to the contrary. We first establish that, in the general case, robustness to backdoors implies model robustness to adversarial examples, a major open problem in itself. Furthermore, detecting the presence of a backdoor in a FL model is unlikely assuming first-order oracles or polynomial time. We couple our theoretical results with a new family of backdoor attacks, which we refer to as edge-case backdoors. An edge-case backdoor forces a model to misclassify on seemingly easy inputs that are however unlikely to be part of the training, or test data, i.e., they live on the tail of the input distribution. We explain how these edge-case backdoors can lead to unsavory failures and may have serious repercussions on fairness. We further exhibit that, with careful tuning at the side of the adversary, one can insert them across a range of machine learning tasks (e.g., image classification, OCR, text prediction, sentiment analysis), and bypass state-of-the-art defense mechanisms.

Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial perturbations to the input data. Although DA is widely used, its capacity to provably improve robustness is not fully understood. In this work, we analyze the robustness that DA begets by quantifying the margin that DA enforces on empirical risk minimizers. We first focus on linear separators, and then a class of nonlinear models whose labeling is constant within small convex hulls of data points. We present lower bounds on the number of augmented data points required for non-zero margin, and show that commonly used DA techniques may only introduce significant margin after adding exponentially many points to the data set.

To improve the resilience of distributed training to worst-case, or Byzantine node failures, several recent methods have replaced gradient averaging with robust aggregation methods. Such techniques can have high computational costs, often quadratic in the number of compute nodes, and only have limited robustness guarantees. Other methods have instead used redundancy to guarantee robustness, but can only tolerate limited numbers of Byzantine failures. In this work, we present DETOX, a Byzantine-resilient distributed training framework that combines algorithmic redundancy with robust aggregation. DETOX operates in two steps, a filtering step that uses limited redundancy to significantly reduce the effect of Byzantine nodes, and a hierarchical aggregation step that can be used in tandem with any state-of-the-art robust aggregation method. We show theoretically that this leads to a substantial increase in robustness, and has a per iteration runtime that can be nearly linear in the number of compute nodes. We provide extensive experiments over real distributed setups across a variety of large-scale machine learning tasks, showing that DETOX leads to orders of magnitude accuracy and speedup improvements over many state-of-the-art Byzantine-resilient approaches.