Large Language Models (LLMs) have demonstrated exceptional performance in natural language processing tasks, yet their massive size makes serving them inefficient and costly. Semi-structured pruning has emerged as an effective method for model acceleration, but existing approaches are suboptimal because they focus on local, layer-wise optimizations using heuristic rules, failing to leverage global feedback. We present ProxSparse, a learning-based framework for mask selection enabled by regularized optimization. ProxSparse transforms the rigid, non-differentiable mask selection process into a smoother optimization procedure, allowing gradual mask exploration with flexibility. ProxSparse does not involve additional weight updates once the mask is determined. Our extensive evaluations on 7 widely used models show that ProxSparse consistently outperforms previously proposed semi-structured mask selection methods with significant improvement, demonstrating the effectiveness of our learned approach towards semi-structured pruning.

The prohibitive sizes of Large Language Models (LLMs) today make it difficult to deploy them on memory-constrained edge devices. This work introduces $\rm CALDERA$ -- a new post-training LLM compression algorithm that harnesses the inherent low-rank structure of a weight matrix $\mathbf{W}$ by approximating it via a low-rank, low-precision decomposition as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$. Here, $\mathbf{L}$ and $\mathbf{R}$ are low rank factors, and the entries of $\mathbf{Q}$, $\mathbf{L}$ and $\mathbf{R}$ are quantized. The model is compressed by substituting each layer with its $\mathbf{Q} + \mathbf{L}\mathbf{R}$ decomposition, and the zero-shot performance of the compressed model is evaluated. Additionally, $\mathbf{L}$ and $\mathbf{R}$ are readily amenable to low-rank adaptation, consequently enhancing the zero-shot performance. $\rm CALDERA$ obtains this decomposition by formulating it as an optimization problem $\min_{\mathbf{Q},\mathbf{L},\mathbf{R}}\lVert(\mathbf{Q} + \mathbf{L}\mathbf{R} - \mathbf{W})\mathbf{X}^\top\rVert_{\rm F}^2$, where $\mathbf{X}$ is the calibration data, and $\mathbf{Q}, \mathbf{L}, \mathbf{R}$ are constrained to be representable using low-precision formats. Theoretical upper bounds on the approximation error of $\rm CALDERA$ are established using a rank-constrained regression framework, and the tradeoff between compression ratio and model performance is studied by analyzing the impact of target rank and quantization bit budget. Results illustrate that compressing LlaMa-$2$ $7$B/$13$B/$70$B and LlaMa-$3$ $8$B models obtained using $\rm CALDERA$ outperforms existing post-training LLM compression techniques in the regime of less than $2.5$ bits per parameter.

Intermittent connectivity of clients to the parameter server (PS) is a major bottleneck in federated edge learning frameworks. The lack of constant connectivity induces a large generalization gap, especially when the local data distribution amongst clients exhibits heterogeneity. To overcome intermittent communication outages between clients and the central PS, we introduce the concept of collaborative relaying wherein the participating clients relay their neighbors’ local updates to the PS in order to boost the participation of clients with poor connectivity to the PS. We propose a semi-decentralized federated learning framework in which at every communication round, each client initially computes a local averaging of a subset of its neighboring clients’ updates, and eventually transmits to the PS a weighted average of its own update and those of its neighbors’. We appropriately optimize these local averaging weights to ensure that the global update at the PS is unbiased with minimal variance – consequently improving the convergence rate. Numerical evaluations on the CIFAR-10 dataset demonstrate that our collaborative relaying approach outperforms federated averaging-based benchmarks for learning over intermittently-connected networks such as when the clients communicate over millimeter wave channels with intermittent blockages.

The large memory footprint of high dimensional models require quantization to a lower precision for deployment on resource constrained edge devices. With this motivation, we consider the problems of learning a (i) linear regressor, and a (ii) linear classifier from a given training dataset, and quantizing the learned model parameters subject to a pre-specified bit-budget. The error metric is the prediction risk of the quantized model, and our proposed randomized embedding-based quantization methods attain near-optimal error while being computationally efficient. We provide fundamental bounds on the bit-budget constrained minimax risk that, together with our proposed algorithms, characterize the minimum threshold budget required to achieve a risk comparable to the unquantized setting. We also show the efficacy of our strategy by quantizing a two-layer ReLU neural network for non-linear regression. Numerical simulations show the improved performance of our proposed scheme as well as its closeness to the lower bound.

This work considers the problem of Distributed Mean Estimation (DME) over networks with intermittent connectivity, where the goal is to learn a global statistic over the data samples localized across distributed nodes with the help of a central server. To mitigate the impact of intermittent links, nodes can collaborate with their neighbors to compute local consensus which they forward to the central server. In such a setup, the communications between any pair of nodes must satisfy local differential privacy constraints. We study the tradeoff between collaborative relaying and privacy leakage due to the additional data sharing among nodes and, subsequently, propose a novel differentially private collaborative algorithm for DME to achieve the optimal tradeoff. Finally, we present numerical simulations to substantiate our theoretical findings.

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. Although prohibitively large, such matrices are often approximately low rank. We propose an algorithm that exploits this structure to obtain a low rank decomposition of any matrix $\mathbf{A}$ as $\mathbf{A} \approx \mathbf{L}\mathbf{R}$, where $\mathbf{L}$ and $\mathbf{R}$ are the low rank factors. The total number of elements in $\mathbf{L}$ and $\mathbf{R}$ can be significantly less than that in $\mathbf{A}$. Furthermore, the entries of $\mathbf{L}$ and $\mathbf{R}$ are quantized to low precision formats -- compressing $\mathbf{A}$ by giving us a low rank and low precision factorization. Our algorithm first computes an approximate basis of the range space of $\mathbf{A}$ by randomly sketching its columns, followed by a quantization of the vectors constituting this basis. It then computes approximate projections of the columns of $\mathbf{A}$ onto this quantized basis. We derive upper bounds on the approximation error of our algorithm, and analyze the impact of target rank and quantization bit-budget. The tradeoff between compression ratio and approximation accuracy allows for flexibility in choosing these parameters based on specific application requirements. We empirically demonstrate the efficacy of our algorithm in image compression, nearest neighbor classification of image and text embeddings, and compressing the layers of LlaMa-$7$b. Our results illustrate that we can achieve compression ratios as aggressive as one bit per matrix coordinate, all while surpassing or maintaining the performance of traditional compression techniques.

When humans collaborate with each other, they often make decisions by observing others and considering the consequences that their actions may have on the entire team, instead of greedily doing what is best for just themselves. We would like our AI agents to effectively collaborate in a similar way by capturing a model of their partners. In this work, we propose and analyze a decentralized Multi-Armed Bandit (MAB) problem with coupled rewards as an abstraction of more general multi-agent collaboration. We demonstrate that naive extensions of single-agent optimal MAB algorithms fail when applied for decentralized bandit teams. Instead, we propose a Partner-Aware strategy for joint sequential decision-making that extends the well-known single-agent Upper Confidence Bound algorithm. We analytically show that our proposed strategy achieves logarithmic regret, and provide extensive experiments involving human-AI and human-robot collaboration to validate our theoretical findings. Our results show that the proposed partner-aware strategy outperforms other known methods, and our human subject studies suggest humans prefer to collaborate with AI agents implementing our partner-aware strategy.

We present a semi-decentralized federated learning algorithm wherein clients collaborate by relaying their neighbors’ local updates to a central parameter server (PS). At every communication round to the PS, each client computes a local consensus of the updates from its neighboring clients and eventually transmits a weighted average of its own update and those of its neighbors to the PS. We appropriately optimize these averaging weights to ensure that the global update at the PS is unbiased and to reduce the variance of the global update at the PS, consequently improving the rate of convergence. Numerical simulations substantiate our theoretical claims and demonstrate settings with intermittent connectivity between the clients and the PS, where our proposed algorithm shows an improved convergence rate and accuracy in comparison with the federated averaging algorithm.

In decentralized optimization, multiple nodes in a network collaborate to minimize the sum of their local loss functions. The information exchange between nodes required for this task, is often limited by network connectivity. We consider a setting in which communication between nodes is hindered by both (i) a finite rate-constraint on the signal transmitted by any node, and (ii) additive noise corrupting the signal received by any node. We propose a novel algorithm for this scenario: Decentralized Lazy Mirror Descent with Differential Exchanges (DLMD-DiffEx), which guarantees convergence of the local estimates to the optimal solution under the given communication constraints. A salient feature of DLMD-DiffEx is the introduction of additional proxy variables that are maintained by the nodes to account for the disagreement in their estimates due to channel noise and rate-constraints. Convergence to the optimal solution is attained by having nodes iteratively exchange these disagreement terms until consensus is achieved. In order to prevent noise accumulation during this exchange, DLMD-DiffEx relies on two sequences: one controlling the power of the transmitted signal, and the other determining the consensus rate. We provide insights on the design of these two sequences which highlights the interplay between consensus rate and noise amplification. We investigate the performance of DLMD-DiffEx both from a theoretical perspective as well as through numerical evaluations on synthetic data and MNIST. MATLAB and Python implementations can be found athttps://github.com/rajarshisaha95/DLMD-DiffEx.

In decentralized optimization, multiple nodes in a network collaborate to minimize the sum of their local loss functions. The information exchange between nodes required for this task is often limited by network connectivity. We consider a generalization of this setting, in which communication is further hindered by (i) a finite data-rate constraint on the signal transmitted by any node, and (ii) an additive noise corrupting the signal received by any node. We develop a novel algorithm for this scenario: Decentralized Lazy Mirror Descent with Differential Exchanges (DLMD-DiffEx), which guarantees convergence of the local estimates to the optimal solution. A salient feature of DLMD-DiffEx is the introduction of additional proxy variables that are maintained by the nodes to account for the disagreement in their estimates due to channel noise and data-rate constraints. We investigate the performance of DLMD-DiffEx both from a theoretical perspective as well as through numerical evaluations.