Each sublayer adds a skip-connection (ADD) and batch normalization (BN). The decoder sequentially chooses a node according to a probability distribution produced by the node embeddings to construct a solution. The scaled symmetric sampling method is shown in Algorithm 2. The scaled factor The uniform division of the weight space is illustrated as follows. Thus, its approximate Pareto optimal solutions are commonly pursued. V ehicles must serve all the customers and finally return to the depot.

Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MO-COPs).

Suppose an n x d design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number k << n of the responses, and then produce a weight vector whose sum of squares loss over points is at most 1+epsilon times the minimum. When k is very small (e.g., k=d), jointly sampling diverse subsets of points is crucial. One such method called volume sampling has a unique and desirable property that the weight vector it produces is an unbiased estimate of the optimum. It is therefore natural to ask if this method offers the optimal unbiased estimate in terms of the number of responses k needed to achieve a 1+epsilon loss approximation. Surprisingly we show that volume sampling can have poor behavior when we require a very accurate approximation -- indeed worse than some i.i.d.

Machine learning models exhibit strong performance on datasets with abundant labeled samples.

We propose the position-based scaled gradient (PSG) that scales the gradient depending on the position of a weight vector to make it more compression-friendly. First, we theoretically show that applying PSG to the standard gradient descent (GD), which is called PSGD, is equivalent to the GD in the warped weight space, a space made by warping the original weight space via an appropriately designed invertible function. Second, we empirically show that PSG acting as a regularizer to a weight vector is favorable for model compression domains such as quantization and pruning. PSG reduces the gap between the weight distributions of a full-precision model and its compressed counterpart. This enables the versatile deployment of a model either as an uncompressed mode or as a compressed mode depending on the availability of resources. The experimental results on CIFAR-10/100 and ImageNet datasets show the effectiveness of the proposed PSG in both domains of pruning and quantization even for extremely low bits. The code is released in Github.

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex.These models learn a shared set of nonlinear basis functions, which are linearly combined via a learned weight vector to represent a neuron's function.Such weight vectors, which can be thought as embeddings of neuronal function, have been proposed to define functional cell types via unsupervised clustering.However, as deep models are usually highly overparameterized, the learning problem is unlikely to have a unique solution, which raises the question if such embeddings can be used in a meaningful way for downstream analysis.In this paper, we investigate how stable neuronal embeddings are with respect to changes in model architecture and initialization. We find that $L_1$ regularization to be an important ingredient for structured embeddings and develop an adaptive regularization that adjusts the strength of regularization per neuron. This regularization improves both predictive performance and how consistently neuronal embeddings cluster across model fits compared to uniform regularization.To overcome overparametrization, we propose an iterative feature pruning strategy which reduces the dimensionality of performance-optimized models by half without loss of performance and improves the consistency of neuronal embeddings with respect to clustering neurons.Our results suggest that to achieve an objective taxonomy of cell types or a compact representation of the functional landscape, we need novel architectures or learning techniques that improve identifiability.

Network weights can be reverse-engineered given enough informative samples of a network's input-output function. In a teacher-student setup, this translates into collecting a dataset of the teacher mapping -- querying the teacher -- and fitting a student to imitate such mapping. A sensible choice of queries is the dataset the teacher is trained on. But current methods fail when the teacher parameters are more numerous than the training data, because the student overfits to the queries instead of aligning its parameters to the teacher. In this work, we explore augmentation techniques to best sample the input-output mapping of a teacher network, with the goal of eliciting a rich set of representations from the teacher hidden layers. We discover that standard augmentations such as rotation, flipping, and adding noise, bring little to no improvement to the identification problem. We design new data augmentation techniques tailored to better sample the representational space of the network's hidden layers. With our augmentations we extend the state-of-the-art range of recoverable network sizes. To test their scalability, we show that we can recover networks of up to 100 times more parameters than training data-points.

As Large Language Models (LLMs) continue to grow in size, storing and transmitting them on edge devices becomes increasingly challenging. Traditional methods like quantization and pruning struggle to achieve extreme compression of LLMs without sacrificing accuracy. In this paper, we introduce PocketLLM, a novel approach to compress LLMs in a latent space via meta-networks. A simple encoder network is proposed to project the weights of LLMs into discrete latent vectors, which are then represented using a compact codebook. A lightweight decoder network is employed to map the codebook's representative vectors back to the original weight space. This method allows for significant compression of the large weights in LLMs, consisting solely of a small decoder, a concise codebook, and an index. Extensive experiments show that PocketLLM achieves superior performance even at significantly high compression ratios, e.g., compressing Llama 2-7B by 10x with a negligible drop in accuracy.

In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are functions of the form $\vct{x}\mapsto \max(0,\langle \vct{w},\vct{x}\rangle)$ with $\vct{w}\in\R^d$ denoting the weight vector. We study this problem in the high-dimensional regime where the number of observations are fewer than the dimension of the weight vector. We assume that the weight vector belongs to some closed set (convex or nonconvex) which captures known side-information about its structure. We focus on the realizable model where the inputs are chosen i.i.d.~from a Gaussian distribution and the labels are generated according to a planted weight vector. We show that projected gradient descent, when initialized at $\vct{0}$, converges at a linear rate to the planted model with a number of samples that is optimal up to numerical constants. Our results on the dynamics of convergence of these very shallow neural nets may provide some insights towards understanding the dynamics of deeper architectures.