Recent years have witnessed a significant increase in the storage density of NAND flash memory, making it a critical component in modern electronic devices. However, with the rise in storage capacity comes an increased likelihood of errors in data storage and retrieval. The growing number of errors poses ongoing challenges for system designers and engineers, in terms of the characterization, modeling, and optimization of NAND-based systems. We present a novel approach for modeling and preventing errors by utilizing the capabilities of generative and unsupervised machine learning methods. As part of our research, we constructed and trained a neural modulator that translates information bits into programming operations on each memory cell in NAND devices. Our modulator, tailored explicitly for flash memory channels, provides a smart writing scheme that reduces programming errors as well as compensates for data degradation over time. Specifically, the modulator is based on an auto-encoder architecture with an additional channel model embedded between the encoder and the decoder. A conditional generative adversarial network (cGAN) was used to construct the channel model. Optimized for the end-of-life work-point, the learned memory system outperforms the prior art by up to 56\% in raw bit error rate (RBER) and extends the lifetime of the flash memory block by up to 25\%.

Combinatorial optimization (CO) problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions. We demonstrate the efficacy of this approach to obtain valid solutions to the maximum clique problem and to perform local graph clustering. Our method achieves competitive results on both real datasets and synthetic hard instances.

The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding near-optimal ESPP, enabled by an unsupervised graph neural network that jointly learns node value estimates and edge-selection probabilities via a surrogate loss function. The loss provides a high probability certificate of finding near-optimal ESPP solutions by simultaneously reducing negative-cost cycles and embedding the desired algorithmic alignment. At inference time, a decoding algorithm transforms the learned edge probabilities into an elementary path. Experiments on graphs of up to 100 nodes show that the proposed method surpasses both unsupervised baselines and classical heuristics, while exhibiting high performance in cross-size and cross-topology generalization on unseen synthetic graphs.

Summary and Contributions: This paper considers the problem of learning to do combinatorial optimization on graphs. In particular, it focuses on a set of constrained minimization problems: given an objective function and a constraint, find a set of nodes minimizing the objective function subject to the constraint. This is a broad family that includes many NP-hard problems. The goal is to train a neural network such that, when given a new instance of one of these problems, it can efficiently compute a solution satisfying the constraints whose cost is "close" to the optimal cost. This work proposes a novel framework for unsupervised combinatorial optimization on graphs, which is inspired by Erdos's probabilistic proof technique and makes it more likely that the outputs produce a valid solution when compared to previous approaches.

This is a surprising, novel, and principled framework for unsupervised ML-based combinatorial optimization. The paper should be improved following suggestions discussed in the rebuttal, but this should be straightforward. Overall, I'll quote R2: "Unlike many recent papers in this space which are rather incremental in combining GNN with reinforcement learning in various ways, this paper proposes a fresh, fundamentally new perspective."

Recent years have witnessed a significant increase in the storage density of NAND flash memory, making it a critical component in modern electronic devices. However, with the rise in storage capacity comes an increased likelihood of errors in data storage and retrieval. The growing number of errors poses ongoing challenges for system designers and engineers, in terms of the characterization, modeling, and optimization of NAND-based systems. We present a novel approach for modeling and preventing errors by utilizing the capabilities of generative and unsupervised machine learning methods. As part of our research, we constructed and trained a neural modulator that translates information bits into programming operations on each memory cell in NAND devices.

Combinatorial optimization (CO) problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions.

The Maximum Minimal Cut Problem (MMCP), a NP-hard combinatorial optimization (CO) problem, has not received much attention due to the demanding and challenging bi-connectivity constraint. Moreover, as a CO problem, it is also a daunting task for machine learning, especially without labeled instances. To deal with these problems, this work proposes an unsupervised learning framework combined with heuristics for MMCP that can provide valid and high-quality solutions. As far as we know, this is the first work that explores machine learning and heuristics to solve MMCP. The unsupervised solver is inspired by a relaxation-plus-rounding approach, the relaxed solution is parameterized by graph neural networks, and the cost and penalty of MMCP are explicitly written out, which can train the model end-to-end. A crucial observation is that each solution corresponds to at least one spanning tree. Based on this finding, a heuristic solver that implements tree transformations by adding vertices is utilized to repair and improve the solution quality of the unsupervised solver. Alternatively, the graph is simplified while guaranteeing solution consistency, which reduces the running time. We conduct extensive experiments to evaluate our framework and give a specific application. The results demonstrate the superiority of our method against two techniques designed.

--In many optimization problems in wireless communications, the expressions of objective function or constraints are hard or even impossible to derive, which makes the solutions difficult to find. In this paper, we propose a model-free learning framework to solve constrained optimization problems without the supervision of the optimal solution. Neural networks are used respectively for parameterizing the function to be optimized, parameterizing the Lagrange multiplier associated with instantaneous constraints, and approximating the unknown objective function or constraints. We provide learning algorithms to train all the neural networks simultaneously, and reveal the connections of the proposed framework with reinforcement learning. Numerical and simulation results validate the proposed framework and demonstrate the efficiency of model-free learning by taking power control problem as an example. I NTRODUCTION V arious resource allocation and transceivers in wireless networks, such as power allocation, beamforming, and caching policy, can be designed by solving optimization problems with constraints, say imposed by the maximal transmit power, cache size, and the minimal data rate requirement [1, 2]. Depending on the applications, the objective function, constraints and the policy to be optimized may vary in different timescales.