arXiv subjects

Bo Bai

Publications and source records attributed to Bo Bai.

At least 37 records · Page 2Linked to original sources

arXiv2024

Towards Faster Graph Partitioning via Pre-training and Inductive Inference

Graph partitioning (GP) is a classic problem that divides the node set of a graph into densely-connected blocks. Following the IEEE HPEC Graph Challenge and recent advances in pre-training techniques (e.g., large-language models), we propose PR-GPT (Pre-trained & Refined Graph ParTitioning) based on a novel pre-training & refinement paradigm. We first conduct the offline pre-training of a deep graph learning (DGL) model on small synthetic graphs with various topology properties. By using the inductive inference of DGL, one can directly generalize the pre-trained model (with frozen model parameters) to large graphs and derive feasible GP results. We also use the derived partition as a good initialization of an efficient GP method (e.g., InfoMap) to further refine the quality of partitioning. In this setting, the online generalization and refinement of PR-GPT can not only benefit from the transfer ability regarding quality but also ensure high inference efficiency without re-training. Based on a mechanism of reducing the scale of a graph to be processed by the refinement method, PR-GPT also has the potential to support streaming GP. Experiments on the Graph Challenge benchmark demonstrate that PR-GPT can ensure faster GP on large-scale graphs without significant quality degradation, compared with running a refinement method from scratch. We will make our code public at https://github.com/KuroginQin/PRGPT.

cs.LG↗

arXiv2024

A Mean Field Ansatz for Zero-Shot Weight Transfer

The pre-training cost of large language models (LLMs) is prohibitive. One cutting-edge approach to reduce the cost is zero-shot weight transfer, also known as model growth for some cases, which magically transfers the weights trained in a small model to a large model. However, there are still some theoretical mysteries behind the weight transfer. In this paper, inspired by prior applications of mean field theory to neural network dynamics, we introduce a mean field ansatz to provide a theoretical explanation for weight transfer. Specifically, we propose the row-column (RC) ansatz under the mean field point of view, which describes the measure structure of the weights in the neural network (NN) and admits a close measure dynamic. Thus, the weights of different sizes NN admit a common distribution under proper assumptions, and weight transfer methods can be viewed as sampling methods. We empirically validate the RC ansatz by exploring simple MLP examples and LLMs such as GPT-3 and Llama-3.1. We show the mean-field point of view is adequate under suitable assumptions which can provide theoretical support for zero-shot weight transfer.

cs.LG↗

arXiv2024

Error Correction Decoding Algorithms of RS Codes Based on An Earlier Termination Algorithm to Find The Error Locator Polynomial

Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for solving the Welch-Berlekamp (WB) key-equation problem to find the error locator polynomial that needs $2t$ steps, where $t$ is the error correction capability. In this paper, we first present a new MA algorithm that only requires $2e$ steps and then propose two fast decoding algorithms for RS codes based on our MA algorithm, where $e$ is the number of errors and $e\leq t$. We propose Improved-Frequency Domain Modular Approach (I-FDMA) algorithm that needs $2e$ steps to solve the error locator polynomial and present our first decoding algorithm based on the I-FDMA algorithm. We show that, compared with the existing methods based on MA algorithms, our I-FDMA algorithm can effectively reduce the decoding complexity of RS codes when $e<t$. Furthermore, we propose the $t_0$-Shortened I-FDMA ($t_0$-SI-FDMA) algorithm ($t_0$ is a predetermined even number less than $2t-1$) based on the new termination mechanism to solve the error number $e$ quickly. We propose our second decoding algorithm based on the SI-FDMA algorithm for RS codes and show that the multiplication complexity of our second decoding algorithm is lower than our first decoding algorithm (the I-FDMA decoding algorithm) when $2e<t_0+1$.

cs.IT↗

arXiv2024

Retrieval Meets Reasoning: Dynamic In-Context Editing for Long-Text Understanding

Current Large Language Models (LLMs) face inherent limitations due to their pre-defined context lengths, which impede their capacity for multi-hop reasoning within extensive textual contexts. While existing techniques like Retrieval-Augmented Generation (RAG) have attempted to bridge this gap by sourcing external information, they fall short when direct answers are not readily available. We introduce a novel approach that re-imagines information retrieval through dynamic in-context editing, inspired by recent breakthroughs in knowledge editing. By treating lengthy contexts as malleable external knowledge, our method interactively gathers and integrates relevant information, thereby enabling LLMs to perform sophisticated reasoning steps. Experimental results demonstrate that our method effectively empowers context-limited LLMs, such as Llama2, to engage in multi-hop reasoning with improved performance, which outperforms state-of-the-art context window extrapolation methods and even compares favorably to more advanced commercial long-context models. Our interactive method not only enhances reasoning capabilities but also mitigates the associated training and computational costs, making it a pragmatic solution for enhancing LLMs' reasoning within expansive contexts.

cs.CL↗

arXiv2024

Set Transformation: Trade-off Between Repair Bandwidth and Sub-packetization

Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization level being one, however, they require large repair bandwidth defined as the total amount of symbols downloaded from other surviving nodes during single-node failure/repair. In this paper, we present the {\em set transformation}, which can transform any MDS code into set transformed code such that (i) the sub-packetization level is flexible and ranges from 2 to $(n-k)^{\lfloor\frac{n}{n-k}\rfloor}$ in which $n$ is the number of nodes and $k$ is the number of data nodes, (ii) the new code is MDS code, (iii) the new code has lower repair bandwidth for any single-node failure. We show that our set transformed codes have both lower repair bandwidth and lower field size than the existing related MDS array codes, such as elastic transformed codes \cite{10228984}. Specifically, our set transformed codes have $2\%-6.6\%$ repair bandwidth reduction compared with elastic transformed codes \cite{10228984} for the evaluated typical parameters.

cs.IT↗

arXiv2024

Extreme Video Compression with Pre-trained Diffusion Models

Diffusion models have achieved remarkable success in generating high quality image and video data. More recently, they have also been used for image compression with high perceptual quality. In this paper, we present a novel approach to extreme video compression leveraging the predictive power of diffusion-based generative models at the decoder. The conditional diffusion model takes several neural compressed frames and generates subsequent frames. When the reconstruction quality drops below the desired level, new frames are encoded to restart prediction. The entire video is sequentially encoded to achieve a visually pleasing reconstruction, considering perceptual quality metrics such as the learned perceptual image patch similarity (LPIPS) and the Frechet video distance (FVD), at bit rates as low as 0.02 bits per pixel (bpp). Experimental results demonstrate the effectiveness of the proposed scheme compared to standard codecs such as H.264 and H.265 in the low bpp regime. The results showcase the potential of exploiting the temporal relations in video data using generative models. Code is available at: https://github.com/ElesionKyrie/Extreme-Video-Compression-With-Prediction-Using-Pre-trainded-Diffusion-Models-

eess.IV↗

arXiv2024

A Constrained BA Algorithm for Rate-Distortion and Distortion-Rate Functions

The Blahut-Arimoto (BA) algorithm has played a fundamental role in the numerical computation of rate-distortion (RD) functions. This algorithm possesses a desirable monotonic convergence property by alternatively minimizing its Lagrangian with a fixed multiplier. In this paper, we propose a novel modification of the BA algorithm, wherein the multiplier is updated through a one-dimensional root-finding step using a monotonic univariate function, efficiently implemented by Newton's method in each iteration. Consequently, the modified algorithm directly computes the RD function for a given target distortion, without exploring the entire RD curve as in the original BA algorithm. Moreover, this modification presents a versatile framework, applicable to a wide range of problems, including the computation of distortion-rate (DR) functions. Theoretical analysis shows that the outputs of the modified algorithms still converge to the solutions of the RD and DR functions with rate $O(1/n)$, where $n$ is the number of iterations. Additionally, these algorithms provide $\varepsilon$-approximation solutions with $O\left(\frac{MN\log N}{\varepsilon}(1+\log |\log \varepsilon|)\right)$ arithmetic operations, where $M,N$ are the sizes of source and reproduced alphabets respectively. Numerical experiments demonstrate that the modified algorithms exhibit significant acceleration compared with the original BA algorithms and showcase commendable performance across classical source distributions such as discretized Gaussian, Laplacian and uniform sources.

cs.IT↗

arXiv2023

Localization and Discrete Beamforming with a Large Reconfigurable Intelligent Surface

In millimeter-wave (mmWave) cellular systems, reconfigurable intelligent surfaces (RISs) are foreseeably deployed with a large number of reflecting elements to achieve high beamforming gains. The large-sized RIS will make radio links fall in the near-field localization regime with spatial non-stationarity issues. Moreover, the discrete phase restriction on the RIS reflection coefficient incurs exponential complexity for discrete beamforming. It remains an open problem to find the optimal RIS reflection coefficient design in polynomial time. To address these issues, we propose a scalable partitioned-far-field protocol that considers both the near-filed non-stationarity and discrete beamforming. The protocol approximates near-field signal propagation using a partitioned-far-field representation to inherit the sparsity from the sophisticated far-field and facilitate the near-field localization scheme. To improve the theoretical localization performance, we propose a fast passive beamforming (FPB) algorithm that optimally solves the discrete RIS beamforming problem, reducing the search complexity from exponential order to linear order. Furthermore, by exploiting the partitioned structure of RIS, we introduce a two-stage coarse-to-fine localization algorithm that leverages both the time delay and angle information. Numerical results demonstrate that centimeter-level localization precision is achieved under medium and high signal-to-noise ratios (SNR), revealing that RISs can provide support for low-cost and high-precision localization in future cellular systems.

cs.IT↗

arXiv2023

Extending Context Window of Large Language Models via Semantic Compression

Transformer-based Large Language Models (LLMs) often impose limitations on the length of the text input to ensure the generation of fluent and relevant responses. This constraint restricts their applicability in scenarios involving long texts. We propose a novel semantic compression method that enables generalization to texts that are 6-8 times longer, without incurring significant computational costs or requiring fine-tuning. Our proposed framework draws inspiration from source coding in information theory and employs a pre-trained model to reduce the semantic redundancy of long inputs before passing them to the LLMs for downstream tasks. Experimental results demonstrate that our method effectively extends the context window of LLMs across a range of tasks including question answering, summarization, few-shot learning, and information retrieval. Furthermore, the proposed semantic compression method exhibits consistent fluency in text generation while reducing the associated computational overhead.

cs.CL↗

arXiv2023

RaftGP: Random Fast Graph Partitioning

Graph partitioning (GP), a.k.a. community detection, is a classic problem that divides the node set of a graph into densely-connected blocks. Following prior work on the IEEE HPEC Graph Challenge benchmark and recent advances in graph machine learning, we propose a novel RAndom FasT Graph Partitioning (RaftGP) method based on an efficient graph embedding scheme. It uses the Gaussian random projection to extract community-preserving features from classic GP objectives. These features are fed into a graph neural network (GNN) to derive low-dimensional node embeddings. Surprisingly, our experiments demonstrate that a randomly initialized GNN even without training is enough for RaftGP to derive informative community-preserving embeddings and support high-quality GP. To enable the derived embeddings to tackle GP, we introduce a hierarchical model selection algorithm that simultaneously determines the number of blocks and the corresponding GP result. We evaluate RaftGP on the Graph Challenge benchmark and compare the performance with five baselines, where our method can achieve a better trade-off between quality and efficiency. In particular, compared to the baseline algorithm of the IEEE HPEC Graph Challenge, our method is 6.68x -- 23.9x faster on graphs with 1E3 -- 5E4 nodes and at least 64.5x faster on larger (1E5 node) graphs on which the baseline takes more than 1E4 seconds. Our method achieves better accuracy on all test cases. We also develop a new graph generator to address some limitations of the original generator in the benchmark.

cs.SI↗

arXiv2023

Conditional graph entropy as an alternating minimization problem

Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. This also leads to a new formula which shows that conditional graph entropy is part of a more general framework: the solution of an optimization problem over a convex corner. In the special case of graph entropy (i.e., unconditioned version) this was known due to Csiszár, Körner, Lovász, Marton, and Simonyi. In that case the role of the convex corner was played by the so-called vertex packing polytope. In the conditional version it is a more intricate convex body but the function to minimize is the same. Furthermore, we describe a dual problem that leads to an optimality check and an error bound for the iterative algorithm.

cs.IT↗

arXiv2023

Generalized Simple Regenerating Codes: Trading Sub-packetization and Fault Tolerance

Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes.

cs.IT↗

arXiv2023

MDS Array Codes With Small Sub-packetization Levels and Small Repair Degrees

High-rate minimum storage regenerating (MSR) codes are known to require a large sub-packetization level, which can make meta-data management difficult and hinder implementation in practical systems. A few maximum distance separable (MDS) array code constructions have been proposed to attain a much smaller sub-packetization level by sacrificing a bit of repair bandwidth. However, to the best of our knowledge, only one construction by Guruswami et al. can support the repair of a failed node without contacting all the surviving nodes. This construction is certainly of theoretical interest but not yet practical due to its requirement for very large code parameters. In this paper, we propose a generic transformation that can convert any $(\overline{n}, \overline{k})$ MSR code with a repair degree of $\overline{d}<\overline{n}-1$ into another $(n=s\overline{n},k)$ MDS array code that supports $d<n-1$ with a small sub-packetization level and $(1+ε)$-optimal repair bandwidth (i.e., $1+ε$ times the optimal value) under a specific condition. We obtain three MDS array codes with small sub-packetization levels and $(1+ε)$-optimal repair bandwidth by applying this transformation to three known MSR codes. All the new MDS array codes have a small repair degree of $d<n-1$ and work for both small and large code parameters.

cs.IT↗

arXiv2023

Information Bottleneck Revisited: Posterior Probability Perspective with Optimal Transport

Information bottleneck (IB) is a paradigm to extract information in one target random variable from another relevant random variable, which has aroused great interest due to its potential to explain deep neural networks in terms of information compression and prediction. Despite its great importance, finding the optimal bottleneck variable involves a difficult nonconvex optimization problem due to the nonconvexity of mutual information constraint. The Blahut-Arimoto algorithm and its variants provide an approach by considering its Lagrangian with fixed Lagrange multiplier. However, only the strictly concave IB curve can be fully obtained by the BA algorithm, which strongly limits its application in machine learning and related fields, as strict concavity cannot be guaranteed in those problems. To overcome the above difficulty, we derive an entropy regularized optimal transport (OT) model for IB problem from a posterior probability perspective. Correspondingly, we use the alternating optimization procedure and generalize the Sinkhorn algorithm to solve the above OT model. The effectiveness and efficiency of our approach are demonstrated via numerical experiments.

cs.IT↗

arXiv2023

Generalizing Körner's graph entropy to graphons

Körner introduced the notion of graph entropy in 1973 as the minimal code rate of a natural coding problem where not all pairs of letters can be distinguished in the alphabet. Later it turned out that it can be expressed as the solution of a minimization problem over the so-called vertex-packing polytope. In this paper we generalize this notion to graphons. We show that the analogous minimization problem provides an upper bound for graphon entropy. We also give a lower bound in the shape of a maximization problem. The main result of the paper is that for most graphons these two bounds actually coincide and hence precisely determine the entropy in question. Furthermore, graphon entropy has a nice connection to the fractional chromatic number and the fractional clique number.

math.CO↗

arXiv2023

A Hybrid Wireless Image Transmission Scheme with Diffusion

We propose a hybrid joint source-channel coding (JSCC) scheme, in which the conventional digital communication scheme is complemented with a generative refinement component to improve the perceptual quality of the reconstruction. The input image is decomposed into two components: the first is a coarse compressed version, and is transmitted following the conventional separation based approach. An additional component is obtained through the diffusion process by adding independent Gaussian noise to the input image, and is transmitted using DeepJSCC. The decoder combines the two signals to produce a high quality reconstruction of the source. Experimental results show that the hybrid design provides bandwidth savings and enables graceful performance improvement as the channel quality improves.

cs.IT↗

arXiv2023

Phase Transitions of Structured Codes of Graphs

We consider the symmetric difference of two graphs on the same vertex set $[n]$, which is the graph on $[n]$ whose edge set consists of all edges that belong to exactly one of the two graphs. Let $\mathcal{F}$ be a class of graphs, and let $M_{\mathcal{F}}(n)$ denote the maximum possible cardinality of a family $\mathcal{G}$ of graphs on $[n]$ such that the symmetric difference of any two members in $\mathcal{G}$ belongs to $\mathcal{F}$. These concepts are recently investigated by Alon, Gujgiczer, Körner, Milojević, and Simonyi, with the aim of providing a new graphic approach to coding theory. In particular, $M_{\mathcal{F}}(n)$ denotes the maximum possible size of this code. Existing results show that as the graph class $\mathcal{F}$ changes, $M_{\mathcal{F}}(n)$ can vary from $n$ to $2^{(1+o(1))\binom{n}{2}}$. We study several phase transition problems related to $M_{\mathcal{F}}(n)$ in general settings and present a partial solution to a recent problem posed by Alon et. al.

math.CO↗

arXiv2023

dMAPAR-HMM: Reforming Traffic Model for Improving Performance Bound with Stochastic Network Calculus

A popular branch of stochastic network calculus (SNC) utilizes moment-generating functions (MGFs) to characterize arrivals and services, which enables end-to-end performance analysis. However, existing traffic models for SNC cannot effectively represent the complicated nature of real-world network traffic such as dramatic burstiness. To conquer this challenge, we propose an adaptive spatial-temporal traffic model: dMAPAR-HMM. Specifically, we model the temporal on-off switching process as a dual Markovian arrival process (dMAP) and the arrivals during the on phases as an autoregressive hidden Markov model (AR-HMM). The dMAPAR-HMM model fits in with the MGF-SNC analysis framework, unifies various state-of-the-art arrival models, and matches real-world data more closely. We perform extensive experiments with real-world traces under different network topologies and utilization levels. Experimental results show that dMAPAR-HMM significantly outperforms prevailing models in MGF-SNC.

cs.NI↗