We have recently witnessed that "Intelligence" and " Compression" are the two sides of the same coin, where the language large model (LLM) with unprecedented intelligence is a general-purpose lossless compressor for various data modalities. This attribute particularly appeals to the lossless image compression community, given the increasing need to compress high-resolution images in the current streaming media era. Consequently, a spontaneous envision emerges: Can the compression performance of the LLM elevate lossless image compression to new heights? However, our findings indicate that the naive application of LLM-based lossless image compressors suffers from a considerable performance gap compared with existing state-of-the-art (SOTA) codecs on common benchmark datasets. In light of this, we are dedicated to fulfilling the unprecedented intelligence (compression) capacity of the LLM for lossless image compression tasks, thereby bridging the gap between theoretical and practical compression performance. Specifically, we propose P2-LLM, a next-pixel prediction-based LLM, which integrates various elaborated insights and methodologies, e.g., pixel-level priors, the in-context ability of LLM, and a pixel-level semantic preservation strategy, to enhance the understanding capacity of pixel sequences for better next-pixel predictions. Extensive experiments on benchmark datasets demonstrate that P2-LLM can beat SOTA classical and learned codecs.

Recent efforts in neural compression have focused on the rate-distortion-perception (RDP) tradeoff, where the perception constraint ensures the source and reconstruction distributions are close in terms of a statistical divergence. Theoretical work on RDP describes properties of RDP-optimal compressors without providing constructive and low complexity solutions. While classical rate-distortion theory shows that optimal compressors should efficiently pack space, RDP theory additionally shows that infinite randomness shared between the encoder and decoder may be necessary for RDP optimality. In this paper, we propose neural compressors that are low complexity and benefit from high packing efficiency through lattice coding and shared randomness through shared dithering over the lattice cells. For two important settings, namely infinite shared and zero shared randomness, we analyze the RDP tradeoff achieved by our proposed neural compressors and show optimality in both cases. Experimentally, we investigate the roles that these two components of our design, lattice coding and randomness, play in the performance of neural compressors on synthetic and real-world data. We observe that performance improves with more shared randomness and better lattice packing.

Arithmetic circuit optimization remains a fundamental challenge in modern integrated circuit design. Recent advances have cast this problem within the Learning to Optimize (L2O) paradigm, where intelligent agents autonomously explore high-performance design spaces with encouraging results. However, existing approaches predominantly target coarse-grained architectural configurations, while the crucial interconnect optimization stage is often relegated to oversimplified proxy models or a heuristic approach. This disconnect undermines design quality, leading to suboptimal solutions in the circuit topology search space. To bridge this gap, we present ARITH-DAS, a Differentiable Architecture Search framework for Arithmetic circuits. To the best of our knowledge, ARITH-DAS is the first to formulate interconnect optimization within arithmetic circuits as a differentiable edge prediction problem over a multi-relational directed acyclic graph, enabling fine-grained, proxy-free optimization at the interconnection level. We evaluate ARITH-DAS on a suite of representative arithmetic circuits, including multipliers and multiply-accumulate units. Experiments show substantial improvements over state-of-the-art L2O and conventional methods, achieving up to 27.05% gain in hypervolume of area-delay Pareto frontiers, a standard metric for evaluating multi-objective optimization performance.

Due to the high communication overhead when training machine learning models in a distributed environment, modern algorithms invariably rely on lossy communication compression. However, when untreated, the errors caused by compression propagate, and can lead to severely unstable behavior, including exponential divergence. Almost a decade ago, Seide et al. [2014] proposed an error feedback (EF) mechanism, which we refer to as EF14, as an immensely effective heuristic for mitigating this issue. However, despite steady algorithmic and theoretical advances in the EF field in the last decade, our understanding is far from complete. In this work we address one of the most pressing issues.

Communication compression is a common technique in distributed optimization that can alleviate communication overhead by transmitting compressed gradients and model parameters. However, compression can introduce information distortion, which slows down convergence and incurs more communication rounds to achieve desired solutions. Given the trade-off between lower per-round communication costs and additional rounds of communication, it is unclear whether communication compression reduces the total communication cost. This paper explores the conditions under which unbiased compression, a widely used form of compression, can reduce the total communication cost, as well as the extent to which it can do so. To this end, we present the first theoretical formulation for characterizing the total communication cost in distributed optimization with unbiased compressors. We demonstrate that unbiased compression alone does not necessarily save the total communication cost, but this outcome can be achieved if the compressors used by all workers are further assumed independent. We establish lower bounds on the communication rounds required by algorithms using independent unbiased compressors to minimize smooth convex functions and show that these lower bounds are tight by refining the analysis for ADIANA. Our results reveal that using independent unbiased compression can reduce the total communication cost by a factor of up to Θ( p min{n,κ}) when all local smoothness constants are constrained by a common upper bound, where nis the number of workers and κis the condition number of the functions being minimized. These theoretical findings are supported by experimental results.

Stochastic gradient descent (SGD) is a prevalent optimization technique for largescale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck in the distributed setting. Gradient compression methods can be used to alleviate this problem, and a recent line of work shows that SGD augmented with gradient compression converges to an ε-first-order stationary point. In this paper we extend these results to convergence to an ε-second-order stationary point (ε-SOSP), which is to the best of our knowledge the first result of this type. In addition, we show that, when the stochastic gradient is not Lipschitz, compressed SGD with RANDOMK compressor converges to an ε-SOSP with the same number of iterations as uncompressed SGD [25], while improving the total communication by a factor of Θ( dε 3/4), where dis the dimension of the optimization problem. We present additional results for the cases when the compressor is arbitrary and when the stochastic gradient is Lipschitz.

Gradient compression is a widely-established remedy to tackle the communication bottleneck in distributed training of large deep neural networks (DNNs). Under the error-feedback framework, Top-k sparsification, sometimes with k as little as 0.1% of the gradient size, enables training to the same model quality as the uncompressed case for a similar iteration count. From the optimization perspective, we find that Top-k is the communication-optimal sparsifier given a per-iteration k element budget. We argue that to further the benefits of gradient sparsification, especially for DNNs, a different perspective is necessary -- one that moves from per-iteration optimality to consider optimality for the entire training. We identify that the total error -- the sum of the compression errors for all iterations -- encapsulates sparsification throughout training.