In order to overcome overestimation bias, ensemble methods for Q-learning have been investigated to exploit the diversity of multiple Q-functions. Since network initialization has been the predominant approach to promote diversity in Q-functions, heuristically designed diversity injection methods have been studied in the literature. However, previous studies have not attempted to approach guaranteed independence over an ensemble from a theoretical perspective.

Alleviating overestimation bias is a critical challenge for deep reinforcement learning to achieve successful performance on more complex tasks or offline datasets containing out-of-distribution data. In order to overcome overestimation bias, ensemble methods for Q-learning have been investigated to exploit the diversity of multiple Q-functions. Since network initialization has been the predominant approach to promote diversity in Q-functions, heuristically designed diversity injection methods have been studied in the literature. However, previous studies have not attempted to approach guaranteed independence over an ensemble from a theoretical perspective. By introducing a novel regularization loss for Q-ensemble independence based on random matrix theory, we propose spiked Wishart Q-ensemble independence regularization (SPQR) for reinforcement learning. Specifically, we modify the intractable hypothesis testing criterion for the Q-ensemble independence into a tractable KL divergence between the spectral distribution of the Q-ensemble and the target Wigner's semicircle distribution. We implement SPQR in several online and offline ensemble Q-learning algorithms. In the experiments, SPQR outperforms the baseline algorithms in both online and offline RL benchmarks.

As Large Language Models (LLMs) continue to scale in parameter count, deploying them on commodity hardware has become increasingly challenging. Post-Training Quantization (PTQ) addresses this by reducing the precision of model weights, typically to 4-bit or lower. However, uniform quantization often leads to significant performance degradation due to the presence of ``outlier features'' -- weights that, while few in number, are critical for maintaining model accuracy. Current state-of-the-art methods such as AWQ (Activation-aware Weight Quantization) and SpQR (Sparse Quantization Representations) rely on calibration data to identify these salient weights via activation magnitudes or Hessian sensitivity. In scenarios where data privacy is paramount or calibration data is unavailable, these methods are inapplicable. In this work, we propose a data-free, structure-aware hypothesis: that the weights identified as Principal Components via Singular Value Decomposition (SVD) are intrinsically important to the model's downstream performance. We introduce a novel selection heuristic that preserves the top-$k$ weights aligned with the principal components in FP32, while aggressively quantizing the residual weights. We compare our method against activation-aware (AWQ) and second-order (SpQR) methods across GLUE benchmarks (MRPC, RTE, QNLI) using a DistilBERT backbone. Our experiments reveal that structural importance is highly correlated with functional importance. On the challenging RTE task, our SVD-based method achieves an accuracy of 66.06\%, outperforming both AWQ (65.34\%) and SpQR (65.34\%) at high protection budgets, validating that intrinsic matrix structure can serve as a robust proxy for weight saliency without the need for forward passes or calibration data.

In order to overcome overestimation bias, ensemble methods for Q-learning have been investigated to exploit the diversity of multiple Q-functions. Since network initialization has been the predominant approach to promote diversity in Q-functions, heuristically designed diversity injection methods have been studied in the literature. However, previous studies have not attempted to approach guaranteed independence over an ensemble from a theoretical perspective.

Post-training quantization (PTQ) reduces a model's memory footprint by mapping full precision weights into low bit weights without costly retraining, but can degrade its downstream performance especially in low 2- to 3-bit settings. We develop a new mixed-precision PTQ approach, Task-Circuit Quantization (TaCQ), that draws parallels to automated circuit discovery, directly conditioning the quantization process on specific weight circuits -- which we define as sets of weights associated with downstream task performance. These weights are kept as 16-bit weights, while others are quantized, maintaining performance while only adding a marginal memory cost. Specifically, TaCQ contrasts unquantized model weights with a uniformly-quantized model to estimate the expected change in weights due to quantization and uses gradient information to predict the resulting impact on task performance, allowing us to preserve task-specific weights. We compare TaCQ-based quantization to existing mixed-precision quantization methods when conditioning both on general-purpose and task-specific data. Across QA, math reasoning, and text-to-SQL tasks for both Llama-3 and Qwen2.5, we find that TaCQ outperforms baselines using the same calibration data and a lower weight budget, achieving major improvements in the 2 and 3-bit regime. With only 3.1 bits we are able to recover 96% of Llama-3-8B-Instruct's unquantized 16-bit MMLU performance, obtaining a 5.25% absolute improvement over SPQR. We also observe consistently large gains over existing methods in the 2-bit regime, with an average gain of 14.74% over the strongest baseline, SliM-LLM. Moreover, we observe a 7.20% gain without conditioning on specific tasks, showing TaCQ's ability to identify important weights is not limited to task-conditioned settings.

Alleviating overestimation bias is a critical challenge for deep reinforcement learning to achieve successful performance on more complex tasks or offline datasets containing out-of-distribution data. In order to overcome overestimation bias, ensemble methods for Q-learning have been investigated to exploit the diversity of multiple Q-functions. Since network initialization has been the predominant approach to promote diversity in Q-functions, heuristically designed diversity injection methods have been studied in the literature. However, previous studies have not attempted to approach guaranteed independence over an ensemble from a theoretical perspective. By introducing a novel regularization loss for Q-ensemble independence based on random matrix theory, we propose spiked Wishart Q-ensemble independence regularization (SPQR) for reinforcement learning. Specifically, we modify the intractable hypothesis testing criterion for the Q-ensemble independence into a tractable KL divergence between the spectral distribution of the Q-ensemble and the target Wigner's semicircle distribution.

Alleviating overestimation bias is a critical challenge for deep reinforcement learning to achieve successful performance on more complex tasks or offline datasets containing out-of-distribution data. In order to overcome overestimation bias, ensemble methods for Q-learning have been investigated to exploit the diversity of multiple Q-functions. Since network initialization has been the predominant approach to promote diversity in Q-functions, heuristically designed diversity injection methods have been studied in the literature. However, previous studies have not attempted to approach guaranteed independence over an ensemble from a theoretical perspective. By introducing a novel regularization loss for Q-ensemble independence based on random matrix theory, we propose spiked Wishart Q-ensemble independence regularization (SPQR) for reinforcement learning. Specifically, we modify the intractable hypothesis testing criterion for the Q-ensemble independence into a tractable KL divergence between the spectral distribution of the Q-ensemble and the target Wigner's semicircle distribution. We implement SPQR in several online and offline ensemble Q-learning algorithms. In the experiments, SPQR outperforms the baseline algorithms in both online and offline RL benchmarks.

With the rising popularity of Large Language Models (LLMs), there has been an increasing interest in compression techniques that enable their efficient deployment. This study focuses on the Post-Training Quantization (PTQ) of LLMs. Drawing from recent advances, our work introduces QuantEase, a layer-wise quantization framework where individual layers undergo separate quantization. The problem is framed as a discrete-structured non-convex optimization, prompting the development of algorithms rooted in Coordinate Descent (CD) techniques. These CD-based methods provide high-quality solutions to the complex non-convex layer-wise quantization problems. Notably, our CD-based approach features straightforward updates, relying solely on matrix and vector operations, circumventing the need for matrix inversion or decomposition. We also explore an outlier-aware variant of our approach, allowing for retaining significant weights (outliers) with complete precision. Our proposal attains state-of-the-art performance in terms of perplexity and zero-shot accuracy in empirical evaluations across various LLMs and datasets, with relative improvements up to 15% over methods such as GPTQ. Leveraging careful linear algebra optimizations, QuantEase can quantize models like Falcon-180B on a single NVIDIA A100 GPU in $\sim$3 hours. Particularly noteworthy is our outlier-aware algorithm's capability to achieve near or sub-3-bit quantization of LLMs with an acceptable drop in accuracy, obviating the need for non-uniform quantization or grouping techniques, improving upon methods such as SpQR by up to two times in terms of perplexity.

Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops and mobile phones, enabling personalized use. However, quantization down to 3-4 bits per parameter usually leads to moderate-to-high accuracy losses, especially for smaller models in the 1-10B parameter range, which are well-suited for edge deployments. To address this accuracy issue, we introduce the Sparse-Quantized Representation (SpQR), a new compressed format and quantization technique which enables for the first time near-lossless compression of LLMs across model scales, while reaching similar compression levels to previous methods. SpQR works by identifying and isolating outlier weights, which cause particularly-large quantization errors, and storing them in higher precision, while compressing all other weights to 3-4 bits, and achieves relative accuracy losses of less than 1% in perplexity for highly-accurate LLaMA and Falcon LLMs. This makes it possible to run 33B parameter LLM on a single 24 GB consumer GPU without any performance degradation at 15% speedup thus making powerful LLMs available to consumer without any downsides. SpQR comes with efficient algorithms for both encoding weights into its format, as well as decoding them efficiently at runtime. Specifically, we provide an efficient GPU inference algorithm for SpQR which yields faster inference than 16-bit baselines at similar accuracy, while enabling memory compression gains of more than 4x.

We develop an R package SPQR that implements the semi-parametric quantile regression (SPQR) method in Xu and Reich (2021). The method begins by fitting a flexible density regression model using monotonic splines whose weights are modeled as data-dependent functions using artificial neural networks. Subsequently, estimates of conditional density and quantile process can all be obtained. Unlike many approaches to quantile regression that assume a linear model, SPQR allows for virtually any relationship between the covariates and the response distribution including non-linear effects and different effects on different quantile levels. To increase the interpretability and transparency of SPQR, model-agnostic statistics developed by Apley and Zhu (2020) are used to estimate and visualize the covariate effects and their relative importance on the quantile function. In this article, we detail how this framework is implemented in SPQR and illustrate how this package should be used in practice through simulated and real data examples.