The inherent quadratic complexity of the attention mechanism in transformer models has driven the research community to explore alternative architectures with sub-quadratic complexity, such as state-space models. Mamba has established itself as a leading model within this emerging paradigm, achieving state-of-the-art results in various language modeling benchmarks. However, despite its impressive performance, Mamba's effectiveness is limited by its pre-training context length, resulting in a pronounced degradation when the model is tasked with handling longer contexts. Our investigation reveals that Mamba's inability to generalize effectively to long contexts is primarily due to the out-of-distribution (OOD) discretization steps. To address this critical limitation, we introduce _**MambaExtend**_, a novel framework designed to significantly enhance the context extension capabilities of Mamba. Specifically, MambaExtend leverages a _**training-free**_ approach to calibrate _only_ the scaling factors of discretization modules for different layers. We demonstrate both gradient-based and gradient-free zeroth-order optimization to learn the optimal scaling factors for each Mamba layer, requiring orders of magnitude fewer updates as opposed to the parameter fine-tuning-based alternatives. Using this approach, we achieve a training-free context extension of up to 32x, expanding the context from 2k to 64k tokens with minimal increases in perplexity. In contrast to existing fine-tuning methods, MambaExtend selectively calibrates the scaling factors, requiring up to $\mathbf{5.42 * 10^6} \times$ fewer parameter updates and incurring up to $\mathbf{3.87} \times$ lower peak memory usage, while delivering comparable or superior long-context performance across multiple tasks. Codes and checkpoints are available here$^1$.

Large language models (LLMs), despite their impressive performance across a wide range of tasks, often struggle to balance two competing objectives in open-ended text generation: fostering diversity and creativity while preserving logical coherence. Existing truncated sampling techniques, including temperature scaling, top-*p* (nucleus) sampling, and min-*p* sampling, aim to manage this trade-off. However, they exhibit limitations, particularly in the effective incorporation of the confidence of the model into the corresponding sampling strategy. For example, min-*p* sampling relies on a single top token as a heuristic for confidence, eventually underutilizing the information of the probability distribution. To effectively incorporate the model confidence, this paper presents **_top-H_ decoding**. We first establish the theoretical foundation of the interplay between creativity and coherence in truncated sampling by formulating an **entropy-constrained minimum divergence** problem. We then prove this minimization problem to be equivalent to an **entropy-constrained mass maximization (ECMM)** problem, which is NP-hard. Finally, we present top-H decoding, a computationally efficient greedy algorithm to solve the ECMM problem. Extensive empirical evaluations demonstrate that top-H outperforms the state-of-the-art (SoTA) alternative of min-*p* sampling by up to **25.63%** on creative writing benchmarks, while maintaining robustness on question-answering datasets such as GPQA, GSM8K, and MT-Bench. Additionally, an *LLM-as-judge* evaluation confirms that top-H indeed produces coherent outputs even at higher temperatures, where creativity is especially critical. In summary, top-H advances SoTA in open-ended text generation and can be *easily integrated* into creative writing applications. The code is available at [https://github.com/ErfanBaghaei/Top-H-Decoding](https://github.com/ErfanBaghaei/Top-H-Decoding).

Given the ever-growing complexity and computational requirements of deep learning models, it has become imperative to efficiently optimize neural network architectures. This paper presents an automated, search-based method for opti-mizing the bit-width and layer-width of individual neural network layers, achieving substantial reductions in the size and processing requirements of these models. Our unique approach employs Hessian-based search space pruning to discard unpromising so-lutions, greatly reducing the search space. We further refine the optimization process by introducing a novel, adaptive algorithm that combines k-means clustering with tree-structured Parzen estimation. This allows us to dynamically adjust a figure of merit used in tree-structured Parzen estimation, i.e., the desirability of a particular bit-width and layer-width configuration, thereby expediting the identification of optimal configurations. Through extensive experiments on benchmark datasets, we validate the efficacy of our method. More precisely, our method outperforms existing techniques by achieving an average 20 % reduction in model size without sacrificing any output accuracy. It also boasts a$12\times$acceleration in search time compared to the most advanced search-based approaches.

The deployment of Vision Transformers (ViTs) on hardware platforms, specially Field-Programmable Gate Arrays (FPGAs), presents many challenges, which are mainly due to the substantial computational and power requirements of their non-linear functions, notably layer normalization, softmax, and Gaussian Error Linear Unit (GELU). These critical functions pose significant obstacles to efficient hardware implementation due to their complex mathematical operations and the inherent resource count and architectural limitations of FPGAs. PEANO-ViT offers a novel approach to streamlining the implementation of the layer normalization layer by introducing a division-free technique that simultaneously approximates the division and square root function. Additionally, PEANO-ViT provides a multi-scale division strategy to eliminate division operations in the softmax layer, aided by a Padé-based approximation for the exponential function. Finally, PEANO-ViT introduces a piece-wise linear approximation for the GELU function, carefully designed to bypass the computationally intensive operations associated with GELU. In our comprehensive evaluations, PEANO-ViT exhibits minimal accuracy degradation ≤ 0.5% for DeiT-B) while significantly enhancing power efficiency, achieving improvements of 1.91X, 1.39X, and 8.01X for layer normalization, softmax, and GELU, respectively. This improvement is achieved through substantial reductions in DSP, LUT, and register counts for these non-linear operations. Consequently, PEANO-ViT enables efficient deployment of Vision Transformers on resource- and power-constrained FPGA platforms.

This article presents a mixed-computation neural network processing approach for edge applications that incorporates low-precision (low-width) Posit and low-precision fixed point (FixP) number systems. This mixed-computation approach uses 4-bit Posit (Posit4), which has higher precision around 0, for representing weights with high sensitivity, while it uses 4-bit FixP (FixP4) for representing other weights. A heuristic for analyzing the importance and the quantization error of the weights is presented to assign the proper number system to different weights. In addition, a gradient approximation for Posit representation is introduced to improve the quality of weight updates in the backpropagation process. Due to the high energy consumption of the fully Posit-based computations, neural network operations are carried out in FixP or Posit/FixP. An efficient hardware implementation of an MAC operation with a first Posit operand and FixP for a second operand and accumulator is presented. The efficacy of the proposed low-precision mixed-computation approach is extensively assessed on vision and language models. The results show that on average, the accuracy of the mixed-computation is about 1.5% higher than that of FixP with a cost of 0.19% energy overhead.