Despite advances in limited precision inference in recent years, training of neural networks in low bit-width remains a challenging problem.

The substantial memory bandwidth and computational demands of large language models (LLMs) present critical challenges for efficient inference. To tackle this, the literature has explored heterogeneous systems that combine neural processing units (NPUs) with DRAM-based processing-in-memory (PIM) for LLM acceleration. However, existing high-precision (e.g., FP16) PIM compute units incur significant area and power overhead in DRAM technology, limiting the effective computation throughput. In this paper, we introduce P3-LLM, a novel NPU-PIM integrated accelerator for LLM inference using hybrid numerical formats. Our approach is threefold: First, we propose a flexible mixed-precision quantization scheme, which leverages hybrid numerical formats to quantize different LLM operands with high compression efficiency and minimal accuracy loss. Second, we architect an efficient PIM accelerator for P3-LLM, featuring enhanced compute units to support hybrid numerical formats. Our careful choice of numerical formats allows to co-design low-precision PIM compute units that significantly boost the computation throughput under iso-area constraints. Third, we optimize the low-precision dataflow of different LLM modules by applying operator fusion to minimize the overhead of runtime dequantization. Evaluation on a diverse set of representative LLMs and tasks demonstrates that P3-LLM achieves state-of-the-art accuracy in terms of both KV-cache quantization and weight-activation quantization. Combining the proposed quantization scheme with PIM architecture co-design, P3-LLM yields an average of $4.9\times$, $2.0\times$, and $3.4\times$ speedups over the state-of-the-art LLM accelerators HBM-PIM, Ecco, and Pimba, respectively. Our quantization code is available at https://github.com/yc2367/P3-LLM.git

Quantization is essential for Neural Network (NN) compression, reducing model size and computational demands by using lower bit-width data types, though aggressive reduction often hampers accuracy. Mixed Precision (MP) mitigates this tradeoff by varying the numerical precision across network layers. This study focuses on automatically selecting an optimal MP configuration within Post-Training Quantization (PTQ) for inference. The first key contribution is a novel sensitivity metric derived from a first-order Taylor series expansion of the loss function as a function of quantization errors in weights and activations. This metric, based on the Mean Square Error (MSE) of the loss, is efficiently calculated per layer using high-precision forward and backward passes over a small calibration dataset. The metric is additive across layers, with low calibration memory overhead as weight optimization is unnecessary. The second contribution is an accurate hardware-aware method for predicting MP time gain by modeling it as additive for sequential sub-graphs. An algorithm partitions the model graph into sequential subgraphs, measuring time gain for each configuration using a few samples. After calibrating per-layer sensitivity and time gain, an Integer Programming (IP) problem is formulated to maximize time gain while keeping loss MSE below a set threshold. Memory gain and theoretical time gain based on Multiply and Accumulate (MAC) operations are also considered. Rigorous experiments on the Intel Gaudi 2 accelerator validate the approach on several Large Language Models (LLMs).

Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neural networks in low bit-width remains a challenging problem. Here we present the Flexpoint data format, aiming at a complete replacement of 32-bit floating point format training and inference, designed to support modern deep network topologies without modifications. Flexpoint tensors have a shared exponent that is dynamically adjusted to minimize overflows and maximize available dynamic range. We validate Flexpoint by training AlexNet [1], a deep residual network [2, 3] and a generative adversarial network [4], using a simulator implemented with the neon deep learning framework. We demonstrate that 16-bit Flexpoint closely matches 32-bit floating point in training all three models, without any need for tuning of model hyperparameters. Our results suggest Flexpoint as a promising numerical format for future hardware for training and inference.

As deep learning methodologies have developed, it has been generally agreed that increasing neural network size improves model quality. However, this is at the expense of memory and compute requirements, which also need to be increased. Various efficiency techniques have been proposed to rein in hardware costs, one being the use of low precision numerics. Recent accelerators have introduced several different 8-bit data types to help accommodate DNNs in terms of numerics. In this paper, we identify a metric driven methodology to aid in the choice of numerics. We demonstrate how such a methodology can help scale training of a language representation model. The technique can be generalized to other model architectures.

The amounts of data that need to be transmitted, processed, and stored by the modern deep neural networks have reached truly enormous volumes in the last few years calling for the invention of new paradigms both in hardware and software development. One of the most promising and rapidly advancing frontiers here is the creation of new numerical formats. In this work we focus on the family of block floating point numerical formats due to their combination of wide dynamic range, numerical accuracy, and efficient hardware implementation of inner products using simple integer arithmetic. These formats are characterized by a block of mantissas with a shared scale factor. The basic Block Floating Point (BFP) format quantizes the block scales into the nearest powers of two on the right. Its simple modification - Scaled BFP (SBFP) - stores the same scales in full precision and thus allows higher accuracy. In this paper, we study the statistical behavior of both these formats rigorously. We develop asymptotic bounds on the inner product error in SBFP- and BFP-quantized normally distributed vectors. Next, we refine those asymptotic results to finite dimensional settings and derive high-dimensional tight bounds for the same errors. Based on the obtained results we introduce a performance measure assessing accuracy of any block format. This measure allows us to determine the optimal parameters, such as the block size, yielding highest accuracy. In particular, we show that if the precision of the BFP format is fixed at 4 bits, the optimal block size becomes 64. All theoretical derivations are supported by numerical experiments and studies on the weights of publicly available pretrained neural networks.

In this tutorial we will discuss label encoding in Python. In data science, we often work with datasets that contain categorical variables, where the values are represented by strings. For example, when we work with datasets for salary estimation based on different sets of features, we often see job title being entered in words, for example: Manager, Director, Vice-President, President, and so on. The complication it creates is the fact that machine learning algorithms in fact can work with categorical features, yet they have to be in numeric form. There are multiple ways to solve this problem and a lot depends on the algorithm you will be working with.

Growing up as a child, we all at some point in time must have wanted to learn to play musical instruments, be it piano, violin, guitar, ukelele, drums, or saxophone. However, I was not good at playing any of the instruments, and playing a musical instrument remained a dream for me until now. So I decided to make an Artificial Intelligence model which could generate unique and unlimited music for me. Yes! Now, I would never get tired of hearing the same songs again. The Artificial Intelligence model would generate each time a unique and melodious song that I can listen to.

In this research, we propose a new low-precision framework, TENT, to leverage the benefits of a tapered fixed-point numerical format in TinyML models. We introduce a tapered fixed-point quantization algorithm that matches the numerical format's dynamic range and distribution to that of the deep neural network model's parameter distribution at each layer. An accelerator architecture for the tapered fixed-point with TENT framework is proposed. Results show that the accuracy on classification tasks improves up to ~31 % with an energy overhead of ~17-30 % as compared to fixed-point, for ConvNet and ResNet-18 models.

This is the second part of the neural network tutorial. The first part can be found here: https://link.medium.com/YCEAECVp0W Now that we have seen how a neural network is represented, we can go on to see how exactly it works. Since there are many layers having many neurons, there exists a complex set of weights to get an output from some input variables. Each weight in this network can be changed and hence there are countless configurations a neural network can have.