Search

As large language models (LLMs) evolve to handle increasingly longer contexts, serving inference requests for context lengths in the range of millions of tokens presents unique challenges. While existing techniques are effective for training, they fail to address the unique challenges of inference, such as varying prefill and decode phases and their associated latency constraints - like Time to First Token (TTFT) and Time Between Tokens (TBT). Furthermore, there are no long context inference solutions that allow batching requests to increase the hardware utilization today. In this paper, we propose three key innovations for efficient interactive long context LLM inference, without resorting to any approximation: adaptive chunking to reduce prefill overheads in mixed batching, Sequence Pipeline Parallelism (SPP) to lower TTFT, and KV Cache Parallelism (KVP) to minimize TBT. These contributions are combined into a 3D parallelism strategy, enabling Mnemosyne to scale interactive inference to context lengths at least up to 10 million tokens with high throughput enabled with batching. To our knowledge, Mnemosyne is the first to be able to achieve support for 10 million long context inference efficiently, while satisfying production-grade SLOs on TBT (30ms) on contexts up to and including 10 million.

Serving large language models (LLMs) in production can incur substantial costs, which has prompted recent advances in inference system optimizations. Today, these systems are evaluated against conventional latency and throughput metrics (eg. TTFT, TBT, Normalised Latency and TPOT). However, these metrics fail to fully capture the nuances of LLM inference, leading to an incomplete assessment of user-facing performance crucial for real-time applications such as chat and translation. In this paper, we first identify the pitfalls of current performance metrics in evaluating LLM inference systems. We then propose Etalon, a comprehensive performance evaluation framework that includes fluidity-index -- a novel metric designed to reflect the intricacies of the LLM inference process and its impact on real-time user experience. Finally, we evaluate various existing open-source platforms and model-as-a-service offerings using Etalon, discussing their strengths and weaknesses. Etalon is available at https://github.com/project-etalon/etalon.

CNNs are increasingly deployed across different hardware, dynamic environments, and low-power embedded devices. This has led to the design and training of CNN architectures with the goal of maximizing accuracy subject to such variable deployment constraints. As the number of deployment scenarios grows, there is a need to find scalable solutions to design and train specialized CNNs. Once-for-all training has emerged as a scalable approach that jointly co-trains many models (subnets) at once with a constant training cost and finds specialized CNNs later. The scalability is achieved by training the full model and simultaneously reducing it to smaller subnets that share model weights (weight-shared shrinking). However, existing once-for-all training approaches incur huge training costs reaching 1200 GPU hours. We argue this is because they either start the process of shrinking the full model too early or too late. Hence, we propose Delayed $\epsilon$-Shrinking (D$\epsilon$pS) that starts the process of shrinking the full model when it is partially trained (~50%) which leads to training cost improvement and better in-place knowledge distillation to smaller models. The proposed approach also consists of novel heuristics that dynamically adjust subnet learning rates incrementally (E), leading to improved weight-shared knowledge distillation from larger to smaller subnets as well. As a result, DEpS outperforms state-of-the-art once-for-all training techniques across different datasets including CIFAR10/100, ImageNet-100, and ImageNet-1k on accuracy and cost. It achieves 1.83% higher ImageNet-1k top1 accuracy or the same accuracy with 1.3x reduction in FLOPs and 2.5x drop in training cost (GPU*hrs), Comment: Accepted to the 18th European Conference on Computer Vision (ECCV 2024)

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in ${\mathbb C}^n$. In an earlier paper of 1990, the authors proved the result for connected linear Lie groups. In this paper we give examples of non-linear groups for which the result still holds., Comment: 6 pages

Optimizing the deployment of Large language models (LLMs) is expensive today since it requires experimentally running an application workload against an LLM implementation while exploring large configuration space formed by system knobs such as parallelization strategies, batching techniques, and scheduling policies. To address this challenge, we present Vidur - a large-scale, high-fidelity, easily-extensible simulation framework for LLM inference performance. Vidur models the performance of LLM operators using a combination of experimental profiling and predictive modeling, and evaluates the end-to-end inference performance for different workloads by estimating several metrics of interest such as latency and throughput. We validate the fidelity of Vidur on several LLMs and show that it estimates inference latency with less than 9% error across the range. Further, we present Vidur-Search, a configuration search tool that helps optimize LLM deployment. Vidur-Search uses Vidur to automatically identify the most cost-effective deployment configuration that meets application performance constraints. For example, Vidur-Search finds the best deployment configuration for LLaMA2-70B in one hour on a CPU machine, in contrast to a deployment-based exploration which would require 42K GPU hours - costing ~218K dollars. Source code for Vidur is available at https://github.com/microsoft/vidur.

Each LLM serving request goes through two phases. The first is prefill which processes the entire input prompt and produces the first output token and the second is decode which generates the rest of output tokens, one-at-a-time. Prefill iterations have high latency but saturate GPU compute due to parallel processing of the input prompt. In contrast, decode iterations have low latency but also low compute utilization because a decode iteration processes only a single token per request. This makes batching highly effective for decodes and consequently for overall throughput. However, batching multiple requests leads to an interleaving of prefill and decode iterations which makes it challenging to achieve both high throughput and low latency. We introduce an efficient LLM inference scheduler, Sarathi-Serve, to address this throughput-latency tradeoff. Sarathi-Serve introduces chunked-prefills which splits a prefill request into near equal sized chunks and creates stall-free schedules that adds new requests in a batch without pausing ongoing decodes. Stall-free scheduling unlocks the opportunity to improve throughput with large batch sizes while minimizing the effect of batching on latency. Furthermore, uniform batches in Sarathi-Serve ameliorate the imbalance between iterations resulting in minimal pipeline bubbles. Our techniques yield significant improvements in inference performance across models and hardware under tail latency constraints. For Mistral-7B on single A100 GPUs, we achieve 2.6x higher serving capacity and up to 3.7x higher serving capacity for the Yi-34B model on two A100 GPUs as compared to vLLM. When used with pipeline parallelism on Falcon-180B, Sarathi-Serve provides up to 5.6x gain in the end-to-end serving capacity. The source code for Sarathi-Serve is available at https://github.com/microsoft/sarathi-serve.

The Molchanov's condition is a necessary condition for the compactness of the resolvent for a wide class of ordinary differential operators of arbitrary order, but for the Sturm-Liouville operator it is not sufficient, even if the real part of the potential is non-negative. Molchanov's criterion remains valid in the formulation closest to the original one for potentials that take values in a narrower sector than the half-plane, separated from the negative half-axis. This work is devoted to these questions., Comment: in Russian language

The increasing deployment of ML models on the critical path of production applications in both datacenter and the edge requires ML inference serving systems to serve these models under unpredictable and bursty request arrival rates. Serving models under such conditions requires these systems to strike a careful balance between the latency and accuracy requirements of the application and the overall efficiency of utilization of scarce resources. State-of-the-art systems resolve this tension by either choosing a static point in the latency-accuracy tradeoff space to serve all requests or load specific models on the critical path of request serving. In this work, we instead resolve this tension by simultaneously serving the entire-range of models spanning the latency-accuracy tradeoff space. Our novel mechanism, SubNetAct, achieves this by carefully inserting specialized operators in weight-shared SuperNetworks. These operators enable SubNetAct to dynamically route requests through the network to meet a latency and accuracy target. SubNetAct requires upto 2.6x lower memory to serve a vastly-higher number of models than prior state-of-the-art. In addition, SubNetAct's near-instantaneous actuation of models unlocks the design space of fine-grained, reactive scheduling policies. We explore the design of one such extremely effective policy, SlackFit and instantiate both SubNetAct and SlackFit in a real system, SuperServe. SuperServe achieves 4.67% higher accuracy for the same SLO attainment and 2.85x higher SLO attainment for the same accuracy on a trace derived from the real-world Microsoft Azure Functions workload and yields the best trade-offs on a wide range of extremely-bursty synthetic traces automatically.

Efficient inference of Deep Neural Networks (DNNs) on resource-constrained edge devices is essential. Quantization and sparsity are key algorithmic techniques that translate to repetition and sparsity within tensors at the hardware-software interface. This paper introduces the concept of repetition-sparsity trade-off that helps explain computational efficiency during inference. We propose Signed Binarization, a unified co-design framework that synergistically integrates hardware-software systems, quantization functions, and representation learning techniques to address this trade-off. Our results demonstrate that Signed Binarization is more accurate than binarization with the same number of non-zero weights. Detailed analysis indicates that signed binarization generates a smaller distribution of effectual (non-zero) parameters nested within a larger distribution of total parameters, both of the same type, for a DNN block. Finally, our approach achieves a 26% speedup on real hardware, doubles energy efficiency, and reduces density by 2.8x compared to binary methods for ResNet 18, presenting an alternative solution for deploying efficient models in resource-limited environments.

Graph Neural Networks (GNNs) have proven to be quite versatile for a variety of applications, including recommendation systems, fake news detection, drug discovery, and even computer vision. Due to the expanding size of graph-structured data, GNN models have also increased in complexity, leading to substantial latency issues. This is primarily attributed to the irregular structure of graph data and its access pattern into memory. The natural solution to reduce latency is to compress large GNNs into small GNNs. One way to do this is via knowledge distillation (KD). However, most KD approaches for GNNs only consider the outputs of the last layers and do not consider the outputs of the intermediate layers of the GNNs; these layers may contain important inductive biases indicated by the graph structure. To address this shortcoming, we propose a novel KD approach to GNN compression that we call Attention-Based Knowledge Distillation (ABKD). ABKD is a KD approach that uses attention to identify important intermediate teacher-student layer pairs and focuses on aligning their outputs. ABKD enables higher compression of GNNs with a smaller accuracy dropoff compared to existing KD approaches. On average, we achieve a 1.79% increase in accuracy with a 32.3x compression ratio on OGBN-Mag, a large graph dataset, compared to state-of-the-art approaches.

We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar $\mathcal{N}=4$ super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the $m=2$ tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the 't Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data., Comment: 54 pages, 15 figures, minor corrections, journal version

Traditional computer vision models often necessitate extensive data acquisition, annotation, and validation. These models frequently struggle in real-world applications, resulting in high false positive and negative rates, and exhibit poor adaptability to new scenarios, often requiring costly retraining. To address these issues, we present Ethosight, a flexible and adaptable zero-shot video analytics system. Ethosight begins from a clean slate based on user-defined video analytics, specified through natural language or keywords, and leverages joint embedding models and reasoning mechanisms informed by ontologies such as WordNet and ConceptNet. Ethosight operates effectively on low-cost edge devices and supports enhanced runtime adaptation, thereby offering a new approach to continuous learning without catastrophic forgetting. We provide empirical validation of Ethosight's promising effectiveness across diverse and complex use cases, while highlighting areas for further improvement. A significant contribution of this work is the release of all source code and datasets to enable full reproducibility and to foster further innovation in both the research and commercial domains.

The spectral properties of the singular Schr\"odinger operator with complex-valued potential which takes values in a wider region than the half-plane, have been little studied. In general case, the operator is non-sectorial, and the numerical range coincides with the entire complex plane. In this situation we propose sufficient conditions for discreteness of the spectrum and compactness of the resolvent.

Model-serving systems have become increasingly popular, especially in real-time web applications. In such systems, users send queries to the server and specify the desired performance metrics (e.g., desired accuracy, latency). The server maintains a set of models (model zoo) in the back-end and serves the queries based on the specified metrics. This paper examines the security, specifically robustness against model extraction attacks, of such systems. Existing black-box attacks assume a single model can be repeatedly selected for serving inference requests. Modern inference serving systems break this assumption. Thus, they cannot be directly applied to extract a victim model, as models are hidden behind a layer of abstraction exposed by the serving system. An attacker can no longer identify which model she is interacting with. To this end, we first propose a query-efficient fingerprinting algorithm to enable the attacker to trigger any desired model consistently. We show that by using our fingerprinting algorithm, model extraction can have fidelity and accuracy scores within $1\%$ of the scores obtained when attacking a single, explicitly specified model, as well as up to $14.6\%$ gain in accuracy and up to $7.7\%$ gain in fidelity compared to the naive attack. Second, we counter the proposed attack with a noise-based defense mechanism that thwarts fingerprinting by adding noise to the specified performance metrics. The proposed defense strategy reduces the attack's accuracy and fidelity by up to $9.8\%$ and $4.8\%$, respectively (on medium-sized model extraction). Third, we show that the proposed defense induces a fundamental trade-off between the level of protection and system goodput, achieving configurable and significant victim model extraction protection while maintaining acceptable goodput ($>80\%$). We implement the proposed defense in a real system with plans to open source., Comment: 17 pages, 9 figures, 6 tables

A growing number of applications depend on Machine Learning (ML) functionality and benefits from both higher quality ML predictions and better timeliness (latency) at the same time. A growing body of research in computer architecture, ML, and systems software literature focuses on reaching better latency-accuracy tradeoffs for ML models. Efforts include compression, quantization, pruning, early-exit models, mixed DNN precision, as well as ML inference accelerator designs that minimize latency and energy, while preserving delivered accuracy. All of them, however, yield improvements for a single static point in the latency-accuracy tradeoff space. We make a case for applications that operate in dynamically changing deployment scenarios, where no single static point is optimal. We draw on a recently proposed weight-shared SuperNet mechanism to enable serving a stream of queries that uses (activates) different SubNets within this weight-shared construct. This creates an opportunity to exploit the inherent temporal locality with our proposed SubGraph Stationary (SGS) optimization. We take a hardware-software co-design approach with a real implementation of SGS in SushiAccel and the implementation of a software scheduler SushiSched controlling which SubNets to serve and what to cache in real-time. Combined, they are vertically integrated into SUSHI-an inference serving stack. For the stream of queries, SUSHI yields up to 25% improvement in latency, 0.98% increase in served accuracy. SUSHI can achieve up to 78.7% off-chip energy savings., Comment: 16 pages; MLSYS 2023

With the increase in the scale of Deep Learning (DL) training workloads in terms of compute resources and time consumption, the likelihood of encountering in-training failures rises substantially, leading to lost work and resource wastage. Such failures are typically offset by a checkpointing mechanism, which comes at the cost of storage and network bandwidth overhead. State-of-the-art approaches involve lossy model compression mechanisms, which induce a tradeoff between the resulting model quality (accuracy) and compression ratio. Delta compression is then used to further reduce the overhead by only storing the difference between consecutive checkpoints. We make a key enabling observation that the sensitivity of model weights to compression varies during training, and different weights benefit from different quantization levels (ranging from retaining full precision to pruning). We propose (1) a non-uniform quantization scheme that leverages this variation, (2) an efficient search mechanism that dynamically finds the best quantization configurations, and (3) a quantization-aware delta compression mechanism that rearranges weights to minimize checkpoint differences, thereby maximizing compression. We instantiate these contributions in DynaQuant - a framework for DL workload checkpoint compression. Our experiments show that DynaQuant consistently achieves a better tradeoff between accuracy and compression ratios compared to prior works, enabling a compression ratio up to 39x and withstanding up to 10 restores with negligible accuracy impact for fault-tolerant training. DynaQuant achieves at least an order of magnitude reduction in checkpoint storage overhead for training failure recovery as well as transfer learning use cases without any loss of accuracy.

Neural Architecture Search (NAS) for Federated Learning (FL) is an emerging field. It automates the design and training of Deep Neural Networks (DNNs) when data cannot be centralized due to privacy, communication costs, or regulatory restrictions. Recent federated NAS methods not only reduce manual effort but also help achieve higher accuracy than traditional FL methods like FedAvg. Despite the success, existing federated NAS methods still fall short in satisfying diverse deployment targets common in on-device inference like hardware, latency budgets, or variable battery levels. Most federated NAS methods search for only a limited range of neuro-architectural patterns, repeat them in a DNN, thereby restricting achievable performance. Moreover, these methods incur prohibitive training costs to satisfy deployment targets. They perform the training and search of DNN architectures repeatedly for each case. SuperFedNAS addresses these challenges by decoupling the training and search in federated NAS. SuperFedNAS co-trains a large number of diverse DNN architectures contained inside one supernet in the FL setting. Post-training, clients perform NAS locally to find specialized DNNs by extracting different parts of the trained supernet with no additional training. SuperFedNAS takes O(1) (instead of O(N)) cost to find specialized DNN architectures in FL for any N deployment targets. As part of SuperFedNAS, we introduce MaxNet - a novel FL training algorithm that performs multi-objective federated optimization of a large number of DNN architectures ($\approx 5*10^8$) under different client data distributions. Overall, SuperFedNAS achieves upto 37.7% higher accuracy for the same MACs or upto 8.13x reduction in MACs for the same accuracy than existing federated NAS methods., Comment: Accepted at ECCV 2024

In this note, we show that the canonical solution operator to the $\bar\partial-$equation in the polydisc preserves H\"older regularity. It is a well-known fact that such solution operators do not improve H\"older regularity, and as such, our solution operator is optimal in this regard.

Efficient inference of Deep Neural Networks (DNNs) is essential to making AI ubiquitous. Two important algorithmic techniques have shown promise for enabling efficient inference - sparsity and binarization. These techniques translate into weight sparsity and weight repetition at the hardware-software level enabling the deployment of DNNs with critically low power and latency requirements. We propose a new method called signed-binary networks to improve efficiency further (by exploiting both weight sparsity and weight repetition together) while maintaining similar accuracy. Our method achieves comparable accuracy on ImageNet and CIFAR10 datasets with binary and can lead to 69% sparsity. We observe real speedup when deploying these models on general-purpose devices and show that this high percentage of unstructured sparsity can lead to a further reduction in energy consumption on ASICs., Comment: it is being updated

Slow sand filtration is most appropriate where there is funding to subsidize the initial cost of the filter, available training for use and maintenance, locally available sand, and a transportation network capable of moving the filter. Since the experimental study of slow filtration is taking a long time, theoretical analysis, modelling and simulation studies become important. Theoretical models of slow filtration are not yet sufficiently developed. Several reasons are hindering modelling and simulation: due to the complexity of the interaction of water and pollution with filters and the lack of detailed values for the kinetic coefficients in elementary processes. Multiphysics modelling using Comsol, where a complex set of Navier-Stokes equations is numerically solved together, with the molecular awareness for the kinetic coefficients, was used to studying various geometries and construction types of slow filtration., Comment: 14 pages, 7 Figures

Machine Learning (ML) research has focused on maximizing the accuracy of predictive tasks. ML models, however, are increasingly more complex, resource intensive, and costlier to deploy in resource-constrained environments. These issues are exacerbated for prediction tasks with sequential classification on progressively transitioned stages with ''happens-before'' relation between them.We argue that it is possible to ''unfold'' a monolithic single multi-class classifier, typically trained for all stages using all data, into a series of single-stage classifiers. Each single-stage classifier can be cascaded gradually from cheaper to more expensive binary classifiers that are trained using only the necessary data modalities or features required for that stage. UnfoldML is a cost-aware and uncertainty-based dynamic 2D prediction pipeline for multi-stage classification that enables (1) navigation of the accuracy/cost tradeoff space, (2) reducing the spatio-temporal cost of inference by orders of magnitude, and (3) early prediction on proceeding stages. UnfoldML achieves orders of magnitude better cost in clinical settings, while detecting multi-stage disease development in real time. It achieves within 0.1% accuracy from the highest-performing multi-class baseline, while saving close to 20X on spatio-temporal cost of inference and earlier (3.5hrs) disease onset prediction. We also show that UnfoldML generalizes to image classification, where it can predict different level of labels (from coarse to fine) given different level of abstractions of a image, saving close to 5X cost with as little as 0.4% accuracy reduction., Comment: To be published in NeurIPS'22

We consider a problem whether a CR mapping of a generic manifold in complex space is uniquely determined by its finite jet at a point, which is referred to as finite jet determination. We derive the finite jet determination for CR mappings of smooth Levi nondegenerate manifolds of arbitrary codimension from the finite dimensionality of the algebras of infinitesimal automorphisms of the corresponding quadrics. Previously, this implication was known for real analytic manifolds. We prove a new 2-jet determination result that covers most affirmative results on this matter obtained so far., Comment: 17 pages

This paper introduces a novel approach to automatic ahead-of-time (AOT) parallelization and optimization of sequential Python programs for execution on distributed heterogeneous platforms. Our approach enables AOT source-to-source transformation of Python programs, driven by the inclusion of type hints for function parameters and return values. These hints can be supplied by the programmer or obtained by dynamic profiler tools; multi-version code generation guarantees the correctness of our AOT transformation in all cases. Our compilation framework performs automatic parallelization and sophisticated high-level code optimizations for the target distributed heterogeneous hardware platform. It includes extensions to the polyhedral framework that unify user-written loops and implicit loops present in matrix/tensor operators, as well as automated section of CPU vs. GPU code variants. Further, our polyhedral optimizations enable both intra-node and inter-node parallelism. Finally, the optimized output code is deployed using the Ray runtime for scheduling distributed tasks across multiple heterogeneous nodes in a cluster. Our empirical evaluation shows significant performance improvements relative to sequential Python in both single-node and multi-node experiments, with a performance improvement of over 20,000$\times$ when using 24 nodes and 144 GPUs in the OLCF Summit supercomputer for the Space-Time Adaptive Processing (STAP) radar application., Comment: 14 pages, 10 figures, under submission to Euro-Par 2022 conference (https://2022.euro-par.org)

Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The coefficients of this expansion are decomposed in terms of several elementary building blocks and can be determined at finite 't Hooft coupling using bootstrap and integrability techniques. Some of these blocks are known from an analogous expansion of scattering amplitudes. In addition to these, the expansion for form factors includes a new type of building block, called {\it form factor transitions}, that encode information about the local operator. In the present paper, we consider the form factor of the chiral part of the stress-tensor supermultiplet. We bootstrap the corresponding form factor transitions of two-particle flux-tube states and use them to predict the leading term in the collinear expansion at finite coupling. The transitions we find can be expressed in terms of a quantity that previously appeared in a seemingly unrelated context, namely the octagon kernel. Lastly, we use a factorized ansatz to determine the multi-particle form factor transitions at finite coupling, which we use to predict the first subleading term in the collinear expansion. A perfect match is found between our predictions and the available perturbative data., Comment: 36 pages, 4 figures, v2: typos fixed and a reference added, matches published version

We study the Sturm--Liouville operator $$ T(\varepsilon)y=-\frac{1}{\varepsilon}y''+ p(x)y, $$ with concrete $\mathcal{PT}$-- symmetric potential $p(x) = ix$ and Dirichlet boundary conditions on the segment $[-1,1]$. Here $\varepsilon \in (0, \infty)$ is a physical parameter. We explicitly describe a beautiful phenomenon of the eigenvalue behavior when $\varepsilon$ changes from $0$ to $\infty$. All the critical values of $\varepsilon$ which determine the eigenvalue dynamics, are found in terms of the special Airy functions.

In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress-strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor's dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIF) are evaluated as a function of the intrinsic material length, characterising the scale at which gradient effects become significant. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress-strain state are determined. In pure mode I, the geometrically necessary dislocation (GND) density is located symmetrically with respect to the blunted crack tip. On the contrary, under pure mode II, the GND density becomes concentrated in the blunted and sharp parts of the crack tip. In this case, fracture initiation is shown to be likely to occur near the blunted region of the crack tip, where both the stress triaxiality and the GND density are at their maximum. The relation between the equilibrium state of dislocation densities and the intrinsic material length as well as the plastic SIF as a function of the work hardening exponent is discussed.