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Alexis Ohanian is a billionaire from the United States, well-known as the co-founder of Reddit, one of the internet's most popular social media and discussion platforms. Apart from Reddit, Alexis co-founded a venture capital firm called Initialized Capital in 2011.

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Get the most recent info and news about Initialized on HackerNoon, where 10k+ technologists publish stories for 4M+ monthly readers.

Initialized

Ending The Crypto Winter with Garry Tan and Brett Gibson of Initialized Capital

This is Part 6 of a 11-part series based on the research paper “Reinforcement Learning In Agent-based Market Simulation: Unveiling Realistic Stylized Facts And Behavior”. Use the table of links below to navigate to the next part. Table of Links Part 1: Abstract & Introduction Part 2: Important Concepts Part 3: System Description Part 4: Agents & Simulation Details Part 5: Experiment Design Part 6: Continual Learning Part 7: Experiment Results Part 8: Market and Agent Responsiveness to External Events Part 9: Conclusion & References Part 10: Additional Simulation Results Part 11: Simulation Configuration 4.2 Continual Learning We introduce three groups of agents in the simulation. • Group A - Continual Training Group. The agents are pre-trained for 10 hours (36,000 steps), and training continues throughout the time of the simulation (for another 10 hours or 36,000 steps). • Group B - Testing Group. The agents in this group are pre-trained for 10 hours and are used in the simulation without continuing training. • Group C - Untrained Group. The third group serves as a control to understand the performance improvement obtained from training. The agents in this group load the random initialized parameters and run simulations without training. For each random seed, we generate the parameters of the neural networks for the Group C agents directly. Each agent in Group C is trained for 10 hours and their parameters become the parameters used for each agent in Group B. The same parameters are used to initialize the agents in Group A. We are describing the process in detail as this is similar to a matched pairs testing design to minimize randomness for comparison purposes. This is important because we only repeat this process for 10 random seeds, that is 10 simulations. Each simulation takes 20 hours when running all of them in parallel and there are a lot of computational resources required for this study. This process is illustrated in Figure 2. To compare the results produced by the RL agents we introduce an additional simulation model using 100 ZeroIntelligence (ZI) agents. This system is using the agent design in Farmer et al.’s work [9] and [22]. We analyze and compare stylized facts obtained using the RL agents system, the ZI agents system, and real data. Additionally, we investigate the evolution of Market-Maker (MM) agents’ inventory and PnL components across different groups. To assess responsiveness, we introduce a sequence of flash sale events, and we examine the price impact during the flash sale period. We also examine the MM’s change in behavior due to the flash sale, and we evaluate the adaptability of continual learning agents by comparing policies before and after training with the flash sale prices. Authors:
(1) Zhiyuan Yao, Stevens Institute of Technology, Hoboken, New Jersey, USA (zyao9@stevens.edu);
(2) Zheng Li, Stevens Institute of Technology, Hoboken, New Jersey, USA (zli149@stevens.edu);
(3) Matthew Thomas, Stevens Institute of Technology, Hoboken, New Jersey, USA (mthomas3@stevens.edu);
(4) Ionut Florescu, Stevens Institute of Technology, Hoboken, New Jersey, USA (ifloresc@stevens.edu). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This is Part 6 of a 11-part series based on the research paper “Reinforcement Learning In Agent-based Market Simulation: Unveiling Realistic Stylized Facts And Behavior”. Use the table of links below to navigate to the next part. This is Part 6 of a 11-part series based on the research paper “ Reinforcement Learning In Agent-based Market Simulation: Unveiling Realistic Stylized Facts And Behavior ”. Use the table of links below to navigate to the next part. Part 6 Reinforcement Learning In Agent-based Market Simulation: Unveiling Realistic Stylized Facts And Behavior Table of Links Part 1: Abstract & Introduction Part 1: Abstract & Introduction Part 2: Important Concepts Part 2: Important Concepts Part 3: System Description Part 3: System Description Part 4: Agents & Simulation Details Part 4: Agents & Simulation Details Part 5: Experiment Design Part 5: Experiment Design Part 6: Continual Learning Part 6: Continual Learning Part 7: Experiment Results Part 7: Experiment Results Part 8: Market and Agent Responsiveness to External Events Part 8: Market and Agent Responsiveness to External Events Part 9: Conclusion & References Part 9: Conclusion & References Part 10: Additional Simulation Results Part 10: Additional Simulation Results Part 11: Simulation Configuration Part 11: Simulation Configuration 4.2 Continual Learning We introduce three groups of agents in the simulation. • Group A - Continual Training Group. The agents are pre-trained for 10 hours (36,000 steps), and training continues throughout the time of the simulation (for another 10 hours or 36,000 steps). • Group B - Testing Group. The agents in this group are pre-trained for 10 hours and are used in the simulation without continuing training. without • Group C - Untrained Group. The third group serves as a control to understand the performance improvement obtained from training. The agents in this group load the random initialized parameters and run simulations without training. For each random seed, we generate the parameters of the neural networks for the Group C agents directly. Each agent in Group C is trained for 10 hours and their parameters become the parameters used for each agent in Group B. The same parameters are used to initialize the agents in Group A. We are describing the process in detail as this is similar to a matched pairs testing design to minimize randomness for comparison purposes. This is important because we only repeat this process for 10 random seeds, that is 10 simulations. Each simulation takes 20 hours when running all of them in parallel and there are a lot of computational resources required for this study. This process is illustrated in Figure 2. To compare the results produced by the RL agents we introduce an additional simulation model using 100 ZeroIntelligence (ZI) agents. This system is using the agent design in Farmer et al.’s work [9] and [22]. We analyze and compare stylized facts obtained using the RL agents system, the ZI agents system, and real data. Additionally, we investigate the evolution of Market-Maker (MM) agents’ inventory and PnL components across different groups. To assess responsiveness, we introduce a sequence of flash sale events, and we examine the price impact during the flash sale period. We also examine the MM’s change in behavior due to the flash sale, and we evaluate the adaptability of continual learning agents by comparing policies before and after training with the flash sale prices. Authors: (1) Zhiyuan Yao, Stevens Institute of Technology, Hoboken, New Jersey, USA (zyao9@stevens.edu); (2) Zheng Li, Stevens Institute of Technology, Hoboken, New Jersey, USA (zli149@stevens.edu); (3) Matthew Thomas, Stevens Institute of Technology, Hoboken, New Jersey, USA (mthomas3@stevens.edu); (4) Ionut Florescu, Stevens Institute of Technology, Hoboken, New Jersey, USA (ifloresc@stevens.edu). Authors: Authors: (1) Zhiyuan Yao, Stevens Institute of Technology, Hoboken, New Jersey, USA (zyao9@stevens.edu); (2) Zheng Li, Stevens Institute of Technology, Hoboken, New Jersey, USA (zli149@stevens.edu); (3) Matthew Thomas, Stevens Institute of Technology, Hoboken, New Jersey, USA (mthomas3@stevens.edu); (4) Ionut Florescu, Stevens Institute of Technology, Hoboken, New Jersey, USA (ifloresc@stevens.edu). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Continual Learning in Reinforcement Learning Agents with Pre-trained, Testing, and Untrained Groups

Here's How Developers Can Ensure Sensitive Data Does Not Accidentally Reach Another Device

Así pueden los desarrolladores garantizar que los datos confidenciales no lleguen accidentalmente a otro dispositivo

Így biztosíthatják a fejlesztők, hogy az érzékeny adatok véletlenül ne érjenek el egy másik eszközt

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開発者が機密データが誤って別のデバイスに届かないようにする方法

აი, როგორ შეუძლიათ დეველოპერებს დარწმუნდნენ, რომ მგრძნობიარე მონაცემები შემთხვევით არ მოხვდება სხვა მოწყობილობაზე

នេះជារបៀបដែលអ្នកអភិវឌ្ឍន៍អាចធានាថាទិន្នន័យរសើបមិនទៅដល់ឧបករណ៍មួយផ្សេងទៀតដោយចៃដន្យ

Mona ke Kamoo Bahlami ba ka Netefatšago gore Datha ye e nago le Bohloko ga e Fihlelele Sedirišwa se Seng ka Phošo

Iată cum dezvoltatorii se pot asigura că datele sensibile nu ajung accidental la alt dispozitiv

Heano Mashandisiro Anogona Kuita Vagadziri Vese Sensitive Dhata Haisviki Netsaona Imwe Chishandiso

Waa kan sida ay horumariyayaashu u hubin karaan in xogta xasaasiga ahi aanay si lama filaan ah u gaadhin qalab kale

Ось як розробники можуть гарантувати, що конфіденційні дані випадково не потраплять на інший пристрій

Nantsi indlela abaPhuhlisi abanokuqinisekisa ngayo ukuba iDatha enovakalelo ayifikeleli kwesinye isixhobo ngengozi

Master React by Designing Effective APIs With the useImperativeHandle Hook

Meester reageer deur doeltreffende API's te ontwerp met die useImperativeHandle Hook

إتقان React من خلال تصميم واجهات برمجة تطبيقات فعالة باستخدام هوك useImperativeHandle

Domine React diseñando API efectivas con el gancho useImperativeHandle

Master React՝ նախագծելով արդյունավետ API-ներ useImperativeHandle Hook-ով

useImperativeHandle フックを使用して効果的な API を設計し、React をマスターする

Master React ka go Rala di-API tše di Atlegago Ka useImperativeHandle Hook

Opanuj React, projektując efektywne interfejsy API za pomocą hooka useImperativeHandle

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ImperativeHandle Hookஐப் பயன்படுத்தி பயனுள்ள APIகளை வடிவமைப்பதன் மூலம் மாஸ்டர் ரியாக்ட்

Master React hi ku Dizayina Ti-API leti Humelelaka Hi useImperativeHandle Hook

I-Master React ngokuYila ii-APIs eziSebenzayo Nge-useImperativeHandle Hook

使用 useImperativeHandle Hook 设计有效的 API 来掌握 React

Authors:
(1) Hoon Kim, Beeble AI, and contributed equally to this work;
(2) Minje Jang, Beeble AI, and contributed equally to this work;
(3) Wonjun Yoon, Beeble AI, and contributed equally to this work;
(4) Jisoo Lee, Beeble AI, and contributed equally to this work;
(5) Donghyun Na, Beeble AI, and contributed equally to this work;
(6) Sanghyun Woo, New York University, and contributed equally to this work. Editor's Note: This is Part 11 of 14 of a study introducing a method for improving how light and shadows can be applied to human portraits in digital images. Read the rest below. Table of Links Abstract and 1. Introduction
2. Related Work
3. SwitchLight and 3.1. Preliminaries
3.2. Problem Formulation
3.3. Architecture
3.4. Objectives
4. Multi-Masked Autoencoder Pre-training
5. Data
6. Experiments
7. Conclusion Appendix A. Implementation Details
B. User Study Interface
C. Video Demonstration
D. Additional Qualitative Results & References A. Implementation Details We pre-train a single U-Net architecture during this process. In the subsequent fine-tuning stage, the weights from this pre-trained model are transferred to multiple U-Nets - NormalNet, DiffuseNet, SpecularNet, and RenderNet. In contrast, IllumNet, which does not follow the U-Net architecture, is initialized with random weights. To ensure compatibility with the varying input channels of each network, we modify the weights as necessary. For example, weights pre-trained for RGB channels are copied and adapted to fit networks with 6 or 9 channels. Data To generate the relighting training pairs, we randomly select each image from the OLAT dataset. Two randomly chosen HDRI lighting environment maps are then projected onto these images to form a training pair. The images undergo processing in linear space. For managing the dynamic range effectively, we apply logarithmic normalization using the log(1 + x) function. Architecture SwitchLight employs a UNet-based architecture, consistently applied across its Normal Net, Diffuse Net, Specular Net, and Render Net. This approach is inspired by recent advancements in diffusion-based models [12]. Unlike standard diffusion methods, we omit the temporal embedding layer. The architecture is characterized by several hyperparameters: the number of input channels, a base channel, and channel multipliers that determine the channel count at each stage. Each downsampling stage features two residual blocks, with attention mechanisms integrated at certain resolutions. The key hyperparameters and their corresponding values are summarized in Table. 4. IllumNet is composed of two projection layers, one for transforming the Phong lobe features and another for image features, with the latter using normal bottleneck features as a compact form of image representation. Following this, a cross-attention layer is employed, wherein the Phong lobe serves as the query and the image features function as both key and value. Finally, an output layer generates the final convolved source HDRI. The Discriminator network is utilized during both pretraining and fine-tuning stages, maintaining the same architectural design, although the weights are not shared between these stages. This network is composed of a series of residual blocks, each containing two 3×3 convolution layers, interspersed with Leaky ReLU activations. The number of filters progressively increases across these layers: 64, 128, 256, and 512. Correspondingly, as the channel filter count increases, the resolution of the features decreases, and finally, the network compresses its output with a 3x3 convolution into a single channel, yielding a probability value. Regarding the activation functions across different networks: NormalNet processes its outputs through ℓ2 normalization, ensuring they are unit normal vectors. IllumNet, DiffuseNet, and RenderNet utilize a softplus activation (with β = 20) to generate non-negative pixel values. SpecularNet employs a sigmoid activation fuction, ensuring that both the roughness parameter and Fresnel reflectance values fall within a range of 0 to 1. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Hoon Kim, Beeble AI, and contributed equally to this work; (2) Minje Jang, Beeble AI, and contributed equally to this work; (3) Wonjun Yoon, Beeble AI, and contributed equally to this work; (4) Jisoo Lee, Beeble AI, and contributed equally to this work; (5) Donghyun Na, Beeble AI, and contributed equally to this work; (6) Sanghyun Woo, New York University, and contributed equally to this work. Authors: Authors: (1) Hoon Kim, Beeble AI, and contributed equally to this work; (2) Minje Jang, Beeble AI, and contributed equally to this work; (3) Wonjun Yoon, Beeble AI, and contributed equally to this work; (4) Jisoo Lee, Beeble AI, and contributed equally to this work; (5) Donghyun Na, Beeble AI, and contributed equally to this work; (6) Sanghyun Woo, New York University, and contributed equally to this work. Editor's Note: This is Part 11 of 14 of a study introducing a method for improving how light and shadows can be applied to human portraits in digital images. Read the rest below. Editor's Note: This is Part 11 of 14 of a study introducing a method for improving how light and shadows can be applied to human portraits in digital images. Read the rest below. Editor's Note: This is Part 11 of 14 of a study introducing a method for improving how light and shadows can be applied to human portraits in digital images. Read the rest below. Editor's Note: This is Part 11 of 14 of a study introducing a method for improving how light and shadows can be applied to human portraits in digital images. Read the rest below. Table of Links Abstract and 1. Introduction 2. Related Work 3. SwitchLight and 3.1. Preliminaries 3.2. Problem Formulation 3.3. Architecture 3.4. Objectives 4. Multi-Masked Autoencoder Pre-training 5. Data 6. Experiments 7. Conclusion Abstract and 1. Introduction Abstract and 1. Introduction 2. Related Work 2. Related Work 3. SwitchLight and 3.1. Preliminaries 3. SwitchLight and 3.1. Preliminaries 3.2. Problem Formulation 3.2. Problem Formulation 3.3. Architecture 3.3. Architecture 3.4. Objectives 3.4. Objectives 4. Multi-Masked Autoencoder Pre-training 4. Multi-Masked Autoencoder Pre-training 5. Data 5. Data 6. Experiments 6. Experiments 7. Conclusion 7. Conclusion Appendix A. Implementation Details B. User Study Interface C. Video Demonstration D. Additional Qualitative Results & References A. Implementation Details A. Implementation Details B. User Study Interface B. User Study Interface C. Video Demonstration C. Video Demonstration D. Additional Qualitative Results & References D. Additional Qualitative Results & References A. Implementation Details We pre-train a single U-Net architecture during this process. In the subsequent fine-tuning stage, the weights from this pre-trained model are transferred to multiple U-Nets - NormalNet, DiffuseNet, SpecularNet, and RenderNet. In contrast, IllumNet, which does not follow the U-Net architecture, is initialized with random weights. To ensure compatibility with the varying input channels of each network, we modify the weights as necessary. For example, weights pre-trained for RGB channels are copied and adapted to fit networks with 6 or 9 channels. Data To generate the relighting training pairs, we randomly select each image from the OLAT dataset. Two randomly chosen HDRI lighting environment maps are then projected onto these images to form a training pair. The images undergo processing in linear space. For managing the dynamic range effectively, we apply logarithmic normalization using the log(1 + x) function. Data Architecture SwitchLight employs a UNet-based architecture, consistently applied across its Normal Net, Diffuse Net, Specular Net, and Render Net. This approach is inspired by recent advancements in diffusion-based models [12]. Unlike standard diffusion methods, we omit the temporal embedding layer. The architecture is characterized by several hyperparameters: the number of input channels, a base channel, and channel multipliers that determine the channel count at each stage. Each downsampling stage features two residual blocks, with attention mechanisms integrated at certain resolutions. The key hyperparameters and their corresponding values are summarized in Table. 4. Architecture IllumNet is composed of two projection layers, one for transforming the Phong lobe features and another for image features, with the latter using normal bottleneck features as a compact form of image representation. Following this, a cross-attention layer is employed, wherein the Phong lobe serves as the query and the image features function as both key and value. Finally, an output layer generates the final convolved source HDRI. IllumNet The Discriminator network is utilized during both pretraining and fine-tuning stages, maintaining the same architectural design, although the weights are not shared between these stages. This network is composed of a series of residual blocks, each containing two 3×3 convolution layers, interspersed with Leaky ReLU activations. The number of filters progressively increases across these layers: 64, 128, 256, and 512. Correspondingly, as the channel filter count increases, the resolution of the features decreases, and finally, the network compresses its output with a 3x3 convolution into a single channel, yielding a probability value. Discriminator Regarding the activation functions across different networks: NormalNet processes its outputs through ℓ2 normalization, ensuring they are unit normal vectors. IllumNet, DiffuseNet, and RenderNet utilize a softplus activation (with β = 20) to generate non-negative pixel values. SpecularNet employs a sigmoid activation fuction, ensuring that both the roughness parameter and Fresnel reflectance values fall within a range of 0 to 1. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

AI System Uses Teamwork to Create Picture-Perfect Lighting

The One Tool You Absolutely Need to Efficiently Scale Retrieval-Augmented Generation

Github location: https://github.com/philhopkinsML/CUDA/blob/main/dynamictilesize.cpp Modern GPUs vary in shared memory capacity and computational capabilities. This code dynamically adapts to matrix dimensions and hardware configurations, ensuring maximum efficiency without manual tuning. It implements a tiled matrix multiplication algorithm, leveraging shared memory on the GPU to minimize the expensive cost of global memory access. Shared memory is faster than global memory but limited in size, so the algorithm dynamically calculates the optimal tile size based on the GPU's properties, ensuring efficient memory utilization. How It Works Matrix Initialization The program begins by allocating memory for matrices on both the host (CPU) and device (GPU). These matrices are initialized with example values for demonstration purposes but could easily be replaced with real-world data in practical applications. Here's a relevant snippet: // Allocate memory for matrices
float *h_A, *h_B, *h_C;  // Host matrices
float *d_A, *d_B, *d_C;  // Device matrices

int size_A = width * height * sizeof(float);
cudaMalloc((void **)&d_A, size_A);
cudaMalloc((void **)&d_B, size_B);
cudaMalloc((void **)&d_C, size_C);

// Initialize matrices with example values
initializeMatrix(h_A, width, height);
initializeMatrix(h_B, width, height);
cudaMemcpy(d_A, h_A, size_A, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size_B, cudaMemcpyHostToDevice); This code prepares the matrices for computation by allocating GPU memory and copying data from the host to the device. Efficient data transfer is critical in GPU programming to minimize overhead. Dynamic Tile Size Calculation The function DynamicTileSize queries the GPU's properties to determine the optimal tile size. This calculation ensures that: The maximum shared memory per block is respected.
The tile size is large enough for efficient computation but small enough to fit within the shared memory constraints. int DynamicTileSize(int sharedMemPerBlock) {
    int tileSize = sqrt(sharedMemPerBlock / sizeof(float));
    return tileSize;
} This function dynamically calculates the maximum tile size based on the shared memory available on the GPU, ensuring portability across various hardware configurations. Tiled Matrix Multiplication The matrixMulTiledDynamic kernel performs matrix multiplication in a block-wise manner using shared memory. Each block processes a submatrix (tile) of the larger matrices. Shared memory is dynamically allocated, reducing the cost of global memory access. extern __shared__ float sharedMem[];

__global__ void matrixMulTiledDynamic(float *A, float *B, float *C, int N, int tileSize) {
    int tx = threadIdx.x;
    int ty = threadIdx.y;

    float *sharedA = &sharedMem[0];
    float *sharedB = &sharedMem[tileSize * tileSize];

    float result = 0.0f;

    for (int m = 0; m < N / tileSize; ++m) {
        // Load tiles into shared memory
        sharedA[ty * tileSize + tx] = A[row * N + (m * tileSize + tx)];
        sharedB[ty * tileSize + tx] = B[(m * tileSize + ty) * N + col];
        __syncthreads();

        // Perform multiplication
        for (int k = 0; k < tileSize; ++k) {
            result += sharedA[ty * tileSize + k] * sharedB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result to global memory
    C[row * N + col] = result;
} Shared Memory: Dynamically allocated and split between submatrices sharedA and sharedB.
Thread Cooperation: Threads within a block load tiles into shared memory, perform multiplication, and synchronize before writing results back to global memory.
Dynamic Tile Size: The tileSize parameter, calculated earlier, ensures that shared memory is efficiently utilized. Challenges Addressed Scalability: The dynamic tile size adapts to larger matrices and more powerful GPUs, ensuring efficient resource usage.
Portability: By querying GPU properties (e.g., shared memory per block), the code can run on different GPU architectures without manual tuning.
Real-World Usability: Irregular matrix shapes and varying hardware configurations are handled seamlessly. Real-World Applications Deep Learning: Matrix multiplication is at the core of many deep learning algorithms. This implementation can optimize performance for large-scale computations in training and inference.
High-Performance Computing: Scientific simulations often rely on fast and accurate matrix operations, making this code invaluable in fields like physics and engineering.
Real-Time Rendering and Transformations: Gaming and real-time applications can use this approach for efficient transformations or physics simulations. Conclusion This dynamic tiling approach ensures that matrix multiplication leverages GPU hardware to its fullest potential. By adapting tile sizes based on the GPU's shared memory capabilities, the implementation achieves a balance between scalability, portability, and real-world usability. Whether for deep learning, scientific computing, or real-time applications, this code exemplifies how modern GPUs can handle computationally demanding tasks efficiently and elegantly. Github location: Github location: https://github.com/philhopkinsML/CUDA/blob/main/dynamictilesize.cpp https://github.com/philhopkinsML/CUDA/blob/main/dynamictilesize.cpp Modern GPUs vary in shared memory capacity and computational capabilities. This code dynamically adapts to matrix dimensions and hardware configurations, ensuring maximum efficiency without manual tuning. It implements a tiled matrix multiplication algorithm , leveraging shared memory on the GPU to minimize the expensive cost of global memory access. Shared memory is faster than global memory but limited in size, so the algorithm dynamically calculates the optimal tile size based on the GPU's properties, ensuring efficient memory utilization. tiled matrix multiplication algorithm How It Works How It Works Matrix Initialization Matrix Initialization The program begins by allocating memory for matrices on both the host (CPU) and device (GPU). These matrices are initialized with example values for demonstration purposes but could easily be replaced with real-world data in practical applications. Here's a relevant snippet: // Allocate memory for matrices
float *h_A, *h_B, *h_C;  // Host matrices
float *d_A, *d_B, *d_C;  // Device matrices

int size_A = width * height * sizeof(float);
cudaMalloc((void **)&d_A, size_A);
cudaMalloc((void **)&d_B, size_B);
cudaMalloc((void **)&d_C, size_C);

// Initialize matrices with example values
initializeMatrix(h_A, width, height);
initializeMatrix(h_B, width, height);
cudaMemcpy(d_A, h_A, size_A, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size_B, cudaMemcpyHostToDevice); // Allocate memory for matrices
float *h_A, *h_B, *h_C;  // Host matrices
float *d_A, *d_B, *d_C;  // Device matrices

int size_A = width * height * sizeof(float);
cudaMalloc((void **)&d_A, size_A);
cudaMalloc((void **)&d_B, size_B);
cudaMalloc((void **)&d_C, size_C);

// Initialize matrices with example values
initializeMatrix(h_A, width, height);
initializeMatrix(h_B, width, height);
cudaMemcpy(d_A, h_A, size_A, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size_B, cudaMemcpyHostToDevice); This code prepares the matrices for computation by allocating GPU memory and copying data from the host to the device. Efficient data transfer is critical in GPU programming to minimize overhead. Dynamic Tile Size Calculation Dynamic Tile Size Calculation The function DynamicTileSize queries the GPU's properties to determine the optimal tile size. This calculation ensures that: DynamicTileSize The maximum shared memory per block is respected. The tile size is large enough for efficient computation but small enough to fit within the shared memory constraints. The maximum shared memory per block is respected. maximum shared memory per block The tile size is large enough for efficient computation but small enough to fit within the shared memory constraints. tile size int DynamicTileSize(int sharedMemPerBlock) {
    int tileSize = sqrt(sharedMemPerBlock / sizeof(float));
    return tileSize;
} int DynamicTileSize(int sharedMemPerBlock) {
    int tileSize = sqrt(sharedMemPerBlock / sizeof(float));
    return tileSize;
} This function dynamically calculates the maximum tile size based on the shared memory available on the GPU, ensuring portability across various hardware configurations. Tiled Matrix Multiplication Tiled Matrix Multiplication The matrixMulTiledDynamic kernel performs matrix multiplication in a block-wise manner using shared memory. Each block processes a submatrix (tile) of the larger matrices. Shared memory is dynamically allocated, reducing the cost of global memory access. matrixMulTiledDynamic extern __shared__ float sharedMem[];

__global__ void matrixMulTiledDynamic(float *A, float *B, float *C, int N, int tileSize) {
    int tx = threadIdx.x;
    int ty = threadIdx.y;

    float *sharedA = &sharedMem[0];
    float *sharedB = &sharedMem[tileSize * tileSize];

    float result = 0.0f;

    for (int m = 0; m < N / tileSize; ++m) {
        // Load tiles into shared memory
        sharedA[ty * tileSize + tx] = A[row * N + (m * tileSize + tx)];
        sharedB[ty * tileSize + tx] = B[(m * tileSize + ty) * N + col];
        __syncthreads();

        // Perform multiplication
        for (int k = 0; k < tileSize; ++k) {
            result += sharedA[ty * tileSize + k] * sharedB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result to global memory
    C[row * N + col] = result;
} extern __shared__ float sharedMem[];

__global__ void matrixMulTiledDynamic(float *A, float *B, float *C, int N, int tileSize) {
    int tx = threadIdx.x;
    int ty = threadIdx.y;

    float *sharedA = &sharedMem[0];
    float *sharedB = &sharedMem[tileSize * tileSize];

    float result = 0.0f;

    for (int m = 0; m < N / tileSize; ++m) {
        // Load tiles into shared memory
        sharedA[ty * tileSize + tx] = A[row * N + (m * tileSize + tx)];
        sharedB[ty * tileSize + tx] = B[(m * tileSize + ty) * N + col];
        __syncthreads();

        // Perform multiplication
        for (int k = 0; k < tileSize; ++k) {
            result += sharedA[ty * tileSize + k] * sharedB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result to global memory
    C[row * N + col] = result;
} Shared Memory: Dynamically allocated and split between submatrices sharedA and sharedB. Thread Cooperation: Threads within a block load tiles into shared memory, perform multiplication, and synchronize before writing results back to global memory. Dynamic Tile Size: The tileSize parameter, calculated earlier, ensures that shared memory is efficiently utilized. Shared Memory : Dynamically allocated and split between submatrices sharedA and sharedB . Shared Memory sharedA sharedB Thread Cooperation : Threads within a block load tiles into shared memory, perform multiplication, and synchronize before writing results back to global memory. Thread Cooperation Dynamic Tile Size : The tileSize parameter, calculated earlier, ensures that shared memory is efficiently utilized. Dynamic Tile Size tileSize Challenges Addressed Challenges Addressed Scalability: The dynamic tile size adapts to larger matrices and more powerful GPUs, ensuring efficient resource usage. Portability: By querying GPU properties (e.g., shared memory per block), the code can run on different GPU architectures without manual tuning. Real-World Usability: Irregular matrix shapes and varying hardware configurations are handled seamlessly. Scalability : The dynamic tile size adapts to larger matrices and more powerful GPUs, ensuring efficient resource usage. Scalability Portability : By querying GPU properties (e.g., shared memory per block), the code can run on different GPU architectures without manual tuning. Portability Real-World Usability : Irregular matrix shapes and varying hardware configurations are handled seamlessly. Real-World Usability Real-World Applications Real-World Applications Deep Learning: Matrix multiplication is at the core of many deep learning algorithms. This implementation can optimize performance for large-scale computations in training and inference. High-Performance Computing: Scientific simulations often rely on fast and accurate matrix operations, making this code invaluable in fields like physics and engineering. Real-Time Rendering and Transformations: Gaming and real-time applications can use this approach for efficient transformations or physics simulations. Deep Learning : Matrix multiplication is at the core of many deep learning algorithms. This implementation can optimize performance for large-scale computations in training and inference. Deep Learning High-Performance Computing : Scientific simulations often rely on fast and accurate matrix operations, making this code invaluable in fields like physics and engineering. High-Performance Computing Real-Time Rendering and Transformations : Gaming and real-time applications can use this approach for efficient transformations or physics simulations. Real-Time Rendering and Transformations Conclusion Conclusion This dynamic tiling approach ensures that matrix multiplication leverages GPU hardware to its fullest potential. By adapting tile sizes based on the GPU's shared memory capabilities, the implementation achieves a balance between scalability, portability, and real-world usability. Whether for deep learning, scientific computing, or real-time applications, this code exemplifies how modern GPUs can handle computationally demanding tasks efficiently and elegantly.

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