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Excited to share GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training, which received the Best Paper Award at the ICLR 2026 Workshop on Foundation Models for Science. Can we scale neural physics simulation without scaling expensive solver-generated labels? (1/6) (The below results are all predicted by GeoPT.)

Minghao Guo

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A Letter to Our Community: The Road Ahead for Robotics To our Community and Partners, As we step into 2026, our mission at Axis is clearer than ever: Constructing the definitive End-to-End Scaling Layer for Robotics. Our goal is to accelerate the transfer of diverse human intelligence into Robotics General Intelligence (RGI). By owning the critical path of intelligence creation, we are turning the physical limitations of robotics into a scalable, software-driven future. Here is our strategic outlook and roadmap for the year ahead. The Core Thesis: Simulation is the Only Way Out The path to RGI is currently blocked by Data Scarcity, Generalization Fragility, and Hardware Fragmentation. At Axis, we believe Simulation is the only way out. Our Simulation Data Platform and Data Augmentation Engine transform raw data into "Synthetic Gold". Backed by academic milestones like Roboverse, Skill Blending, and GraspVLA, we have proven that pure simulation can achieve the generalization required for the real world. We don’t just collect data; we architect it. The Engine: Why Crypto? We believe RGI should come from all, not a few. Crypto is not just a feature; it is the primitive that powers our entire ecosystem flywheel: - Incentive Mechanism: Democratizing contribution and rewarding the trainers and developers. - Assetization: Turning proprietary data and refined models into liquid, ownable assets. - Verifiable Workflow: We are opening the "Black Box" of AI. By bringing total transparency to the Task Generation → Data Collection → Model Training pipeline, we ensure every byte of intelligence is verifiable, traceable, and secure. 2026 Strategic Deliverables This year, we are committed to delivering three foundational pillars: - The World's Largest Training Dataset for Robots: A robot training set—diverse, high-quality interaction data at an unprecedented scale. - A Robotics Foundation Model: A universal robotic brain trained on our pure simulation and synthetic data, capable of robust cross-embodiment transfer and open-world adaptability. - Evolvable Robot Hardware: Robots deployed with Axis models that autonomously evolve through continuous interaction, turning every deployment into a self-improving node within our RGI network. The Ultimate Vision We are building more than models; we are architecting the Distributed Machine Economy. A future where every dataset, model, and robotic embodiment is a verifiable asset in a global, autonomous network. Thank you for building the future of intelligence with us✌️📷

A Letter to Our Community: The Road Ahead for Robotics To our Community and Partners, As we step into 2026, our mission at Axis is clearer than ever: Constructing the definitive End-to-End Scaling Layer for Robotics. Our goal is to accelerate the transfer of diverse human intelligence into Robotics General Intelligence (RGI). By owning the critical path of intelligence creation, we are turning the physical limitations of robotics into a scalable, software-driven future. Here is our strategic outlook and roadmap for the year ahead. The Core Thesis: Simulation is the Only Way Out The path to RGI is currently blocked by Data Scarcity, Generalization Fragility, and Hardware Fragmentation. At Axis, we believe Simulation is the only way out. Our Simulation Data Platform and Data Augmentation Engine transform raw data into "Synthetic Gold". Backed by academic milestones like Roboverse, Skill Blending, and GraspVLA, we have proven that pure simulation can achieve the generalization required for the real world. We don’t just collect data; we architect it. The Engine: Why Crypto? We believe RGI should come from all, not a few. Crypto is not just a feature; it is the primitive that powers our entire ecosystem flywheel: - Incentive Mechanism: Democratizing contribution and rewarding the trainers and developers. - Assetization: Turning proprietary data and refined models into liquid, ownable assets. - Verifiable Workflow: We are opening the "Black Box" of AI. By bringing total transparency to the Task Generation → Data Collection → Model Training pipeline, we ensure every byte of intelligence is verifiable, traceable, and secure. 2026 Strategic Deliverables This year, we are committed to delivering three foundational pillars: - The World's Largest Training Dataset for Robots: A robot training set—diverse, high-quality interaction data at an unprecedented scale. - A Robotics Foundation Model: A universal robotic brain trained on our pure simulation and synthetic data, capable of robust cross-embodiment transfer and open-world adaptability. - Evolvable Robot Hardware: Robots deployed with Axis models that autonomously evolve through continuous interaction, turning every deployment into a self-improving node within our RGI network. The Ultimate Vision We are building more than models; we are architecting the Distributed Machine Economy. A future where every dataset, model, and robotic embodiment is a verifiable asset in a global, autonomous network. Thank you for building the future of intelligence with us✌️📷

Axis Robotics

28,096 views • 9 months ago

🚀Thrilled to share what we’ve been building at TRI over the past several months: our first Large Behavior Models (LBMs) are here! I’m proud to have been a core contributor to the multi-task policy learning and post-training efforts. At TRI, we’ve been researching how LBMs can help robots learn faster, better, and more efficiently. The key takeaways: ✅ We built an evaluation pipeline to benchmark LBM performance with real 𝐬𝐭𝐚𝐭𝐢𝐬𝐭𝐢𝐜𝐚𝐥 𝐜𝐨𝐧𝐟𝐢𝐝𝐞𝐧𝐜𝐞 ✅ Pre-training on hundreds of tasks makes models more robust—plus, we can teach new, complex tasks with 80% 𝐥𝐞𝐬𝐬 𝐝𝐚𝐭𝐚 ✅ The bigger and more diverse the pre-training, the better the results Check out our overview video, webpage and paper for more details: ✨ 🌎 📄 We hope this work helps move the field of robotics forward!

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Zubair Irshad

20,518 views • 1 year ago

Excited to share a few presentations, demos, and workshop talks from our group and collaborators at #ICRA2026! We will present recent work on real-to-sim-to-real robot policy evaluation, model-based planning with learned dynamics, and multi-modal manipulation. We will also have a joint live demo between SceniX and Analog Devices, Inc. on real-to-sim-to-real cable manipulation at the ICRA exhibition. This is a small teaser of what we have been building, with more to come soon! If you are at ICRA, please stop by the sessions or the demo booth. Happy to chat about robot learning, simulation, world models, and sim-to-real!

Excited to share a few presentations, demos, and workshop talks from our group and collaborators at #ICRA2026! We will present recent work on real-to-sim-to-real robot policy evaluation, model-based planning with learned dynamics, and multi-modal manipulation. We will also have a joint live demo between SceniX and Analog Devices, Inc. on real-to-sim-to-real cable manipulation at the ICRA exhibition. This is a small teaser of what we have been building, with more to come soon! If you are at ICRA, please stop by the sessions or the demo booth. Happy to chat about robot learning, simulation, world models, and sim-to-real!

Yunzhu Li

11,344 views • 4 months ago

Backprop has been the only credit assignment algorithm capable of training large neural nets. Introducing Dust, the first zeroth-order method to pretrain transformers to approach and sometimes even *exceed* backprop with large amounts of computation (bitter lesson!) - Dust is on the order of 1,000 to 10,000x more compute efficient than EGGROLL, the state-of-the-art ES method, for training transformers. - We chose pretraining transformers because it's arguably the hardest task possible for zeroth-order optimization. - Search in high dimensions is really misunderstood: zeroth-order usually gets better with overparameterization, not worse, i.e. at a fixed population size, larger models (up to 120x) reach a lower loss than smaller ones. - Backprop-like gradients emerge from a large population of activation perturbations, and the alignment holds up at every scale we tested, up to 1B tokens, which is critical for scaling. The core idea is a *virtual population*, which helps scale to large populations in transformers by perturbing activations in parallel. w/ Bishwas, serdarml, Akshay

Backprop has been the only credit assignment algorithm capable of training large neural nets. Introducing Dust, the first zeroth-order method to pretrain transformers to approach and sometimes even exceed backprop with large amounts of computation (bitter lesson!) - Dust is on the order of 1,000 to 10,000x more compute efficient than EGGROLL, the state-of-the-art ES method, for training transformers. - We chose pretraining transformers because it's arguably the hardest task possible for zeroth-order optimization. - Search in high dimensions is really misunderstood: zeroth-order usually gets better with overparameterization, not worse, i.e. at a fixed population size, larger models (up to 120x) reach a lower loss than smaller ones. - Backprop-like gradients emerge from a large population of activation perturbations, and the alignment holds up at every scale we tested, up to 1B tokens, which is critical for scaling. The core idea is a virtual population, which helps scale to large populations in transformers by perturbing activations in parallel. w/ Bishwas, serdarml, Akshay

Samip

243,777 views • 3 days ago

Our first test flight is just the beginning! Behind the scenes, we are focused on up-scaling and improving our technology. We are excited to announce that we have successfully tested the central subsystem of our Helix 2.0 oxygen-rich staged-combustion engine: the powerpack. We have performed two successful hot-fire tests in which we have shown steady-state operation and cavitation limits. The powerpack incorporates the turbopump and pre-burner(s). It is the most complex as well as the most mechanically and thermally stressed subsystem of a staged-combustion engine. This milestone validated key technological challenges, such as the simultaneous ignition of multiple pre-burners and turbopump cavitation performance. The results are in-line with the predictions from our design models. The closed-cycle architecture of Helix allows us to push the performance envelope further: Helix 2.0 is designed to deliver double the thrust (200kN), while mass, production technology and costs remain comparable to Helix 1.0. The result for our customers: more payload for a lower budget! Excited about this news? Check out our career portal for employment opportunities and help us to elevate our Helix staged-combustion engine technology to the next level! ➡️

Our first test flight is just the beginning! Behind the scenes, we are focused on up-scaling and improving our technology. We are excited to announce that we have successfully tested the central subsystem of our Helix 2.0 oxygen-rich staged-combustion engine: the powerpack. We have performed two successful hot-fire tests in which we have shown steady-state operation and cavitation limits. The powerpack incorporates the turbopump and pre-burner(s). It is the most complex as well as the most mechanically and thermally stressed subsystem of a staged-combustion engine. This milestone validated key technological challenges, such as the simultaneous ignition of multiple pre-burners and turbopump cavitation performance. The results are in-line with the predictions from our design models. The closed-cycle architecture of Helix allows us to push the performance envelope further: Helix 2.0 is designed to deliver double the thrust (200kN), while mass, production technology and costs remain comparable to Helix 1.0. The result for our customers: more payload for a lower budget! Excited about this news? Check out our career portal for employment opportunities and help us to elevate our Helix staged-combustion engine technology to the next level! ➡️

Rocket Factory Augsburg

35,163 views • 5 months ago

One of the craziest use cases I’ve found for Jev: verifiers. I am so excited about this that I at least wanted to share the high-level idea. I used Jev to build a custom verifier for the /goal feature in my agent harness. It checks whether the goal is actually complete after every turn, making continuous verification cheap enough to scale. This means I can run more of these verifiers (previously handled by another expensive reasoning model) more frequently to keep the agents on track. System One models are perfect for verification. I think of this as scaling harnesses further by cleverly combining System One and System Two models. I have a feeling this will enable a new wave of scalable test-time compute methods. Watch this space closely. I've just started to experiment with this and am already seeing really good results. I need to explore and figure out a way to benchmark it. I will share more once I have more results. This is an insane unlock for long-horizon agents. You heard it here first. And you can expect to see more harnesses embracing this new pattern. Full guide dropping in the next couple of days.

One of the craziest use cases I’ve found for Jev: verifiers. I am so excited about this that I at least wanted to share the high-level idea. I used Jev to build a custom verifier for the /goal feature in my agent harness. It checks whether the goal is actually complete after every turn, making continuous verification cheap enough to scale. This means I can run more of these verifiers (previously handled by another expensive reasoning model) more frequently to keep the agents on track. System One models are perfect for verification. I think of this as scaling harnesses further by cleverly combining System One and System Two models. I have a feeling this will enable a new wave of scalable test-time compute methods. Watch this space closely. I've just started to experiment with this and am already seeing really good results. I need to explore and figure out a way to benchmark it. I will share more once I have more results. This is an insane unlock for long-horizon agents. You heard it here first. And you can expect to see more harnesses embracing this new pattern. Full guide dropping in the next couple of days.

elvis

60,123 views • 19 days ago

The concept of creating an exact digital replica of the physical world has always fascinated me: environments that look and behave exactly like our everyday reality, precisely captured in the digital domain. This is the essence of 𝐖𝐨𝐫𝐥𝐝 𝐌𝐨𝐝𝐞𝐥𝐬, simulated realities indistinguishable from our own. Generating these models is the core mission behind what we are building at SpAItial AI. True World Models must capture both photorealistic appearance and underlying physics, spatially-consistent across the environment. For static scenes, current models already deliver impressive results, unlocking downstream applications from gaming to 3D design. However, the true frontier lies in modeling dynamics, which will enable the training of AI agents whose learned behaviors can bridge the sim-to-real gap, thus unlocking countless real-world applications.

The concept of creating an exact digital replica of the physical world has always fascinated me: environments that look and behave exactly like our everyday reality, precisely captured in the digital domain. This is the essence of 𝐖𝐨𝐫𝐥𝐝 𝐌𝐨𝐝𝐞𝐥𝐬, simulated realities indistinguishable from our own. Generating these models is the core mission behind what we are building at SpAItial AI. True World Models must capture both photorealistic appearance and underlying physics, spatially-consistent across the environment. For static scenes, current models already deliver impressive results, unlocking downstream applications from gaming to 3D design. However, the true frontier lies in modeling dynamics, which will enable the training of AI agents whose learned behaviors can bridge the sim-to-real gap, thus unlocking countless real-world applications.

Matthias Niessner

21,730 views • 7 months ago

Model-Free Reinforcement Learning (MFRL) has been alluring, especially with supercharged compute with physics on GPU. However, the methods use 0-th order gradients, and are often not the best optimizers. Can we do better than PPO in continuous control for robotics? Turns out yes! 🥳 tl;dr: Faster, better RL than PPO in continuous control 💪 The answer lies in using more information from the simulation. We are juicing the simulation on GPU as it is, why not use it for gradients as well? This has been a driving question in a series of our works. We first studied this problem in ICLR 2022 paper on Short Horizon Actor Critic Naive gradient based methods are stuck in local minima and have exploding/vanishing gradients. SHAC solved this problem truncated rollouts and model based value estimation, where the model is Differentiable Sim. This boosted sample efficiency and wall-clock time immensely especially in high dimensional systems such as humanoids Yet, given enough compute PPO often caught up. Our follow up paper on on Adaptive Horizon Actor Critic at ICML 2024 discovers the cause and provides a fix. However, we find that even when given ground-truth dynamics, not all gradients are useful due to sample error. 1st-Order Model-Based Reinforcement Learning methods employing differentiable simulation provide gradients with reduced variance but are susceptible to bias in scenarios involving stiff dynamics, such as physical contact. We find that back-propagating through contact and long trajectories drastically reduces gradient accuracy. Using this insight, we propose AHAC to dynamically adapt its roll-out horizon to avoid differentiating through stiff contact. AHAC is a first-order model-based RL algorithm that learns high-dimensional tasks in minutes (wall clock) and outperforms PPO by 40%, even in the limit of data provided to PPO. This work is led by Ignat Georgiev alongside Krishnan Srinivasan, Jie Xu, Eric Heiden and ample assistance from warp team at NVIDIA Robotics (Miles Macklin)

Model-Free Reinforcement Learning (MFRL) has been alluring, especially with supercharged compute with physics on GPU. However, the methods use 0-th order gradients, and are often not the best optimizers. Can we do better than PPO in continuous control for robotics? Turns out yes! 🥳 tl;dr: Faster, better RL than PPO in continuous control 💪 The answer lies in using more information from the simulation. We are juicing the simulation on GPU as it is, why not use it for gradients as well? This has been a driving question in a series of our works. We first studied this problem in ICLR 2022 paper on Short Horizon Actor Critic Naive gradient based methods are stuck in local minima and have exploding/vanishing gradients. SHAC solved this problem truncated rollouts and model based value estimation, where the model is Differentiable Sim. This boosted sample efficiency and wall-clock time immensely especially in high dimensional systems such as humanoids Yet, given enough compute PPO often caught up. Our follow up paper on on Adaptive Horizon Actor Critic at ICML 2024 discovers the cause and provides a fix. However, we find that even when given ground-truth dynamics, not all gradients are useful due to sample error. 1st-Order Model-Based Reinforcement Learning methods employing differentiable simulation provide gradients with reduced variance but are susceptible to bias in scenarios involving stiff dynamics, such as physical contact. We find that back-propagating through contact and long trajectories drastically reduces gradient accuracy. Using this insight, we propose AHAC to dynamically adapt its roll-out horizon to avoid differentiating through stiff contact. AHAC is a first-order model-based RL algorithm that learns high-dimensional tasks in minutes (wall clock) and outperforms PPO by 40%, even in the limit of data provided to PPO. This work is led by Ignat Georgiev alongside Krishnan Srinivasan, Jie Xu, Eric Heiden and ample assistance from warp team at NVIDIA Robotics (Miles Macklin)

Animesh Garg

52,308 views • 2 years ago

Introducing ASAL: Automating the Search for Artificial Life with Foundation Models Artificial Life (ALife) research holds key insights that can transform and accelerate progress in AI. By speeding up ALife discovery with AI, we accelerate our understanding of emergence, evolution, and intelligence–core principles that can inspire the next generation of AI systems! We proudly collaborated with MIT, OpenAI, Swiss AI Lab IDSIA, and Ken Stanley on this exciting project. Full Paper (Website): Full Paper (arxiv): Code: In this work, we propose a new algorithm called Automated Search for Artificial Life (“ASAL”) to automate the discovery of artificial life using vision-language foundation models. Instead of tediously hand-designing every tiny rule of an Alife simulation, simply describe the space of simulations to search over, and ASAL will automatically discover the most interesting and open-ended artificial lifeforms! Because of the generality of foundation models, ASAL can discover new lifeforms across a diverse range of seminal ALife simulations, including Boids, Particle Life, Game of Life, Lenia, and Neural Cellular Automata. ASAL even discovered novel cellular automata rules that are more open-ended and expressive than the original Conway’s Game of Life. We believe this new paradigm may reignite ALife research by overcoming the bottleneck of manually designed simulations, thus advancing beyond the limits of human ingenuity.

Introducing ASAL: Automating the Search for Artificial Life with Foundation Models Artificial Life (ALife) research holds key insights that can transform and accelerate progress in AI. By speeding up ALife discovery with AI, we accelerate our understanding of emergence, evolution, and intelligence–core principles that can inspire the next generation of AI systems! We proudly collaborated with MIT, OpenAI, Swiss AI Lab IDSIA, and Ken Stanley on this exciting project. Full Paper (Website): Full Paper (arxiv): Code: In this work, we propose a new algorithm called Automated Search for Artificial Life (“ASAL”) to automate the discovery of artificial life using vision-language foundation models. Instead of tediously hand-designing every tiny rule of an Alife simulation, simply describe the space of simulations to search over, and ASAL will automatically discover the most interesting and open-ended artificial lifeforms! Because of the generality of foundation models, ASAL can discover new lifeforms across a diverse range of seminal ALife simulations, including Boids, Particle Life, Game of Life, Lenia, and Neural Cellular Automata. ASAL even discovered novel cellular automata rules that are more open-ended and expressive than the original Conway’s Game of Life. We believe this new paradigm may reignite ALife research by overcoming the bottleneck of manually designed simulations, thus advancing beyond the limits of human ingenuity.

Sakana AI

751,904 views • 1 year ago

Double News Clickteam gave a slight update on Five Laps At Freddy’s, stating: “When we are allowed to share news we will.” The game is still listed with a planned 2026 release date on Steam. Scary Movie 6 launched a website where users can prompt Ghostface to perform different actions — including a recreation of the popular “Join Us For A Bite” Burger King dance by typing “FNAF”! Link below to Source:

Double News Clickteam gave a slight update on Five Laps At Freddy’s, stating: “When we are allowed to share news we will.” The game is still listed with a planned 2026 release date on Steam. Scary Movie 6 launched a website where users can prompt Ghostface to perform different actions — including a recreation of the popular “Join Us For A Bite” Burger King dance by typing “FNAF”! Link below to Source:

Five Nights at Freddy’s Alerts

16,761 views • 4 months ago

Today, we released Lyra 2.0, a framework for generating persistent, explorable 3D worlds at scale, from NVIDIA Research. Generating large-scale, complex environments is difficult for AI models. Current models often “forget” what spaces look like and lose track of movement over time, causing objects to shift, blur, or appear inconsistent. This prevents them from creating the reliable 3D environments required for downstream simulations. Lyra 2.0 solves these issues by: ✅ Maintaining per-frame 3D geometry to retrieve past frames and establish spatial correspondences ✅ Using self-augmented training to correct its own temporal drifting. Lyra 2.0 turns an image into a 3D world you can walk through, look back, and drop a robot into for real-time rendering, simulation, and immersive applications. ➡️ Learn more: 📄 Read the paper:

Today, we released Lyra 2.0, a framework for generating persistent, explorable 3D worlds at scale, from NVIDIA Research. Generating large-scale, complex environments is difficult for AI models. Current models often “forget” what spaces look like and lose track of movement over time, causing objects to shift, blur, or appear inconsistent. This prevents them from creating the reliable 3D environments required for downstream simulations. Lyra 2.0 solves these issues by: ✅ Maintaining per-frame 3D geometry to retrieve past frames and establish spatial correspondences ✅ Using self-augmented training to correct its own temporal drifting. Lyra 2.0 turns an image into a 3D world you can walk through, look back, and drop a robot into for real-time rendering, simulation, and immersive applications. ➡️ Learn more: 📄 Read the paper:

NVIDIA AI Developer

441,125 views • 5 months ago

A viral paper "Language Model Represents Space and Time" recently claims that LLMs learn "world models". As much as I like Max Tegmark's works, I disagree with their definition of world model. World model is a core concept in AI agent and decision making. It is our mental simulation of how the world works given interventions (or lack thereof). A world model captures causality and intuitive physics, telling the agent what is likely and what is impossible. It can and should be used for counterfactual reasoning, i.e. "what ifs": what would happen if I knock over a cup of water? Where would I have been if I had not taken that bus? Yann LeCun Yann LeCun says it well in his position paper ( I quote: "Using such world models, animals can learn new skills with very few trials. They can predict the consequences of their actions, they can reason, plan, explore, and imagine new solutions to problems. Importantly, they can also avoid making dangerous mistakes when facing an unknown situation." The first use of the term World Model in deep policy learning is attributed to hardmaru & Jürgen Schmidhuber: In their seminal paper, an agent masters shooting skills in the popular game Doom (demo below) by learning in imagination, using an internal world model as a "physics simulator". To put in a simple Python math formula, world model learns a function F(s[0:t-1], a) -> s[t:], which takes as input the observed past and current action, and outputs plausible future states. Now the definition of World Model in Tegmark's paper seems to be about predicting GPS coordinates and time eras. I see this as just a classification task with no causal learning and simulation going on. You cannot make meaningful interventions against that model, nor can you optimize any decision making in a closed feedback loop. As for the "space & time neurons", I think they are most similar to the "sentiment neuron" that OpenAI published in 2017: Predicting GPS is conceptually no different from predicting sentiment in my opinion. I don't think their experimental results are wrong - just that their conclusion is on shaky grounds. I welcome any debate! Paper link:

A viral paper "Language Model Represents Space and Time" recently claims that LLMs learn "world models". As much as I like Max Tegmark's works, I disagree with their definition of world model. World model is a core concept in AI agent and decision making. It is our mental simulation of how the world works given interventions (or lack thereof). A world model captures causality and intuitive physics, telling the agent what is likely and what is impossible. It can and should be used for counterfactual reasoning, i.e. "what ifs": what would happen if I knock over a cup of water? Where would I have been if I had not taken that bus? Yann LeCun Yann LeCun says it well in his position paper ( I quote: "Using such world models, animals can learn new skills with very few trials. They can predict the consequences of their actions, they can reason, plan, explore, and imagine new solutions to problems. Importantly, they can also avoid making dangerous mistakes when facing an unknown situation." The first use of the term World Model in deep policy learning is attributed to hardmaru & Jürgen Schmidhuber: In their seminal paper, an agent masters shooting skills in the popular game Doom (demo below) by learning in imagination, using an internal world model as a "physics simulator". To put in a simple Python math formula, world model learns a function F(s[0:t-1], a) -> s[t:], which takes as input the observed past and current action, and outputs plausible future states. Now the definition of World Model in Tegmark's paper seems to be about predicting GPS coordinates and time eras. I see this as just a classification task with no causal learning and simulation going on. You cannot make meaningful interventions against that model, nor can you optimize any decision making in a closed feedback loop. As for the "space & time neurons", I think they are most similar to the "sentiment neuron" that OpenAI published in 2017: Predicting GPS is conceptually no different from predicting sentiment in my opinion. I don't think their experimental results are wrong - just that their conclusion is on shaky grounds. I welcome any debate! Paper link:

Jim Fan

594,014 views • 3 years ago

[Dropout] by hand ✍️ Dropout is a simple yet effective way of reducing overfitting and improving generalization. This by-hand exercise lets students practice calculating dropout, thereby gaining insight into its inner workings. As an additional bonus, students get to practice calculating the gradients of the Mean Square Error (MSE) loss. After the practice, students are often surprised by how simple it is. -- 𝗡𝗲𝘁𝘄𝗼𝗿𝗸 𝗔𝗿𝗰𝗵𝗶𝘁𝗲𝗰𝘁𝘂𝗿𝗲 -- 1. Linear(2,4) 2. ReLU 3. Dropout(0.5) 4. Linear(4,3) 5. ReLU 6. Dropout(0.33) 7. Linear(3,2) -- 𝗪𝗮𝗹𝗸𝘁𝗵𝗿𝗼𝘂𝗴𝗵 -- 🏋️ Training [1] Given ↳ A training set of 2 examples X1, X2 [2] 🟧 Random: p > 0.5 ↳ Draw 4 random numbers ↳ For each random number, if it is above 0.5, we keep and denote it as ◯. Otherwise we drop and denote it as ╳. ↳ The result is [◯, ╳, ◯, ╳] [3] 🟧 Dropout: Matrix ↳ Calculate the scaling factor: 1 / (1-p) = 2 ↳ Set the diagonal based on [◯, ╳, ◯, ╳], where ◯ = 2 and ╳ = 0 ↳ The purpose is to drop the 2nd and the 4th nodes, and scale the remaining two nodes by 2. [4] 🟦 Random: p > 0.33 ↳ Draw 3 random numbers ↳ For each random number, if it is above 0.33, we keep and denote it as ◯. Otherwise we drop and denote it as ╳. ↳ The result is [◯, ◯, ╳] [5] 🟦 Dropout: Matrix ↳ Calculate the scaling factor: 1 / (1-p) = 1.5 ↳ Set the diagonal based on [◯, ◯, ╳], where ◯ = 1.5 and ╳ = 0 ↳ The purpose is to drop the 3rd node, and scale the remaining two nodes by 1.5. [6] Feed Forward ↳ Now we have all the matrices ready across the layers, perform the feed forward pass by calculating a series of matrix multiplications from the top to the bottom ↳ ReLU activation function is applied along the way to set negative feature values to zeroes, denoted by ╳. ↳ The outputs are Y. [7] 🟥 Loss Gradients of Mean Square Error (MSE) ↳ The formula is 2 * (Y - Y') ↳ First we calculate Outputs (Y) - Targets (Y') ↳ Second we multiply each element by 2 [8] Update Weights ↳ Use loss gradients to start back propagation ↳ Update some weights (light red) ↳ The values of the new weights are for demonstration purpose only, not based on real calculation. 🔍 Inference [9] Deactivate Dropout ↳ We set both dropout matrices to identity matrices ↳ The effect is to keep all the features as is. [10] Feed Forward ↳ Take the forward pass to make predictions about unseen data.

[Dropout] by hand ✍️ Dropout is a simple yet effective way of reducing overfitting and improving generalization. This by-hand exercise lets students practice calculating dropout, thereby gaining insight into its inner workings. As an additional bonus, students get to practice calculating the gradients of the Mean Square Error (MSE) loss. After the practice, students are often surprised by how simple it is. -- 𝗡𝗲𝘁𝘄𝗼𝗿𝗸 𝗔𝗿𝗰𝗵𝗶𝘁𝗲𝗰𝘁𝘂𝗿𝗲 -- 1. Linear(2,4) 2. ReLU 3. Dropout(0.5) 4. Linear(4,3) 5. ReLU 6. Dropout(0.33) 7. Linear(3,2) -- 𝗪𝗮𝗹𝗸𝘁𝗵𝗿𝗼𝘂𝗴𝗵 -- 🏋️ Training [1] Given ↳ A training set of 2 examples X1, X2 [2] 🟧 Random: p > 0.5 ↳ Draw 4 random numbers ↳ For each random number, if it is above 0.5, we keep and denote it as ◯. Otherwise we drop and denote it as ╳. ↳ The result is [◯, ╳, ◯, ╳] [3] 🟧 Dropout: Matrix ↳ Calculate the scaling factor: 1 / (1-p) = 2 ↳ Set the diagonal based on [◯, ╳, ◯, ╳], where ◯ = 2 and ╳ = 0 ↳ The purpose is to drop the 2nd and the 4th nodes, and scale the remaining two nodes by 2. [4] 🟦 Random: p > 0.33 ↳ Draw 3 random numbers ↳ For each random number, if it is above 0.33, we keep and denote it as ◯. Otherwise we drop and denote it as ╳. ↳ The result is [◯, ◯, ╳] [5] 🟦 Dropout: Matrix ↳ Calculate the scaling factor: 1 / (1-p) = 1.5 ↳ Set the diagonal based on [◯, ◯, ╳], where ◯ = 1.5 and ╳ = 0 ↳ The purpose is to drop the 3rd node, and scale the remaining two nodes by 1.5. [6] Feed Forward ↳ Now we have all the matrices ready across the layers, perform the feed forward pass by calculating a series of matrix multiplications from the top to the bottom ↳ ReLU activation function is applied along the way to set negative feature values to zeroes, denoted by ╳. ↳ The outputs are Y. [7] 🟥 Loss Gradients of Mean Square Error (MSE) ↳ The formula is 2 * (Y - Y') ↳ First we calculate Outputs (Y) - Targets (Y') ↳ Second we multiply each element by 2 [8] Update Weights ↳ Use loss gradients to start back propagation ↳ Update some weights (light red) ↳ The values of the new weights are for demonstration purpose only, not based on real calculation. 🔍 Inference [9] Deactivate Dropout ↳ We set both dropout matrices to identity matrices ↳ The effect is to keep all the features as is. [10] Feed Forward ↳ Take the forward pass to make predictions about unseen data.

Tom Yeh

36,026 views • 2 years ago

Introducing Kaleido💮 from AI at Meta — a universal generative neural rendering engine for photorealistic, unified object and scene view synthesis. Kaleido is built on a simple but powerful design philosophy: 3D perception is a form of visual common sense. Following this idea, we formulate rendering purely as a sequence-to-sequence generation problem, successfully unifying neural rendering with the architecture principles behind modern language and video models. Unlike traditional neural rendering methods, Kaleido learns 3D purely in a data-driven way, without explicit 3D representations or structures. It acquires spatial understanding directly through large-scale video pretraining, then multi-view 3D data finetuning, inspired by how LLMs acquire textual common sense from large corpora before specialising in domains like coding. Through extensive ablations, we progressively modernised the architecture design and training strategies and tackled key scaling challenges in sequence-to-sequence generative rendering, arriving at a design that’s simple, versatile, and scalable. Kaleido significantly outperforms prior generative models in few-view settings, and remarkably is the first zero-shot generative method matches InstantNGP-level rendering quality in multi-view settings. We view Kaleido also as an alternative step towards world modeling that flexibly spans a spectrum of “realities": with many views, it faithfully reconstructs grounded reality; with fewer views, it imagines plausible unseen details. 🔗 Explore more results and paper:

Introducing Kaleido💮 from AI at Meta — a universal generative neural rendering engine for photorealistic, unified object and scene view synthesis. Kaleido is built on a simple but powerful design philosophy: 3D perception is a form of visual common sense. Following this idea, we formulate rendering purely as a sequence-to-sequence generation problem, successfully unifying neural rendering with the architecture principles behind modern language and video models. Unlike traditional neural rendering methods, Kaleido learns 3D purely in a data-driven way, without explicit 3D representations or structures. It acquires spatial understanding directly through large-scale video pretraining, then multi-view 3D data finetuning, inspired by how LLMs acquire textual common sense from large corpora before specialising in domains like coding. Through extensive ablations, we progressively modernised the architecture design and training strategies and tackled key scaling challenges in sequence-to-sequence generative rendering, arriving at a design that’s simple, versatile, and scalable. Kaleido significantly outperforms prior generative models in few-view settings, and remarkably is the first zero-shot generative method matches InstantNGP-level rendering quality in multi-view settings. We view Kaleido also as an alternative step towards world modeling that flexibly spans a spectrum of “realities": with many views, it faithfully reconstructs grounded reality; with fewer views, it imagines plausible unseen details. 🔗 Explore more results and paper:

Shikun Liu

22,471 views • 1 year ago

⭐The Year of Inference is here. Featherless is now an official inference provider on Hugging Face, unlocking 6,700+ LLMs for anyone to run, eval, and deploy instantly. It all starts with accessibility. From DeepSeek to Mistral, LLaMA to Qwen — powerful LLMs are one click away. We believe the future of AI is shaped by the long tail: personalized, specialized models tuned to real people’s needs. To get there, inference must be open, affordable, and usable by all. Whether you're fine-tuning, prototyping, or scaling a product, this moment is for you. 🫱🏻‍🫲🏻Let’s make inference the easiest part of building with AI. 📢 Share this so more builders know what’s now possible. Excited to be partnering with clem 🤗 Julien Chaumond Vaibhav (VB) Srivastav Simon Brandeis & Hugging Face team to take this to the next level!

⭐The Year of Inference is here. Featherless is now an official inference provider on Hugging Face, unlocking 6,700+ LLMs for anyone to run, eval, and deploy instantly. It all starts with accessibility. From DeepSeek to Mistral, LLaMA to Qwen — powerful LLMs are one click away. We believe the future of AI is shaped by the long tail: personalized, specialized models tuned to real people’s needs. To get there, inference must be open, affordable, and usable by all. Whether you're fine-tuning, prototyping, or scaling a product, this moment is for you. 🫱🏻‍🫲🏻Let’s make inference the easiest part of building with AI. 📢 Share this so more builders know what’s now possible. Excited to be partnering with clem 🤗 Julien Chaumond Vaibhav (VB) Srivastav Simon Brandeis & Hugging Face team to take this to the next level!

Featherless AI

24,043 views • 1 year ago

𝗣𝗼𝗽𝘂𝗹𝗮𝗿 𝗼𝗽𝗶𝗻𝗶𝗼𝗻: "𝗝𝘂𝘀𝘁 𝗴𝗲𝗻𝗲𝗿𝗮𝘁𝗲 𝗺𝗼𝗿𝗲 𝘀𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻 𝗱𝗮𝘁𝗮." After working with many 𝗿𝗼𝗯𝗼𝘁 𝗺𝗮𝗻𝗶𝗽𝘂𝗹𝗮𝘁𝗶𝗼𝗻 teams who've fallen into the simulation trap, here's what I've learned: Simulation teaches your robot to be really, really good at simulation. Unlike blind locomotion policies that can get away with sim-to-real transfer because they rely mainly on proprioception and contact forces, 𝘃𝗶𝘀𝗶𝗼𝗻-𝗴𝘂𝗶𝗱𝗲𝗱 𝗺𝗮𝗻𝗶𝗽𝘂𝗹𝗮𝘁𝗶𝗼𝗻 𝗶𝘀 𝗲𝘅𝘁𝗿𝗲𝗺𝗲𝗹𝘆 𝘀𝗲𝗻𝘀𝗶𝘁𝗶𝘃𝗲 𝘁𝗼 𝘃𝗶𝘀𝘂𝗮𝗹 𝗱𝗼𝗺𝗮𝗶𝗻 𝗴𝗮𝗽. The subtle differences accumulate: - Simulated friction vs real surface textures - Perfect lighting vs shadows, reflections, glare - Ideal object geometries vs manufacturing tolerances - Instantaneous sensor readings vs real-world noise and latency - Clean backgrounds vs cluttered, dynamic environments 𝗧𝗵𝗲 𝗰𝗹𝗮𝘀𝘀𝗶𝗰 𝗽𝗿𝗼𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻: Week 1: "Our model works perfectly in sim!" Week 2: "Let's collect some real data to fine-tune." Week 3: "The real data completely contradicts what the sim taught..." Week 4: "Okay, let's collect way more real data." Month 2: "We basically need to retrain from scratch." 𝗧𝗵𝗲 𝗽𝗮𝗶𝗻𝗳𝘂𝗹 𝘁𝗿𝘂𝘁𝗵: There's no shortcut to real-world data collection for vision-based manipulation. Simulation is amazing for debugging, prototyping, safety testing, and of course to supplement your real data. But it's not a substitute for understanding how your robot actually behaves in the actual environment. 𝗪𝗵𝗮𝘁 𝘄𝗼𝗿𝗸𝘀: Use simulation strategically - for exploring edge cases, testing safety boundaries, and rapid iteration. But build your production models on real data from real environments. The teams that succeed treat simulation as a powerful tool, not a magic solution. This is why Neuracore focuses on making real-world data collection so much easier and faster. Because the physics of your actual environment can't be simulated away. 𝗪𝗼𝗿𝗹𝗱 𝗺𝗼𝗱𝗲𝗹𝘀, 𝘆𝗼𝘂 𝘀𝗮𝘆? 𝗪𝗲𝗹𝗹, 𝗽𝗲𝗿𝗵𝗮𝗽𝘀 𝗺𝗼𝗿𝗲 𝗼𝗻 𝘁𝗵𝗮𝘁 𝗶𝗻 𝗮𝗻𝗼𝘁𝗵𝗲𝗿 𝗽𝗼𝘀𝘁! 𝗪𝗵𝗮𝘁'𝘀 𝗯𝗲𝗲𝗻 𝘆𝗼𝘂𝗿 𝗲𝘅𝗽𝗲𝗿𝗶𝗲𝗻𝗰𝗲 𝘄𝗶𝘁𝗵 𝘀𝗶𝗺-𝘁𝗼-𝗿𝗲𝗮𝗹 𝘁𝗿𝗮𝗻𝘀𝗳𝗲𝗿? 𝗛𝗮𝘀 𝗶𝘁 𝘄𝗼𝗿𝗸𝗲𝗱 𝗮𝘀 𝘄𝗲𝗹𝗹 𝗮𝘀 𝗲𝘅𝗽𝗲𝗰𝘁𝗲𝗱?

𝗣𝗼𝗽𝘂𝗹𝗮𝗿 𝗼𝗽𝗶𝗻𝗶𝗼𝗻: "𝗝𝘂𝘀𝘁 𝗴𝗲𝗻𝗲𝗿𝗮𝘁𝗲 𝗺𝗼𝗿𝗲 𝘀𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻 𝗱𝗮𝘁𝗮." After working with many 𝗿𝗼𝗯𝗼𝘁 𝗺𝗮𝗻𝗶𝗽𝘂𝗹𝗮𝘁𝗶𝗼𝗻 teams who've fallen into the simulation trap, here's what I've learned: Simulation teaches your robot to be really, really good at simulation. Unlike blind locomotion policies that can get away with sim-to-real transfer because they rely mainly on proprioception and contact forces, 𝘃𝗶𝘀𝗶𝗼𝗻-𝗴𝘂𝗶𝗱𝗲𝗱 𝗺𝗮𝗻𝗶𝗽𝘂𝗹𝗮𝘁𝗶𝗼𝗻 𝗶𝘀 𝗲𝘅𝘁𝗿𝗲𝗺𝗲𝗹𝘆 𝘀𝗲𝗻𝘀𝗶𝘁𝗶𝘃𝗲 𝘁𝗼 𝘃𝗶𝘀𝘂𝗮𝗹 𝗱𝗼𝗺𝗮𝗶𝗻 𝗴𝗮𝗽. The subtle differences accumulate: - Simulated friction vs real surface textures - Perfect lighting vs shadows, reflections, glare - Ideal object geometries vs manufacturing tolerances - Instantaneous sensor readings vs real-world noise and latency - Clean backgrounds vs cluttered, dynamic environments 𝗧𝗵𝗲 𝗰𝗹𝗮𝘀𝘀𝗶𝗰 𝗽𝗿𝗼𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻: Week 1: "Our model works perfectly in sim!" Week 2: "Let's collect some real data to fine-tune." Week 3: "The real data completely contradicts what the sim taught..." Week 4: "Okay, let's collect way more real data." Month 2: "We basically need to retrain from scratch." 𝗧𝗵𝗲 𝗽𝗮𝗶𝗻𝗳𝘂𝗹 𝘁𝗿𝘂𝘁𝗵: There's no shortcut to real-world data collection for vision-based manipulation. Simulation is amazing for debugging, prototyping, safety testing, and of course to supplement your real data. But it's not a substitute for understanding how your robot actually behaves in the actual environment. 𝗪𝗵𝗮𝘁 𝘄𝗼𝗿𝗸𝘀: Use simulation strategically - for exploring edge cases, testing safety boundaries, and rapid iteration. But build your production models on real data from real environments. The teams that succeed treat simulation as a powerful tool, not a magic solution. This is why Neuracore focuses on making real-world data collection so much easier and faster. Because the physics of your actual environment can't be simulated away. 𝗪𝗼𝗿𝗹𝗱 𝗺𝗼𝗱𝗲𝗹𝘀, 𝘆𝗼𝘂 𝘀𝗮𝘆? 𝗪𝗲𝗹𝗹, 𝗽𝗲𝗿𝗵𝗮𝗽𝘀 𝗺𝗼𝗿𝗲 𝗼𝗻 𝘁𝗵𝗮𝘁 𝗶𝗻 𝗮𝗻𝗼𝘁𝗵𝗲𝗿 𝗽𝗼𝘀𝘁! 𝗪𝗵𝗮𝘁'𝘀 𝗯𝗲𝗲𝗻 𝘆𝗼𝘂𝗿 𝗲𝘅𝗽𝗲𝗿𝗶𝗲𝗻𝗰𝗲 𝘄𝗶𝘁𝗵 𝘀𝗶𝗺-𝘁𝗼-𝗿𝗲𝗮𝗹 𝘁𝗿𝗮𝗻𝘀𝗳𝗲𝗿? 𝗛𝗮𝘀 𝗶𝘁 𝘄𝗼𝗿𝗸𝗲𝗱 𝗮𝘀 𝘄𝗲𝗹𝗹 𝗮𝘀 𝗲𝘅𝗽𝗲𝗰𝘁𝗲𝗱?

Stephen James

31,009 views • 1 year ago

NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions paper page: present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions paper page: present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

AK

194,523 views • 3 years ago

Batch Normalization by hand ✍️ ~ 7 steps walkthrough below Batch normalization is common practice for improving training and achieving faster convergence. It sounds simple. But it is often misunderstood. 🤔 Does batch normalization involve trainable parameters, tunable hyper-parameters, or both? 🤔 Is batch normalization applied to inputs, features, weights, biases, or outputs? 🤔 How is batch normalization different from layer normalization? So I drew and calculated one entirely by hand. Goal: normalize a mini-batch of 4 examples to mean 0 and variance 1, then let the network scale it back. = 1. Given = A mini-batch of 4 training examples, each with 3 features. = 2. Linear layer = Let us multiply by the weights and add the biases. Batch norm sits after this, which answers the second question: what gets normalized is features, not inputs, weights or biases. = 3. ReLU = We apply the activation, and -2 becomes 0. Negative values are suppressed before any statistic is taken. = 4. Batch statistics = Let us compute the sum, mean, variance and standard deviation, one row at a time. A row is a feature and the four columns are the four examples, so every number here measures one feature against the rest of the batch. That is the "batch" in batch normalization, and it is exactly what layer normalization does not do. The statistics are rounded to whole numbers, which is what keeps the rest of the page doable in pen. = 5. Shift to mean 0 = We subtract the mean, in green. The four values in each feature now average to zero. = 6. Scale to variance 1 = Let us divide by the standard deviation, in orange. Each feature now has variance one, whatever scale it arrived at. = 7. Scale and shift = We multiply by a linear transformation and pass the result on. The diagonal and the last column are trainable, so having just forced every feature to mean 0 and variance 1, we hand the network the means to undo it. The outputs: Mean of each feature = [2, 1, 2] Std dev of each feature = [1, 1, 2] To the next layer = [2, -2, 2, 0], [-3, 3, 6, -3], [2, 0, 1, 2] The answers: 🤔 Both. The scale and shift are trainable, the statistics are not. Epsilon and the momentum on the running statistics are the hyper-parameters, and one mini-batch by hand needs neither. 🤔 Features, after the linear layer, not inputs, weights or biases. 🤔 Batch norm measures across the batch, one feature at a time. Layer norm measures across the features, one example at a time. 💾 Save this post!

Batch Normalization by hand ✍️ ~ 7 steps walkthrough below Batch normalization is common practice for improving training and achieving faster convergence. It sounds simple. But it is often misunderstood. 🤔 Does batch normalization involve trainable parameters, tunable hyper-parameters, or both? 🤔 Is batch normalization applied to inputs, features, weights, biases, or outputs? 🤔 How is batch normalization different from layer normalization? So I drew and calculated one entirely by hand. Goal: normalize a mini-batch of 4 examples to mean 0 and variance 1, then let the network scale it back. = 1. Given = A mini-batch of 4 training examples, each with 3 features. = 2. Linear layer = Let us multiply by the weights and add the biases. Batch norm sits after this, which answers the second question: what gets normalized is features, not inputs, weights or biases. = 3. ReLU = We apply the activation, and -2 becomes 0. Negative values are suppressed before any statistic is taken. = 4. Batch statistics = Let us compute the sum, mean, variance and standard deviation, one row at a time. A row is a feature and the four columns are the four examples, so every number here measures one feature against the rest of the batch. That is the "batch" in batch normalization, and it is exactly what layer normalization does not do. The statistics are rounded to whole numbers, which is what keeps the rest of the page doable in pen. = 5. Shift to mean 0 = We subtract the mean, in green. The four values in each feature now average to zero. = 6. Scale to variance 1 = Let us divide by the standard deviation, in orange. Each feature now has variance one, whatever scale it arrived at. = 7. Scale and shift = We multiply by a linear transformation and pass the result on. The diagonal and the last column are trainable, so having just forced every feature to mean 0 and variance 1, we hand the network the means to undo it. The outputs: Mean of each feature = [2, 1, 2] Std dev of each feature = [1, 1, 2] To the next layer = [2, -2, 2, 0], [-3, 3, 6, -3], [2, 0, 1, 2] The answers: 🤔 Both. The scale and shift are trainable, the statistics are not. Epsilon and the momentum on the running statistics are the hyper-parameters, and one mini-batch by hand needs neither. 🤔 Features, after the linear layer, not inputs, weights or biases. 🤔 Batch norm measures across the batch, one feature at a time. Layer norm measures across the features, one example at a time. 💾 Save this post!

Tom Yeh

20,848 views • 2 months ago