Beyond the sensitivity analysis, do you see a correlation with downstream evals being impacted by e.g. mlp.down_proj
getting quantized?
Lewis Tunstall PRO
lewtun
AI & ML interests
LLMs, LLMs, LLMs
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reacted to
badaoui's
post with 🚀
12 days ago
Post
3076
Is there a "one-size-fits-all" recipe for quantizing Large Language Models? 🤔
As part of my ongoing work in mixed-precision quantization, I've been exploring this question by measuring layer-by-layer sensitivity. The goal is to see if we can find universal rules for which layers can be quantized aggressively without impacting performance.The results are fascinating and reveal two key insights:
1️⃣ Sensitivity profiles are like architectural "fingerprints." Models from the same family share strikingly similar sensitivity patterns. As you can see in the charts below for the Gemma and SmolLM families, the ranking and relative sensitivity of the layers remain remarkably consistent. This suggests that the underlying architecture is a primary driver of a model's quantization behavior.
2️⃣ A "universal" mixed-precision quantization strategy is challenging. While models within a family are similar, these "fingerprints" change dramatically when comparing different architectures like LLaMA, Qwen, and StableLM. This highlights the difficulty in creating a generalized mixed-precision configuration that works optimally across all model families.
However, there is one near-universal truth we uncovered: the mlp.down_proj layer consistently emerges as one of the most sensitive components across all models studied.
This finding strongly resonates with the work in "The Super Weight in Large Language Models" (by Mengxia Yu et al.). The paper identifies that functionally critical parameters, or "super weights," are concentrated in these down_proj layers. Our empirical results provide clear validation for this theory, showing these layers are highly intolerant to precision loss.
In short, while every architecture has a unique sensitivity profile, a fingerprint shaped not only by its core design but also by its specific training dataset and optimization approach, some components remain universally critical!
What are your thoughts?
As part of my ongoing work in mixed-precision quantization, I've been exploring this question by measuring layer-by-layer sensitivity. The goal is to see if we can find universal rules for which layers can be quantized aggressively without impacting performance.The results are fascinating and reveal two key insights:
1️⃣ Sensitivity profiles are like architectural "fingerprints." Models from the same family share strikingly similar sensitivity patterns. As you can see in the charts below for the Gemma and SmolLM families, the ranking and relative sensitivity of the layers remain remarkably consistent. This suggests that the underlying architecture is a primary driver of a model's quantization behavior.
2️⃣ A "universal" mixed-precision quantization strategy is challenging. While models within a family are similar, these "fingerprints" change dramatically when comparing different architectures like LLaMA, Qwen, and StableLM. This highlights the difficulty in creating a generalized mixed-precision configuration that works optimally across all model families.
However, there is one near-universal truth we uncovered: the mlp.down_proj layer consistently emerges as one of the most sensitive components across all models studied.
This finding strongly resonates with the work in "The Super Weight in Large Language Models" (by Mengxia Yu et al.). The paper identifies that functionally critical parameters, or "super weights," are concentrated in these down_proj layers. Our empirical results provide clear validation for this theory, showing these layers are highly intolerant to precision loss.
In short, while every architecture has a unique sensitivity profile, a fingerprint shaped not only by its core design but also by its specific training dataset and optimization approach, some components remain universally critical!
What are your thoughts?

reacted to
yjernite's
post with ❤️🤗
27 days ago
Post
4047
𝗙𝗶𝗿𝘀𝘁 𝗚𝗣𝗔𝗜 𝗠𝗼𝗱𝗲𝗹 𝘄𝗶𝘁𝗵 𝗘𝗨 𝗗𝗮𝘁𝗮 𝗧𝗿𝗮𝗻𝘀𝗽𝗮𝗿𝗲𝗻𝗰𝘆 𝗧𝗲𝗺𝗽𝗹𝗮𝘁𝗲? 🇪🇺
With the release of the EU data transparency template this week, we finally got to see one of the most meaningful artifacts to come out of the AI Act implementation so far (haven't you heard? AI's all about the data! 📊📚)
The impact of the template will depend on how effectively it establishes a minimum meaningful transparency standard for companies that don't otherwise offer any transparency into their handling of e.g. personal data or (anti?-)competitive practices in commercial licensing - we'll see how those play out as new models are released after August 2nd 👀
In the meantime, I wanted to see how the template works for a fully open-source + commercially viable model, so I filled it out for the SmolLM3 - which my colleagues at Hugging Face earlier this month 🤗 ICYMI, it's fully open-source with 3B parameters and performance matching the best similar-size models (I've switched all my local apps from Qwen3 to it, you should too 💡)
Verdict: congrats to the European Commission AI Office for making it so straightforward! Fully open and transparent models remain a cornerstone of informed regulation and governance, but the different organizational needs of their developers aren't always properly accounted for in new regulation. In this case, it took me all of two hours to fill out and publish the template (including reading the guidelines) - so kudos for making it feasible for smaller and distributed organizations 🙌 Definitely a step forward for transparency 🔍
To learn more have a look at:
- The SmolLM3 model: HuggingFaceTB/SmolLM3-3B
- Its filled out Public Summary of Training Content: hfmlsoc/smollm3-eu-data-transparency
- And if you're interested, some previous remarks on regulatory minimum meaningful standards for data disclosure: https://huggingface.co/blog/yjernite/naiac-data-transparency
With the release of the EU data transparency template this week, we finally got to see one of the most meaningful artifacts to come out of the AI Act implementation so far (haven't you heard? AI's all about the data! 📊📚)
The impact of the template will depend on how effectively it establishes a minimum meaningful transparency standard for companies that don't otherwise offer any transparency into their handling of e.g. personal data or (anti?-)competitive practices in commercial licensing - we'll see how those play out as new models are released after August 2nd 👀
In the meantime, I wanted to see how the template works for a fully open-source + commercially viable model, so I filled it out for the SmolLM3 - which my colleagues at Hugging Face earlier this month 🤗 ICYMI, it's fully open-source with 3B parameters and performance matching the best similar-size models (I've switched all my local apps from Qwen3 to it, you should too 💡)
Verdict: congrats to the European Commission AI Office for making it so straightforward! Fully open and transparent models remain a cornerstone of informed regulation and governance, but the different organizational needs of their developers aren't always properly accounted for in new regulation. In this case, it took me all of two hours to fill out and publish the template (including reading the guidelines) - so kudos for making it feasible for smaller and distributed organizations 🙌 Definitely a step forward for transparency 🔍
To learn more have a look at:
- The SmolLM3 model: HuggingFaceTB/SmolLM3-3B
- Its filled out Public Summary of Training Content: hfmlsoc/smollm3-eu-data-transparency
- And if you're interested, some previous remarks on regulatory minimum meaningful standards for data disclosure: https://huggingface.co/blog/yjernite/naiac-data-transparency

reacted to
andito's
post with 🔥
about 1 month ago
Post
2778
Many VLMs claim to process hours of video. But can they follow the story?🤔
Today, we introduce TimeScope: The benchmark that separates true temporal understanding from marketing hype. Let's see how much VLMs really understand!⏳
We test three skills that matter for real-world use:
🔎 Localized Retrieval: Find a specific action.
🧩 Information Synthesis: Piece together scattered clues.
🏃 Fine-Grained Perception: Analyze detailed motion (e.g., count how many times a person swings an axe).
The results are in, and they're revealing. Only Gemini 2.5 pro handles 1-hour-long videos.
Performance drops sharply with duration, proving that long video understanding is still challenging. We've found the breaking points—now the community can start fixing them.📈
Want to learn more? TimeScope is 100% open-source. Benchmark your model and help us build the next generation of video AI.
📖 Blog:
https://huggingface.co/blog/timescope-video-lmm-benchmark
👩💻 Leaderboard & Demo: Apollo-LMMs/TimeScope
📊 Dataset: Apollo-LMMs/TimeScope
⚙️ Eval Code: https://github.com/EvolvingLMMs-Lab/lmms-eval
Today, we introduce TimeScope: The benchmark that separates true temporal understanding from marketing hype. Let's see how much VLMs really understand!⏳
We test three skills that matter for real-world use:
🔎 Localized Retrieval: Find a specific action.
🧩 Information Synthesis: Piece together scattered clues.
🏃 Fine-Grained Perception: Analyze detailed motion (e.g., count how many times a person swings an axe).
The results are in, and they're revealing. Only Gemini 2.5 pro handles 1-hour-long videos.
Performance drops sharply with duration, proving that long video understanding is still challenging. We've found the breaking points—now the community can start fixing them.📈
Want to learn more? TimeScope is 100% open-source. Benchmark your model and help us build the next generation of video AI.
📖 Blog:
https://huggingface.co/blog/timescope-video-lmm-benchmark
👩💻 Leaderboard & Demo: Apollo-LMMs/TimeScope
📊 Dataset: Apollo-LMMs/TimeScope
⚙️ Eval Code: https://github.com/EvolvingLMMs-Lab/lmms-eval

posted
an
update
6 months ago
Post
3321
Introducing OlympicCoder: a series of open reasoning models that can solve olympiad-level programming problems 🧑💻
- 7B open-r1/OlympicCoder-7B
- 32B open-r1/OlympicCoder-32B
We find that OlympicCoder models outperform Claude 3.7 Sonnet, as well as others over 100x larger 💪
Together with the models, we are releasing:
📊CodeForces-CoTs: new dataset of code problems from the most popular competitive coding platform, with R1 traces in C++ and Python open-r1/codeforces-cots
🏆 IOI'2024: a new benchmark of VERY hard programming problems where even frontier models struggle to match human performance open-r1/ioi
For links to the models and datasets, check out our latest progress report from Open R1: https://huggingface.co/blog/open-r1/update-3
- 7B open-r1/OlympicCoder-7B
- 32B open-r1/OlympicCoder-32B
We find that OlympicCoder models outperform Claude 3.7 Sonnet, as well as others over 100x larger 💪
Together with the models, we are releasing:
📊CodeForces-CoTs: new dataset of code problems from the most popular competitive coding platform, with R1 traces in C++ and Python open-r1/codeforces-cots
🏆 IOI'2024: a new benchmark of VERY hard programming problems where even frontier models struggle to match human performance open-r1/ioi
For links to the models and datasets, check out our latest progress report from Open R1: https://huggingface.co/blog/open-r1/update-3

posted
an
update
7 months ago
Post
5420
Introducing OpenR1-Math-220k!
open-r1/OpenR1-Math-220k
The community has been busy distilling DeepSeek-R1 from inference providers, but we decided to have a go at doing it ourselves from scratch 💪
What’s new compared to existing reasoning datasets?
♾ Based on AI-MO/NuminaMath-1.5: we focus on math reasoning traces and generate answers for problems in NuminaMath 1.5, an improved version of the popular NuminaMath-CoT dataset.
🐳 800k R1 reasoning traces: We generate two answers for 400k problems using DeepSeek R1. The filtered dataset contains 220k problems with correct reasoning traces.
📀 512 H100s running locally: Instead of relying on an API, we leverage vLLM and SGLang to run generations locally on our science cluster, generating 180k reasoning traces per day.
⏳ Automated filtering: We apply Math Verify to only retain problems with at least one correct answer. We also leverage Llama3.3-70B-Instruct as a judge to retrieve more correct examples (e.g for cases with malformed answers that can’t be verified with a rules-based parser)
📊 We match the performance of DeepSeek-Distill-Qwen-7B by finetuning Qwen-7B-Math-Instruct on our dataset.
🔎 Read our blog post for all the nitty gritty details: https://huggingface.co/blog/open-r1/update-2
open-r1/OpenR1-Math-220k
The community has been busy distilling DeepSeek-R1 from inference providers, but we decided to have a go at doing it ourselves from scratch 💪
What’s new compared to existing reasoning datasets?
♾ Based on AI-MO/NuminaMath-1.5: we focus on math reasoning traces and generate answers for problems in NuminaMath 1.5, an improved version of the popular NuminaMath-CoT dataset.
🐳 800k R1 reasoning traces: We generate two answers for 400k problems using DeepSeek R1. The filtered dataset contains 220k problems with correct reasoning traces.
📀 512 H100s running locally: Instead of relying on an API, we leverage vLLM and SGLang to run generations locally on our science cluster, generating 180k reasoning traces per day.
⏳ Automated filtering: We apply Math Verify to only retain problems with at least one correct answer. We also leverage Llama3.3-70B-Instruct as a judge to retrieve more correct examples (e.g for cases with malformed answers that can’t be verified with a rules-based parser)
📊 We match the performance of DeepSeek-Distill-Qwen-7B by finetuning Qwen-7B-Math-Instruct on our dataset.
🔎 Read our blog post for all the nitty gritty details: https://huggingface.co/blog/open-r1/update-2

reacted to
fdaudens's
post with 🔥❤️
7 months ago
Post
9543
Yes, DeepSeek R1's release is impressive. But the real story is what happened in just 7 days after:
- Original release: 8 models, 540K downloads. Just the beginning...
- The community turned those open-weight models into +550 NEW models on Hugging Face. Total downloads? 2.5M—nearly 5X the originals.
The reason? DeepSeek models are open-weight, letting anyone build on top of them. Interesting to note that the community focused on quantized versions for better efficiency & accessibility. They want models that use less memory, run faster, and are more energy-efficient.
When you empower builders, innovation explodes. For everyone. 🚀
The most popular community model? @bartowski 's DeepSeek-R1-Distill-Qwen-32B-GGUF version — 1M downloads alone.
- Original release: 8 models, 540K downloads. Just the beginning...
- The community turned those open-weight models into +550 NEW models on Hugging Face. Total downloads? 2.5M—nearly 5X the originals.
The reason? DeepSeek models are open-weight, letting anyone build on top of them. Interesting to note that the community focused on quantized versions for better efficiency & accessibility. They want models that use less memory, run faster, and are more energy-efficient.
When you empower builders, innovation explodes. For everyone. 🚀
The most popular community model? @bartowski 's DeepSeek-R1-Distill-Qwen-32B-GGUF version — 1M downloads alone.

posted
an
update
7 months ago
Post
10455
We are reproducing the full DeepSeek R1 data and training pipeline so everybody can use their recipe. Instead of doing it in secret we can do it together in the open!
🧪 Step 1: replicate the R1-Distill models by distilling a high-quality reasoning corpus from DeepSeek-R1.
🧠 Step 2: replicate the pure RL pipeline that DeepSeek used to create R1-Zero. This will involve curating new, large-scale datasets for math, reasoning, and code.
🔥 Step 3: show we can go from base model -> SFT -> RL via multi-stage training.
Follow along: https://github.com/huggingface/open-r1
🧪 Step 1: replicate the R1-Distill models by distilling a high-quality reasoning corpus from DeepSeek-R1.
🧠 Step 2: replicate the pure RL pipeline that DeepSeek used to create R1-Zero. This will involve curating new, large-scale datasets for math, reasoning, and code.
🔥 Step 3: show we can go from base model -> SFT -> RL via multi-stage training.
Follow along: https://github.com/huggingface/open-r1

reacted to
prithivMLmods's
post with 🚀
8 months ago
Post
6035
Reasoning SmolLM2 🚀
🎯Fine-tuning SmolLM2 on a lightweight synthetic reasoning dataset for reasoning-specific tasks. Future updates will focus on lightweight, blazing-fast reasoning models. Until then, check out the blog for fine-tuning details.
🔥Blog : https://huggingface.co/blog/prithivMLmods/smollm2-ft
🔼 Models :
+ SmolLM2-CoT-360M : prithivMLmods/SmolLM2-CoT-360M
+ Reasoning-SmolLM2-135M : prithivMLmods/Reasoning-SmolLM2-135M
+ SmolLM2-CoT-360M-GGUF : prithivMLmods/SmolLM2-CoT-360M-GGUF
🤠 Other Details :
+ Demo : prithivMLmods/SmolLM2-CoT-360M
+ Fine-tune nB : prithivMLmods/SmolLM2-CoT-360M
🎯Fine-tuning SmolLM2 on a lightweight synthetic reasoning dataset for reasoning-specific tasks. Future updates will focus on lightweight, blazing-fast reasoning models. Until then, check out the blog for fine-tuning details.
🔥Blog : https://huggingface.co/blog/prithivMLmods/smollm2-ft
🔼 Models :
+ SmolLM2-CoT-360M : prithivMLmods/SmolLM2-CoT-360M
+ Reasoning-SmolLM2-135M : prithivMLmods/Reasoning-SmolLM2-135M
+ SmolLM2-CoT-360M-GGUF : prithivMLmods/SmolLM2-CoT-360M-GGUF
🤠 Other Details :
+ Demo : prithivMLmods/SmolLM2-CoT-360M
+ Fine-tune nB : prithivMLmods/SmolLM2-CoT-360M

posted
an
update
8 months ago
Post
3996
I was initially pretty sceptical about Meta's Coconut paper [1] because the largest perf gains were reported on toy linguistic problems. However, these results on machine translation are pretty impressive!
https://x.com/casper_hansen_/status/1875872309996855343
Together with the recent PRIME method [2] for scaling RL, reasoning for open models is looking pretty exciting for 2025!
[1] Training Large Language Models to Reason in a Continuous Latent Space (2412.06769)
[2] https://huggingface.co/blog/ganqu/prime
https://x.com/casper_hansen_/status/1875872309996855343
Together with the recent PRIME method [2] for scaling RL, reasoning for open models is looking pretty exciting for 2025!
[1] Training Large Language Models to Reason in a Continuous Latent Space (2412.06769)
[2] https://huggingface.co/blog/ganqu/prime

posted
an
update
8 months ago
Post
2373
This paper (
HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs (2412.18925)) has a really interesting recipe for inducing o1-like behaviour in Llama models:
* Iteratively sample CoTs from the model, using a mix of different search strategies. This gives you something like Stream of Search via prompting.
* Verify correctness of each CoT using GPT-4o (needed because exact match doesn't work well in medicine where there are lots of aliases)
* Use GPT-4o to reformat the concatenated CoTs into a single stream that includes smooth transitions like "hmm, wait" etc that one sees in o1
* Use the resulting data for SFT & RL
* Use sparse rewards from GPT-4o to guide RL training. They find RL gives an average ~3 point boost across medical benchmarks and SFT on this data already gives a strong improvement.
Applying this strategy to other domains could be quite promising, provided the training data can be formulated with verifiable problems!
* Iteratively sample CoTs from the model, using a mix of different search strategies. This gives you something like Stream of Search via prompting.
* Verify correctness of each CoT using GPT-4o (needed because exact match doesn't work well in medicine where there are lots of aliases)
* Use GPT-4o to reformat the concatenated CoTs into a single stream that includes smooth transitions like "hmm, wait" etc that one sees in o1
* Use the resulting data for SFT & RL
* Use sparse rewards from GPT-4o to guide RL training. They find RL gives an average ~3 point boost across medical benchmarks and SFT on this data already gives a strong improvement.
Applying this strategy to other domains could be quite promising, provided the training data can be formulated with verifiable problems!

posted
an
update
8 months ago
Post
7045
We outperform Llama 70B with Llama 3B on hard math by scaling test-time compute 🔥
How? By combining step-wise reward models with tree search algorithms :)
We show that smol models can match or exceed the performance of their much larger siblings when given enough "time to think"
We're open sourcing the full recipe and sharing a detailed blog post.
In our blog post we cover:
📈 Compute-optimal scaling: How we implemented DeepMind's recipe to boost the mathematical capabilities of open models at test-time.
🎄 Diverse Verifier Tree Search (DVTS): An unpublished extension we developed to the verifier-guided tree search technique. This simple yet effective method improves diversity and delivers better performance, particularly at large test-time compute budgets.
🧭 Search and Learn: A lightweight toolkit for implementing search strategies with LLMs and built for speed with vLLM
Here's the links:
- Blog post: HuggingFaceH4/blogpost-scaling-test-time-compute
- Code: https://github.com/huggingface/search-and-learn
Enjoy!
How? By combining step-wise reward models with tree search algorithms :)
We show that smol models can match or exceed the performance of their much larger siblings when given enough "time to think"
We're open sourcing the full recipe and sharing a detailed blog post.
In our blog post we cover:
📈 Compute-optimal scaling: How we implemented DeepMind's recipe to boost the mathematical capabilities of open models at test-time.
🎄 Diverse Verifier Tree Search (DVTS): An unpublished extension we developed to the verifier-guided tree search technique. This simple yet effective method improves diversity and delivers better performance, particularly at large test-time compute budgets.
🧭 Search and Learn: A lightweight toolkit for implementing search strategies with LLMs and built for speed with vLLM
Here's the links:
- Blog post: HuggingFaceH4/blogpost-scaling-test-time-compute
- Code: https://github.com/huggingface/search-and-learn
Enjoy!

reacted to
julien-c's
post with 🤗❤️🔥
9 months ago
Post
11004
After some heated discussion 🔥, we clarify our intent re. storage limits on the Hub
TL;DR:
- public storage is free, and (unless blatant abuse) unlimited. We do ask that you consider upgrading to PRO and/or Enterprise Hub if possible
- private storage is paid above a significant free tier (1TB if you have a paid account, 100GB otherwise)
docs: https://huggingface.co/docs/hub/storage-limits
We optimize our infrastructure continuously to scale our storage for the coming years of growth in Machine learning, to the benefit of the community 🔥
cc: @reach-vb @pierric @victor and the HF team
TL;DR:
- public storage is free, and (unless blatant abuse) unlimited. We do ask that you consider upgrading to PRO and/or Enterprise Hub if possible
- private storage is paid above a significant free tier (1TB if you have a paid account, 100GB otherwise)
docs: https://huggingface.co/docs/hub/storage-limits
We optimize our infrastructure continuously to scale our storage for the coming years of growth in Machine learning, to the benefit of the community 🔥
cc: @reach-vb @pierric @victor and the HF team

replied to
dvilasuero's
post
about 1 year ago
Welcome to the team @dvilasuero and Argilla! It’s been really nice collaborating with you on various projects around LLM alignment and I’m excited to see what we’ll build next together!

reacted to
dvilasuero's
post with 🤝❤️
about 1 year ago
Post
8344
Today is a huge day in Argilla’s history. We couldn’t be more excited to share this with the community: we’re joining Hugging Face!
We’re embracing a larger mission, becoming part of a brilliant and kind team and a shared vision about the future of AI.
Over the past year, we’ve been collaborating with Hugging Face on countless projects: launching partner of Docker Spaces, empowering the community to clean Alpaca translations into Spanish and other languages, launching argilla/notus-7b-v1 building on Zephyr’s learnings, the Data is Better Together initiative with hundreds of community contributors, or releasing argilla/OpenHermesPreferences, one of the largest open preference tuning datasets
After more than 2,000 Slack messages and over 60 people collaborating for over a year, it already felt like we were part of the same team, pushing in the same direction. After a week of the smoothest transition you can imagine, we’re now the same team.
To those of you who’ve been following us, this won’t be a huge surprise, but it will be a big deal in the coming months. This acquisition means we’ll double down on empowering the community to build and collaborate on high quality datasets, we’ll bring full support for multimodal datasets, and we’ll be in a better place to collaborate with the Open Source AI community. For enterprises, this means that the Enterprise Hub will unlock highly requested features like single sign-on and integration with Inference Endpoints.
As a founder, I am proud of the Argilla team. We're now part of something bigger and a larger team but with the same values, culture, and goals. Grateful to have shared this journey with my beloved co-founders Paco and Amélie.
Finally, huge thanks to the Chief Llama Officer @osanseviero for sparking this and being such a great partner during the acquisition process.
Would love to answer any questions you have so feel free to add them below!
We’re embracing a larger mission, becoming part of a brilliant and kind team and a shared vision about the future of AI.
Over the past year, we’ve been collaborating with Hugging Face on countless projects: launching partner of Docker Spaces, empowering the community to clean Alpaca translations into Spanish and other languages, launching argilla/notus-7b-v1 building on Zephyr’s learnings, the Data is Better Together initiative with hundreds of community contributors, or releasing argilla/OpenHermesPreferences, one of the largest open preference tuning datasets
After more than 2,000 Slack messages and over 60 people collaborating for over a year, it already felt like we were part of the same team, pushing in the same direction. After a week of the smoothest transition you can imagine, we’re now the same team.
To those of you who’ve been following us, this won’t be a huge surprise, but it will be a big deal in the coming months. This acquisition means we’ll double down on empowering the community to build and collaborate on high quality datasets, we’ll bring full support for multimodal datasets, and we’ll be in a better place to collaborate with the Open Source AI community. For enterprises, this means that the Enterprise Hub will unlock highly requested features like single sign-on and integration with Inference Endpoints.
As a founder, I am proud of the Argilla team. We're now part of something bigger and a larger team but with the same values, culture, and goals. Grateful to have shared this journey with my beloved co-founders Paco and Amélie.
Finally, huge thanks to the Chief Llama Officer @osanseviero for sparking this and being such a great partner during the acquisition process.
Would love to answer any questions you have so feel free to add them below!