Why ResNet is Explicit Euler, and What That Tells Us About Deep Learning
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NoesisLab advances machine learning research in deep contemplation and reflective reasoning to enable more profound and self-aware artificial intelligence.
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zixi-51M: Not a stock voice. A voice. 🐾
NoesisLab/zixi-51m
Everyone is shipping 500B-parameter models. I shipped 51 million. With one voice. On purpose. 🎤
What: open-weights Chinese TTS. VITS2 lineage. 51.43M params. Runs on your laptop CPU — no cloud, no API key, no GPU bill, no meter running.💸
The voice: not a stock voice, not a 5,000-speaker average. One real human's voice — mine. Timbre, rhythm, breath included. The sample on themodel card is one take, default parameters, recorded by absolutely no one. 🎧
What's NOT inside:
• ❌ BERT (zero. the text encoder vibes on phones + tones alone)
• ❌ language routing (Chinese-exclusive: 77 symbols, 6 tones, one job)
• ❌ my training data (the corpus is my own writing and stays mine — open weights, closed corpus, that's the deal 🤝)
The trick: embedding transplant. Phone, tone and speaker rows inherited from the MeloTTS-Chinese base by symbol name — no random init. Themodel woke up already knowing Chinese. 🧠
Built solo, corpus to packaging, by a writer who is also a violinist. Prosody is my day job. 🎻
Use it, fork it, fine-tune your own voice. Just don't put words in a real person's mouth. 🙏
🔗 Weights: NoesisLab/zixi-51m
💻 Code: https://github.com/lizixi-0x2F/zixi-51M
NoesisLab/zixi-51m
Everyone is shipping 500B-parameter models. I shipped 51 million. With one voice. On purpose. 🎤
What: open-weights Chinese TTS. VITS2 lineage. 51.43M params. Runs on your laptop CPU — no cloud, no API key, no GPU bill, no meter running.💸
The voice: not a stock voice, not a 5,000-speaker average. One real human's voice — mine. Timbre, rhythm, breath included. The sample on themodel card is one take, default parameters, recorded by absolutely no one. 🎧
What's NOT inside:
• ❌ BERT (zero. the text encoder vibes on phones + tones alone)
• ❌ language routing (Chinese-exclusive: 77 symbols, 6 tones, one job)
• ❌ my training data (the corpus is my own writing and stays mine — open weights, closed corpus, that's the deal 🤝)
The trick: embedding transplant. Phone, tone and speaker rows inherited from the MeloTTS-Chinese base by symbol name — no random init. Themodel woke up already knowing Chinese. 🧠
Built solo, corpus to packaging, by a writer who is also a violinist. Prosody is my day job. 🎻
Use it, fork it, fine-tune your own voice. Just don't put words in a real person's mouth. 🙏
🔗 Weights: NoesisLab/zixi-51m
💻 Code: https://github.com/lizixi-0x2F/zixi-51M
OzTianlu
updated a
model 7 days ago
OzTianlu
published a
model 7 days ago
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6,348
ResNet is Explicit Euler. GPT is Implicit Euler. What Else is Hiding in Plain Sight?
Read online: https://datawhalechina.github.io/learning-terrain/
I wrote an open-source monograph on learning dynamics — The Terrain of Learning. Bilingual (Chinese/English), 4 volumes, 12 chapters, 30+ print-grade figures. Completely free (CC BY-NC-SA 4.0).
The core argument: gradient descent is not optimization. It's terrain motion. The loss function is a landscape. The gradient is the direction of slope. The optimizer is how you choose each step. Once you see it this way, everything clicks:
ResNet = explicit Euler integration on a vector field. The residual branch is the vector field. Each layer takes one Euler step.
GPT autoregression = implicit-state Euler iteration. Stable where explicit Euler explodes. That's why transformers handle long-range dependencies.
DEQ = the Banach fixed-point theorem in production. The forward pass is root-finding. There are no layers to backprop through.
KL divergence = a Bregman divergence on the entropy landscape. Your belief space is curved, not flat.
Chain-of-thought reasoning = hidden states flowing along a reasoning field toward an attractor basin. Correct answers have wide basins. The number of reasoning steps is determined by the terrain, not by the problem.
Diffusion models = systems flowing downhill along a score vector field, from noise to structure, from high energy to low energy.
The book traces one idea across 337 years — from F=ma (Newton, 1687) to H=T+V (Hamilton, 1833) to loss landscape + gradient field (2020s). Hamilton replaced a catalog of forces with one geometric object. This book does the same for deep learning.
GitHub: https://github.com/datawhalechina/learning-terrain
Discussion: https://github.com/datawhalechina/learning-terrain/discussions/2
Convergence is not hope. Convergence is geometry. You see.
Read online: https://datawhalechina.github.io/learning-terrain/
I wrote an open-source monograph on learning dynamics — The Terrain of Learning. Bilingual (Chinese/English), 4 volumes, 12 chapters, 30+ print-grade figures. Completely free (CC BY-NC-SA 4.0).
The core argument: gradient descent is not optimization. It's terrain motion. The loss function is a landscape. The gradient is the direction of slope. The optimizer is how you choose each step. Once you see it this way, everything clicks:
ResNet = explicit Euler integration on a vector field. The residual branch is the vector field. Each layer takes one Euler step.
GPT autoregression = implicit-state Euler iteration. Stable where explicit Euler explodes. That's why transformers handle long-range dependencies.
DEQ = the Banach fixed-point theorem in production. The forward pass is root-finding. There are no layers to backprop through.
KL divergence = a Bregman divergence on the entropy landscape. Your belief space is curved, not flat.
Chain-of-thought reasoning = hidden states flowing along a reasoning field toward an attractor basin. Correct answers have wide basins. The number of reasoning steps is determined by the terrain, not by the problem.
Diffusion models = systems flowing downhill along a score vector field, from noise to structure, from high energy to low energy.
The book traces one idea across 337 years — from F=ma (Newton, 1687) to H=T+V (Hamilton, 1833) to loss landscape + gradient field (2020s). Hamilton replaced a catalog of forces with one geometric object. This book does the same for deep learning.
GitHub: https://github.com/datawhalechina/learning-terrain
Discussion: https://github.com/datawhalechina/learning-terrain/discussions/2
Convergence is not hope. Convergence is geometry. You see.
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Article
Why ResNet is Explicit Euler, and What That Tells Us About Deep Learning
NoesisLab
• • 1 OzTianlu
authored a
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OzTianlu
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OzTianlu
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OzTianlu
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paper to Daily Papers 5 months ago
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https://github.com/lizixi-0x2F/March
I just released March, an open-source high-performance KV cache sharing library for LLM inference that uses Trie-based prefix deduplication.
When you run LLM services, you often see thousands of requests sharing the same system prompt and conversation history. But traditional KV cache systems store each sequence separately — duplicating the exact same data over and over again. Pure waste.
March uses a Trie structure to automatically detect and reuse identical token prefixes. Instead of storing [system_prompt + history] 1000 times, it's stored once. Everyone shares it.
- 80-97% memory reduction in prefix-heavy workloads (tested on SmolLM2-135M with 500 multi-turn conversations)
- Zero-copy queries — returns direct pointers into the memory pool, no expensive memcpy on the hot path
- Predictable memory usage — fixed-size page pool with O(L) complexity
- Trade-off: slightly slower than dict O(1) lookup, but the memory savings are worth it in production
I just released March, an open-source high-performance KV cache sharing library for LLM inference that uses Trie-based prefix deduplication.
When you run LLM services, you often see thousands of requests sharing the same system prompt and conversation history. But traditional KV cache systems store each sequence separately — duplicating the exact same data over and over again. Pure waste.
March uses a Trie structure to automatically detect and reuse identical token prefixes. Instead of storing [system_prompt + history] 1000 times, it's stored once. Everyone shares it.
- 80-97% memory reduction in prefix-heavy workloads (tested on SmolLM2-135M with 500 multi-turn conversations)
- Zero-copy queries — returns direct pointers into the memory pool, no expensive memcpy on the hot path
- Predictable memory usage — fixed-size page pool with O(L) complexity
- Trade-off: slightly slower than dict O(1) lookup, but the memory savings are worth it in production
- 1 reply
OzTianlu
updated 2
models 7 months ago
Article
Arcade-3B: SLM Optimization via Orthogonal Decoupling of Latent State Spaces
NoesisLab
• • 1 Article
Arcade-3B: 基于隐藏层状态空间正交解耦的 SLM 优化
NoesisLab
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Arcade-3B — SmolReasoner
NoesisLab/Arcade-3B
Arcade-3B is a 3B instruction-following and reasoning model built on SmolLM3-3B. It is the public release from the ARCADE project at NoesisLab, which investigates the State–Constraint Orthogonality Hypothesis: standard Transformer hidden states conflate factual content and reasoning structure in the same subspace, and explicitly decoupling them improves generalization.
NoesisLab/Arcade-3B
Arcade-3B is a 3B instruction-following and reasoning model built on SmolLM3-3B. It is the public release from the ARCADE project at NoesisLab, which investigates the State–Constraint Orthogonality Hypothesis: standard Transformer hidden states conflate factual content and reasoning structure in the same subspace, and explicitly decoupling them improves generalization.
- 5 replies
OzTianlu
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model 7 months ago
OzTianlu
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We deleted the Embedding Layer -- INTRO Our Collins-Embedding-3M
NoesisLab/Collins-Embedding-3M
Most "small" models are just giant vocab tables in a trench coat. Collins-3M changes that. By using 2-Universal Hashing and Chernoff-bound noise suppression, we’ve collapsed the embedding space into a fixed O(1) hash-map.
* STSB: 0.7114 (Beating many 100M+ models)
* Size: 3M (Edge-ready, IoT-ready)
* Tech: Randomized Sign-Hashing + RoPE positional injection.
Built by NoesisLab
NoesisLab/Collins-Embedding-3M
Most "small" models are just giant vocab tables in a trench coat. Collins-3M changes that. By using 2-Universal Hashing and Chernoff-bound noise suppression, we’ve collapsed the embedding space into a fixed O(1) hash-map.
* STSB: 0.7114 (Beating many 100M+ models)
* Size: 3M (Edge-ready, IoT-ready)
* Tech: Randomized Sign-Hashing + RoPE positional injection.
Built by NoesisLab
OzTianlu
published a
model 8 months ago
OzTianlu
updated a
Space 8 months ago