questions. Can « run » algorithms? Model and understand the phenomenon of “in context learning”. Questions: Is a transformer trained only to do “next token prediction” capable of reasoning? Mathematical implications: Practical: Next token prediction Pretraining Finetuning Human alignement Supervised learning Huge ressources → Easy (LORA, etc.) →
(104K citations) Adam (169K citations) Make networks very deep → Adapted to “next token prediction” → Suitable for transformer optimization → ResNet-34
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Positional encoding + <latexit 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Points cloud <latexit 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x1 <latexit 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x2 Demain, dès l'aube, à l'heure où blanchit la campagne, Je partirai. Vois- tu, je sais que tu m’attends. J'irai par la forêt, j'irai par la montagne. Je ne puis demeurer loin de toi plus longtemps. Je marcherai les yeux fixés sur mes pensées,… <latexit sha1_base64="Fgw+vWgPriclgLxpVoHDEicBDLw=">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</latexit> {xi }i Zoom: transformers and the attention mechanism
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Positional encoding + <latexit 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Points cloud <latexit 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x1 <latexit 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x2 Demain, dès l'aube, à l'heure où blanchit la campagne, Je partirai. Vois- tu, je sais que tu m’attends. J'irai par la forêt, j'irai par la montagne. Je ne puis demeurer loin de toi plus longtemps. Je marcherai les yeux fixés sur mes pensées,… <latexit 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{xi }i <latexit sha1_base64="TxVb5GdPgjAMGN+p3Ec+OBLQ8cg=">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</latexit> ˜ xi = xi + P j eKxi,Qxj V xj P j eKxi,Qxj <latexit 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xi <latexit 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Residual <latexit 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Replace convolution by attention: Zoom: transformers and the attention mechanism
(flash attention, triton…) Numerics The future ? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... [Mensch et al 2023]
(flash attention, triton…) Numerics The future ? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... Connect diffusion (continuous) and LLM (discrete) models Theory Understand the “in context learning” process. [Mensch et al 2023]
(flash attention, triton…) Numerics The future ? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... Connect diffusion (continuous) and LLM (discrete) models Theory Understand the “in context learning” process. [Mensch et al 2023] Applications AI for science: beyond next token prediction Towards multimodal (video, 3D, etc.). scGPT
(flash attention, triton…) Numerics The future ? Industry Business model (few qualified engineers + fine tuning)? Open weights vs. open source (training data?) Interface with daily life? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... Connect diffusion (continuous) and LLM (discrete) models Theory Understand the “in context learning” process. [Mensch et al 2023] Applications AI for science: beyond next token prediction Towards multimodal (video, 3D, etc.). scGPT