Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Space
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Abstract (arXiv)
Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model's learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model's learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.
Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). Builds on 87 of its 120 references that are in the map. First posted on arXiv 27 Jun 2024.
Builds on
87 of 120 references.
References · 87
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
- 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
- 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
- 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
- 2022Classifier-Free Diffusion Guidancecited by 5,847
- 2016Layer Normalizationcited by 5,669
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- 2014Deep Learning Face Attributes in the Wildcited by 3,693
- 2024Gemini 1.5: Unlocking multimodal understanding across millions of tokens of contextcited by 3,224
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- 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
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- 2023The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasetscited by 712
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- 2018Disentangling by Factorisingcited by 616
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- 2020Underspecification Presents Challenges for Credibility in Modern Machine Learningcited by 496
- 2023VideoPoet: A Large Language Model for Zero-Shot Video Generationcited by 492
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- 2023Finding Neurons in a Haystack: Case Studies with Sparse Probingcited by 334
- 2022Diffusion Models already have a Semantic Latent Spacecited by 328
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- 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
- 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
- 2016Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICAcited by 273
- 2017Variational Inference of Disentangled Latent Concepts from Unlabeled Observationscited by 241
- 2022Towards Understanding Grokking: An Effective Theory of Representation Learningcited by 230
- 2021Towards Causal Representation Learningcited by 209
- 2022Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limitcited by 187
- 2024Probing the 3D Awareness of Visual Foundation Modelscited by 177
- 2023Linguistic Binding in Diffusion Models: Enhancing Attribute Correspondence through Attention Map Alignmentcited by 171
- 2023Video Language Planningcited by 162
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- 2021Illiterate DALL-E Learns to Composecited by 147
- 2022Omnigrok: Grokking Beyond Algorithmic Datacited by 146
- 2021Can Machines Learn Morality? The Delphi Experimentcited by 141
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