SAEs Are Good for Steering -- If You Select the Right Features
On the map: Mechanistic interpretability → SAE features and their applications
Abstract (arXiv)
Sparse Autoencoders (SAEs) have been proposed as an unsupervised approach to learn a decomposition of a model's latent space. This enables useful applications such as steering - influencing the output of a model towards a desired concept - without requiring labeled data. Current methods identify SAE features to steer by analyzing the input tokens that activate them. However, recent work has highlighted that activations alone do not fully describe the effect of a feature on the model's output. In this work, we draw a distinction between two types of features: input features, which mainly capture patterns in the model's input, and output features, which have a human-understandable effect on the model's output. We propose input and output scores to characterize and locate these types of features, and show that high values for both scores rarely co-occur in the same features. These findings have practical implications: after filtering out features with low output scores, we obtain 2-3x improvements when steering with SAEs, making them competitive with supervised methods.
Key facts. Cited by 78 papers in the map (data through 14 Oct 2026). Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability. Builds on 36 of its 66 references that are in the map. First posted on arXiv 26 May 2025.
Builds on
36 of 66 references.
Closest ancestors · 4
Same direction, newest first
- 2025AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders28 Jan
- 2024Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders27 Oct
- 2024Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders19 Jul
- 2023Sparse Autoencoders Find Highly Interpretable Features in Language Models15 Sep
Other references · 32
- 2024The Llama 3 Herd of Modelscited by 14,715
- 2021Training Verifiers to Solve Math Word Problemscited by 10,109
- 2022Locating and Editing Factual Associations in GPTcited by 2,691
- 2024Gemma 2: Improving Open Language Models at a Practical Sizecited by 1,998
- 2023Pythia: A Suite for Analyzing Large Language Models Across Training and Scalingcited by 1,786
- 2020Transformer Feed-Forward Layers Are Key-Value Memoriescited by 1,336
- 2023Representation Engineering: A Top-Down Approach to AI Transparencycited by 1,336
- 2023Inference-Time Intervention: Eliciting Truthful Answers from a Language Modelcited by 1,302
- 2023Steering Llama 2 via Contrastive Activation Additioncited by 1,085
- 2019BERT Rediscovers the Classical NLP Pipelinecited by 1,059
- 2023Steering Language Models With Activation Engineeringcited by 922
- 2023Dissecting Recall of Factual Associations in Auto-Regressive Language Modelscited by 528
20 more
- 2024Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Modelscited by 435
- 2015Autoencoding beyond pixels using a learned similarity metriccited by 407
- 2024Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2cited by 394
- 2019Linguistic Knowledge and Transferability of Contextual Representationscited by 383
- 2023In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steeringcited by 245
- 2024ReFT: Representation Finetuning for Language Modelscited by 197
- 2017What do Neural Machine Translation Models Learn about Morphology?cited by 166
- 2024The Remarkable Robustness of LLMs: Stages of Inference?cited by 146
- 2019On Identifiability in Transformerscited by 116
- 2018Identifying and Controlling Important Neurons in Neural Machine Translationcited by 111
- 2024Universal Neurons in GPT2 Language Modelscited by 102
- 2025Enhancing Automated Interpretability with Output-Centric Feature Descriptionscited by 41
- 2024Extending Activation Steering to Broad Skills and Multiple Behaviourscited by 40
- 2025FairSteer: Inference Time Debiasing for LLMs with Dynamic Activation Steeringcited by 40
- 2023ReFACT: Updating Text-to-Image Models by Editing the Text Encodercited by 32
- 2024Backward Lens: Projecting Language Model Gradients into the Vocabulary Spacecited by 32
- 2024Style-Specific Neurons for Steering LLMs in Text Style Transfercited by 24
- 2024Constructing Benchmarks and Interventions for Combating Hallucinations in LLMscited by 19
- 2018Language Modeling Teaches You More Syntax than Translation Does: Lessons Learned Through Auxiliary Task Analysiscited by 17
- 2024Using Shapley interactions to understand how models use structurecited by 1
Built on by
Citing papers per year: 2025: 18; 2026: 60.
78 papers.
Sort:
By area:
- 2025Persona Features Control Emergent Misalignmentcited by 86
- 2026Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Modelscited by 27
- 2025The Rogue Scalpel: Activation Steering Compromises LLM Safetycited by 21
- 2026Qwen-Scope: Turning Sparse Features into Development Tools for Large Language Modelscited by 21
- 2025Position: Use Sparse Autoencoders to Discover Unknownscited by 19
- 2025Temporal Sparse Autoencoders: Leveraging the Sequential Nature of Language for Interpretabilitycited by 18
- 2025CorrSteer: Generation-Time LLM Steering via Correlated Sparse Autoencoder Featurescited by 12
- 2025CRISP: Persistent Concept Unlearning via Sparse Autoencoderscited by 11
- 2026The Curse of Multiple Mediators: Hidden Interaction Effects in Activation Patchingcited by 11
- 2025Enhancing LLM Steering through Sparse Autoencoder-Based Vector Refinementcited by 10
- 2025Does higher interpretability imply better utility? A Pairwise Analysis on Sparse Autoencoderscited by 10
- 2025SAEdit: Token-level control for continuous image editing via Sparse AutoEncodercited by 9
38 more
- 2026From Weights to Activations: Is Steering the Next Frontier of Adaptation?cited by 8
- 2025From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?cited by 7
- 2026DLM-Scope: Mechanistic Interpretability of Diffusion Language Models via Sparse Autoencoderscited by 7
- 2025Interpretable and Steerable Concept Bottleneck Sparse Autoencoderscited by 6
- 2026Post-Hoc Reasoning in Chain of Thought: Decoding and Steering Pre-Committed Answerscited by 6
- 2026Steerable but Not Decodable: Function Vectors Operate Beyond the Logit Lenscited by 6
- 2026Steering at the Source: Style Modulation Heads for Robust Persona Controlcited by 5
- 2025Evaluating Sparse Autoencoders for Monosemantic Representationcited by 4
- 2025AlignSAE: Concept-Aligned Sparse Autoencoderscited by 4
- 2026The Confidence Manifold: Geometric Structure of Correctness Representations in Language Modelscited by 4
- 2026Interpreting and Steering State-Space Models via Activation Subspace Bottleneckscited by 3
- 2026Steering Without Breaking: Mechanistically Informed Interventions for Discrete Diffusion Language Modelscited by 3
- 2026Steering LLMs? Actually, Sparse Autoencoders can outperform simple baselinescited by 3
- 2025CE-Bench: Towards a Reliable Contrastive Evaluation Benchmark of Interpretability of Sparse Autoencoderscited by 2
- 2025Can SAEs reveal and mitigate racial biases of LLMs in healthcare?cited by 2
- 2026Geometric Routing Enables Causal Expert Control in Mixture of Expertscited by 2
- 2026Mechanist: AI as a Scientific Instrument for Discovering the Mechanisms of Intelligencecited by 2
- 2025Calibrating Lightweight Sparse Autoencoder Feature Steeringcited by 1
- 2025Measuring Mechanistic Independence: Can Bias Be Removed Without Erasing Demographics?cited by 1
- 2026DSPA: Dynamic SAE Steering for Data-Efficient Preference Alignmentcited by 1
- 2026Auditing Asset-Specific Preferences in Financial Large Language Models: Evidence from Bitcoin Representations and Portfolio Allocationcited by 1
- 2026SAE Interventions are Unreliable: Post-Intervention Recovery of Suppressed Behaviorcited by 1
- 2026Do Sparse Autoencoders Learn Meaningful Concept Hierarchies?cited by 1
- 2026Are Single-Token Sparse Autoencoder Features Causally Necessary? Layer-Depth and SAE-Family Effectscited by 1
- 2026Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effectscited by 1
- 2026CircuitSteer: Geometrically Aligned Multi-Layer Steering via Sparse Autoencoder Circuitscited by 1
- 2026REINS: Refusal-Enhanced Inhibitory Steering with Sparse Autoencoder Featurescited by 1
- 2025When Models Refuse: Political Steerability and Feature Richness as Measures of Ideological Depthcited by 0
- 2026Mechanistic Indicators of Steering Effectiveness in Large Language Modelscited by 0
- 2026Sparse Visual Thought Circuits in Vision-Language Modelscited by 0
- 2026A Universal Vibe? Finding and Controlling Language-Agnostic Informal Register with SAEscited by 0
- 2026Multimodal QUD: Inquisitive Questions from Scientific Figurescited by 0
- 2026MoRFI: Monotonic Sparse Autoencoder Feature Identificationcited by 0
- 2026Steering grids for sparse-autoencoder features: when a top-context label names an activation regime rather than a causal axiscited by 0
- 2026Domain Restriction via Multi SAE Layer Transitionscited by 0
- 2026Transcoders Trace Visual Grounding and Hallucinations in Vision-Language Modelscited by 0
- 2026Steered Generation via Gradient-Based Optimization on Sparse Query Featurescited by 0
- 2026Universal Boosts, Specific Suppressors: Sparse Autoencoder Steering of Medical Vision-Language Modelscited by 0
50 most cited of 78 All 78 (JSON)
- 2026What Do Sparse Autoencoder Feature Discovery Scores Identify? From Activations to Interventions11 Oct 2026
- 2026ScopeSAE: Model-Scope Feature Discovery with Interpretable Layer Selection4 Oct 2026
- 2026Generative modeling of intrinsically disordered protein regions by reinforcing sparse autoencoder features1 Oct 2026
- 2026D-Scope: Decomposing and Steering Diffusion Transformers with Sparse Autoencoders30 Sep 2026
- 2026MetaSteer: Context-Conditioned, nonlinear Steering via Attention-Projection Adaptation30 Sep 2026
- 2026Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable28 Sep 2026
- 2026From Input to Output: A Flexible Agent for Dual-End Interpretation of Sparse Autoencoder Features28 Sep 2026
- 2026Look Before You Steer: Geometry Predicts SAE Feature Steerability19 Sep 2026
- 2026MAxBench: A Multinomial Concept Recovery Benchmark11 Sep 2026
- 2026SAEScientist-Bench: Can AI Agents Conduct Autonomous SAE Interpretability Research?8 Sep 2026
- 2026Tracing Stereotypes from Representation to Output in Multilingual LLMs8 Sep 2026
- 2026LLM Forensics: Where Do Backdoors Hide? Localizing and Controlling Trigger Mechanisms with Sparse Autoencoders7 Sep 2026
38 more
- 2026Encoded Early, Used Late: Where Transformers Begin to Act on an Inferred Partner's Expertise7 Sep 2026
- 2026SharedSAE: One Feature Dictionary Across Language Models3 Sep 2026
- 2026REINS: Refusal-Enhanced Inhibitory Steering with Sparse Autoencoder Features28 Aug 2026
- 2026Mechanist: AI as a Scientific Instrument for Discovering the Mechanisms of Intelligence12 Aug 2026
- 2026Thinking vs. NoThinking: Towards Interpreting Reasoning Mechanisms of Large Language Models via Sparse Autoencoders8 Aug 2026
- 2026CircuitSteer: Geometrically Aligned Multi-Layer Steering via Sparse Autoencoder Circuits6 Aug 2026
- 2026Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effects27 Jul 2026
- 2026Scaling Interpretable Transformers with Parity Bottleneck Layers22 Jul 2026
- 2026Are Single-Token Sparse Autoencoder Features Causally Necessary? Layer-Depth and SAE-Family Effects22 Jul 2026
- 2026Persistent Sparse Autoencoders: Learning Feature-Specific Timescales in Language Model Representations19 Jul 2026
- 2026Data-Efficient Adaptation of LLMs via Attention Head Reweighting15 Jul 2026
- 2026Brand-as-Memory: Vision-Language Models Encode Causal, Mechanistically Localizable Credibility Priors for News Sources3 Jul 2026
- 2026Harnessing the Latent Space: From Steering Vectors to Model Calibrators for Control and Trust30 Jun 2026
- 2026The Curse of Multiple Mediators: Hidden Interaction Effects in Activation Patching25 Jun 2026
- 2026Discovering Millions of Interpretable Features with Sparse Autoencoders25 Jun 2026
- 2026Do Sparse Autoencoders Learn Meaningful Concept Hierarchies?22 Jun 2026
- 2026SAE Interventions are Unreliable: Post-Intervention Recovery of Suppressed Behavior16 Jun 2026
- 2026When Confidence Lacks Concepts: Interpretable OOD Detection via Representation Perturbations15 Jun 2026
- 2026In Defense of Information Leakage in Concept-based Models9 Jun 2026
- 2026Pre-Intervention Prediction of Sparse Autoencoder Steering Side Effects6 Jun 2026
- 2026From Profiles to Steering Vectors: Global Sparse Priors and Local Semantic Calibration for Personalized Text Generation1 Jun 2026
- 2026Auditing Asset-Specific Preferences in Financial Large Language Models: Evidence from Bitcoin Representations and Portfolio Allocation1 Jun 2026
- 2026How Optimality Structures Sparse Dictionaries: Theory for Interpreting SAE Representations1 Jun 2026
- 2026Query Lens: Interpreting Sparse Key-Value Features with Indirect Effects30 May 2026
- 2026Steering LLMs? Actually, Sparse Autoencoders can outperform simple baselines29 May 2026
- 2026Sense Representations Are Inducible Interfaces27 May 2026
- 2026Universal Boosts, Specific Suppressors: Sparse Autoencoder Steering of Medical Vision-Language Models24 May 2026
- 2026Steered Generation via Gradient-Based Optimization on Sparse Query Features21 May 2026
- 2026Transcoders Trace Visual Grounding and Hallucinations in Vision-Language Models21 May 2026
- 2026Domain Restriction via Multi SAE Layer Transitions12 May 2026
- 2026Qwen-Scope: Turning Sparse Features into Development Tools for Large Language Models12 May 2026
- 2026Steering Without Breaking: Mechanistically Informed Interventions for Discrete Diffusion Language Models8 May 2026
- 2026Steering grids for sparse-autoencoder features: when a top-context label names an activation regime rather than a causal axis4 May 2026
- 2026MoRFI: Monotonic Sparse Autoencoder Feature Identification29 Apr 2026
- 2026Multimodal QUD: Inquisitive Questions from Scientific Figures26 Apr 2026
- 2026Geometric Routing Enables Causal Expert Control in Mixture of Experts15 Apr 2026
- 2026From Weights to Activations: Is Steering the Next Frontier of Adaptation?15 Apr 2026
- 2026Steerable but Not Decodable: Function Vectors Operate Beyond the Logit Lens3 Apr 2026
50 newest of 78 All 78 (JSON)
- 2026Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Modelscited by 27
- 2026Qwen-Scope: Turning Sparse Features into Development Tools for Large Language Modelscited by 21
- 2025Position: Use Sparse Autoencoders to Discover Unknownscited by 19
- 2025Temporal Sparse Autoencoders: Leveraging the Sequential Nature of Language for Interpretabilitycited by 18
- 2025CorrSteer: Generation-Time LLM Steering via Correlated Sparse Autoencoder Featurescited by 12
- 2026The Curse of Multiple Mediators: Hidden Interaction Effects in Activation Patchingcited by 11
- 2025Enhancing LLM Steering through Sparse Autoencoder-Based Vector Refinementcited by 10
- 2025Does higher interpretability imply better utility? A Pairwise Analysis on Sparse Autoencoderscited by 10
- 2025Interpretable and Steerable Concept Bottleneck Sparse Autoencoderscited by 6
- 2026Steerable but Not Decodable: Function Vectors Operate Beyond the Logit Lenscited by 6
- 2026Steering at the Source: Style Modulation Heads for Robust Persona Controlcited by 5
- 2025Evaluating Sparse Autoencoders for Monosemantic Representationcited by 4
12 most cited of 44 All 44 (JSON)
- 2026What Do Sparse Autoencoder Feature Discovery Scores Identify? From Activations to Interventions11 Oct 2026
- 2026ScopeSAE: Model-Scope Feature Discovery with Interpretable Layer Selection4 Oct 2026
- 2026Generative modeling of intrinsically disordered protein regions by reinforcing sparse autoencoder features1 Oct 2026
- 2026From Input to Output: A Flexible Agent for Dual-End Interpretation of Sparse Autoencoder Features28 Sep 2026
- 2026Look Before You Steer: Geometry Predicts SAE Feature Steerability19 Sep 2026
- 2026SAEScientist-Bench: Can AI Agents Conduct Autonomous SAE Interpretability Research?8 Sep 2026
- 2026Tracing Stereotypes from Representation to Output in Multilingual LLMs8 Sep 2026
- 2026SharedSAE: One Feature Dictionary Across Language Models3 Sep 2026
- 2026CircuitSteer: Geometrically Aligned Multi-Layer Steering via Sparse Autoencoder Circuits6 Aug 2026
- 2026Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effects27 Jul 2026
- 2026Scaling Interpretable Transformers with Parity Bottleneck Layers22 Jul 2026
- 2026Are Single-Token Sparse Autoencoder Features Causally Necessary? Layer-Depth and SAE-Family Effects22 Jul 2026
12 newest of 44 All 44 (JSON)
- 2025The Rogue Scalpel: Activation Steering Compromises LLM Safetycited by 21
- 2025CRISP: Persistent Concept Unlearning via Sparse Autoencoderscited by 11
- 2026REINS: Refusal-Enhanced Inhibitory Steering with Sparse Autoencoder Featurescited by 1
- 2025When Models Refuse: Political Steerability and Feature Richness as Measures of Ideological Depthcited by 0
- 2026LLM Forensics: Where Do Backdoors Hide? Localizing and Controlling Trigger Mechanisms with Sparse Autoencoderscited by 0
- 2026LLM Forensics: Where Do Backdoors Hide? Localizing and Controlling Trigger Mechanisms with Sparse Autoencoders7 Sep 2026
- 2026REINS: Refusal-Enhanced Inhibitory Steering with Sparse Autoencoder Features28 Aug 2026
- 2025The Rogue Scalpel: Activation Steering Compromises LLM Safety26 Sep 2025
- 2025When Models Refuse: Political Steerability and Feature Richness as Measures of Ideological Depth29 Aug 2025
- 2025CRISP: Persistent Concept Unlearning via Sparse Autoencoders19 Aug 2025
- 2025SAEdit: Token-level control for continuous image editing via Sparse AutoEncodercited by 9
- 2026DLM-Scope: Mechanistic Interpretability of Diffusion Language Models via Sparse Autoencoderscited by 7
- 2026Steering Without Breaking: Mechanistically Informed Interventions for Discrete Diffusion Language Modelscited by 3
- 2026D-Scope: Decomposing and Steering Diffusion Transformers with Sparse Autoencoderscited by 0
- 2026D-Scope: Decomposing and Steering Diffusion Transformers with Sparse Autoencoders30 Sep 2026
- 2026Steering Without Breaking: Mechanistically Informed Interventions for Discrete Diffusion Language Models8 May 2026
- 2026DLM-Scope: Mechanistic Interpretability of Diffusion Language Models via Sparse Autoencoders5 Feb 2026
- 2025SAEdit: Token-level control for continuous image editing via Sparse AutoEncoder6 Oct 2025
- 2026Post-Hoc Reasoning in Chain of Thought: Decoding and Steering Pre-Committed Answerscited by 6
- 2026Transcoders Trace Visual Grounding and Hallucinations in Vision-Language Modelscited by 0
- 2026Thinking vs. NoThinking: Towards Interpreting Reasoning Mechanisms of Large Language Models via Sparse Autoencoderscited by 0
- 2026Thinking vs. NoThinking: Towards Interpreting Reasoning Mechanisms of Large Language Models via Sparse Autoencoders8 Aug 2026
- 2026Transcoders Trace Visual Grounding and Hallucinations in Vision-Language Models21 May 2026
- 2026Post-Hoc Reasoning in Chain of Thought: Decoding and Steering Pre-Committed Answers2 Mar 2026
- 2026Sparse Visual Thought Circuits in Vision-Language Modelscited by 0
- 2026Universal Boosts, Specific Suppressors: Sparse Autoencoder Steering of Medical Vision-Language Modelscited by 0
- 2026Brand-as-Memory: Vision-Language Models Encode Causal, Mechanistically Localizable Credibility Priors for News Sourcescited by 0
- 2026Brand-as-Memory: Vision-Language Models Encode Causal, Mechanistically Localizable Credibility Priors for News Sources3 Jul 2026
- 2026Universal Boosts, Specific Suppressors: Sparse Autoencoder Steering of Medical Vision-Language Models24 May 2026
- 2026Sparse Visual Thought Circuits in Vision-Language Models26 Mar 2026
- 2025Persona Features Control Emergent Misalignmentcited by 86
- 2026From Weights to Activations: Is Steering the Next Frontier of Adaptation?cited by 8
- 2025From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?cited by 7
- 2026Mechanist: AI as a Scientific Instrument for Discovering the Mechanisms of Intelligencecited by 2
- 2025Measuring Mechanistic Independence: Can Bias Be Removed Without Erasing Demographics?cited by 1
- 2026Auditing Asset-Specific Preferences in Financial Large Language Models: Evidence from Bitcoin Representations and Portfolio Allocationcited by 1
- 2026Mechanistic Indicators of Steering Effectiveness in Large Language Modelscited by 0
- 2026Multimodal QUD: Inquisitive Questions from Scientific Figurescited by 0
- 2026Sense Representations Are Inducible Interfacescited by 0
- 2026In Defense of Information Leakage in Concept-based Modelscited by 0
- 2026When Confidence Lacks Concepts: Interpretable OOD Detection via Representation Perturbationscited by 0
- 2026Data-Efficient Adaptation of LLMs via Attention Head Reweightingcited by 0
12 most cited of 16 All 16 (JSON)
- 2026MetaSteer: Context-Conditioned, nonlinear Steering via Attention-Projection Adaptation30 Sep 2026
- 2026Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable28 Sep 2026
- 2026MAxBench: A Multinomial Concept Recovery Benchmark11 Sep 2026
- 2026Encoded Early, Used Late: Where Transformers Begin to Act on an Inferred Partner's Expertise7 Sep 2026
- 2026Mechanist: AI as a Scientific Instrument for Discovering the Mechanisms of Intelligence12 Aug 2026
- 2026Data-Efficient Adaptation of LLMs via Attention Head Reweighting15 Jul 2026
- 2026When Confidence Lacks Concepts: Interpretable OOD Detection via Representation Perturbations15 Jun 2026
- 2026In Defense of Information Leakage in Concept-based Models9 Jun 2026
- 2026Auditing Asset-Specific Preferences in Financial Large Language Models: Evidence from Bitcoin Representations and Portfolio Allocation1 Jun 2026
- 2026Sense Representations Are Inducible Interfaces27 May 2026
- 2026Multimodal QUD: Inquisitive Questions from Scientific Figures26 Apr 2026
- 2026From Weights to Activations: Is Steering the Next Frontier of Adaptation?15 Apr 2026
12 newest of 16 All 16 (JSON)
Similar, not cited
Close in wording, no citation either way
- 2024Can sparse autoencoders be used to decompose and interpret steering vectors?
- 2024Improving Steering Vectors by Targeting Sparse Autoencoder Features
- 2026Enhancing SAE-based Steering via Neighbor Integrated Feature Selection
- 2026Sanity Checks for Sparse Autoencoders: Do SAEs Beat Random Baselines?
- 2025Sparse Autoencoders Trained on the Same Data Learn Different Features
- 2024Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning
- 2024Evaluating Sparse Autoencoders on Targeted Concept Erasure Tasks
- 2025SAE-SSV: Supervised Steering in Sparse Representation Spaces for Reliable Control of Language Models