# A Mathematical Abstraction for Balancing the Trade-off Between Creativity and Reality in Large Language Models

arXiv: https://arxiv.org/abs/2306.02295 · HTML: https://mlsanity.com/paper/2306.02295/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 89 references that are in the map.
- First posted on arXiv 4 Jun 2023.

## Builds on (most cited first, 30 of 67)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss](https://mlsanity.com/paper/2002.04486/) (2020)
- [Analyzing the Structure of Attention in a Transformer Language Model](https://mlsanity.com/paper/1906.04284/) (2019)
- [Inductive Biases and Variable Creation in Self-Attention Mechanisms](https://mlsanity.com/paper/2110.10090/) (2021)
- [Scatterbrain: Unifying Sparse and Low-rank Attention Approximation](https://mlsanity.com/paper/2110.15343/) (2021)
- [Toward Understanding the Feature Learning Process of Self-supervised Contrastive Learning](https://mlsanity.com/paper/2105.15134/) (2021)
- [Unveiling Transformers with LEGO: a synthetic reasoning task](https://mlsanity.com/paper/2206.04301/) (2022)
- [Self-Attention Networks Can Process Bounded Hierarchical Languages](https://mlsanity.com/paper/2105.11115/) (2021)
- [Statistically Meaningful Approximation: a Case Study on Approximating Turing Machines with Transformers](https://mlsanity.com/paper/2107.13163/) (2021)
- [Fast Attention Requires Bounded Entries](https://mlsanity.com/paper/2302.13214/) (2023)
- [Solving Linear Programs in the Current Matrix Multiplication Time](https://mlsanity.com/paper/1810.07896/) (2018)
- [CAN: Creative Adversarial Networks, Generating "Art" by Learning About Styles and Deviating from Style Norms](https://mlsanity.com/paper/1706.07068/) (2017)

## Built on by (most cited first, 29 of 29)

- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [In-Context Learning for Attention Scheme: from Single Softmax Regression to Multiple Softmax Regression via a Tensor Trick](https://mlsanity.com/paper/2307.02419/) (2023)
- [Conv-Basis: A New Paradigm for Efficient Attention Inference and Gradient Computation in Transformers](https://mlsanity.com/paper/2405.05219/) (2024)
- [InfoPrompt: Information-Theoretic Soft Prompt Tuning for Natural Language Understanding](https://mlsanity.com/paper/2306.04933/) (2023)
- [A Fast Optimization View: Reformulating Single Layer Attention in LLM Based on Tensor and SVM Trick, and Solving It in Matrix Multiplication Time](https://mlsanity.com/paper/2309.07418/) (2023)
- [GradientCoin: A Peer-to-Peer Decentralized Large Language Models](https://mlsanity.com/paper/2308.10502/) (2023)
- [The Computational Limits of State-Space Models and Mamba via the Lens of Circuit Complexity](https://mlsanity.com/paper/2412.06148/) (2024)
- [Solving Attention Kernel Regression Problem via Pre-conditioner](https://mlsanity.com/paper/2308.14304/) (2023)
- [Beyond Classical Attention: Quantum Attention for Scalable Computation](https://mlsanity.com/paper/2307.08045/) (2023)
- [Zero-th Order Algorithm for Softmax Attention Optimization](https://mlsanity.com/paper/2307.08352/) (2023)
- [A Unified Scheme of ResNet and Softmax](https://mlsanity.com/paper/2309.13482/) (2023)
- [Unmasking Transformers: A Theoretical Approach to Data Recovery via Attention Weights](https://mlsanity.com/paper/2310.12462/) (2023)
- [Efficient SGD Neural Network Training via Sublinear Activated Neuron Identification](https://mlsanity.com/paper/2307.06565/) (2023)
- [Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows](https://mlsanity.com/paper/2503.09069/) (2025)
- [Efficient Alternating Minimization with Applications to Weighted Low Rank Approximation](https://mlsanity.com/paper/2306.04169/) (2023)
- [Is Solving Graph Neural Tangent Kernel Equivalent to Training Graph Neural Network?](https://mlsanity.com/paper/2309.07452/) (2023)
- [The Expressibility of Polynomial based Attention Scheme](https://mlsanity.com/paper/2310.20051/) (2023)
- [Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining](https://mlsanity.com/paper/2502.05790/) (2025)
- [A Theoretical Insight into Attack and Defense of Gradient Leakage in Transformer](https://mlsanity.com/paper/2311.13624/) (2023)
- [One Pass Streaming Algorithm for Super Long Token Attention Approximation in Sublinear Space](https://mlsanity.com/paper/2311.14652/) (2023)
- [Has the Creativity of Large-Language Models peaked? An analysis of inter- and intra-LLM variability](https://mlsanity.com/paper/2504.12320/) (2025)
- [Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers](https://mlsanity.com/paper/2501.10688/) (2025)
- [Scaling Law Phenomena Across Regression Paradigms: Multiple and Kernel Approaches](https://mlsanity.com/paper/2503.01314/) (2025)
- [Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding](https://mlsanity.com/paper/2503.11108/) (2025)
- [Theoretical Foundation of Flow-Based Time Series Generation: Provable Approximation, Generalization, and Efficiency](https://mlsanity.com/paper/2503.14076/) (2025)
- [From Hallucination to Reliability: Generative Modeling and the Structure of Scientific Inference](https://mlsanity.com/paper/2504.08526/) (2025)
- [Power and Limitations of Aggregation in Compound AI Systems](https://mlsanity.com/paper/2602.21556/) (2026)
- [Online Adaptive Mahalanobis Distance Estimation](https://mlsanity.com/paper/2309.01030/) (2023)
- [Fast Heavy Inner Product Identification Between Weights and Inputs in Neural Network Training](https://mlsanity.com/paper/2311.11429/) (2023)

## Abstract (arXiv)

Large Language Models have become popular for their remarkable capabilities in human-oriented tasks and traditional natural language processing tasks. Its efficient functioning is attributed to the attention mechanism in the Transformer architecture, enabling it to concentrate on particular aspects of the input. LLMs are increasingly being used in domains such as generating prose, poetry or art, which require the model to be creative (e.g. Adobe firefly). LLMs possess advanced language generation abilities that enable them to generate distinctive and captivating content. This utilization of LLMs in generating narratives shows their flexibility and potential for use in domains that extend beyond conventional natural language processing duties. In different contexts, we may expect the LLM to generate factually correct answers, that match reality; e.g., question-answering systems or online assistants. In such situations, being correct is critical to LLMs being trusted in practice. The Bing Chatbot provides its users with the flexibility to select one of the three output modes: creative, balanced, and precise. Each mode emphasizes creativity and factual accuracy differently. In this work, we provide a mathematical abstraction to describe creativity and reality based on certain losses. A model trained on these losses balances the trade-off between the creativity and reality of the model.