Imaginary Intelligence: Balancing Diversity & Feasibility in Large Language Models

Current large language models (LLMs) force users to choose between diversity (creative, varied responses) and feasibility (practical, accurate outputs). ChatGPT at default temperature achieves 4/10 diversity with 9/10 feasibility (13/20 total), while high- temperature variants improve diversity to 6/10 but drop feasibility to 7/10 (still 13/20). This paper presents Imaginary Intelligence (IMI), a fine-tuned Large Language Model addressing this fundamental trade-off through dual-objective optimization. Using QLoRA (4-bit quantization + LoRA adapters) on Llama-3.2-1B as the base model, IMI implements joint optimization: diversity rewards (semantic entropy maximization) combined with feasibility constraints (accuracy-based loss weighting). Employing Gradient Episodic Memory (GEM) and Selective Knowledge LoRA (SC-LoRA), IMI preserves 85%+ of pre- trained model capabilities while achieving balanced 8/10 diversity and 8/10 feasibility scores (16/20 total—a 23% improvement over baselines). The system generates 3-5 practical solution ensembles per query, optimized for creative problem-solving domains: academic ideation, product design, R&D, and consulting. The MVP, developed on Google Colab with 1-5k curated dual-scored training examples, is production-ready with a Gradio web interface deployable on Hugging Face Spaces. Evaluation demonstrates superior performance across diversity metrics (semantic distance < 0.7, n-gram overlap < 30%, entropy > 4.5 bits) and feasibility metrics (BLEU-Score ≥ 0.85, hallucination rate < 5%, implementation viability ≥ 8/10).