Parameter efficient fine tuning (PEFT) is a versatile and extensible approach for adapting a Large Language Model (LLM) for newer tasks. One of the most prominent PEFT approaches, Low Rank Adaptation (LoRA), primarily focuses on adjusting the attention weight matrices within individual decoder blocks of a Generative Pre trained Transformer (GPT2). In contrast, we introduce Solo Connection a novel method that adapts the representation at the decoder-block level rather than modifying individual weight matrices. Not only does Solo Connection outperform LoRA on E2E natural language generation benchmarks, but it also reduces the number of trainable parameters by 59% relative to LoRA and by more than 99% compared to full fine-tuning of GPT2, an early version of Large Language Models (LLMs). Solo Connection is also motivated by homotopy theory: we introduce a trainable linear transformation that gradually interpolates between a zero vector and the task-specific representation, enabling smooth and stable adaptation over time. While skip connections in the original 12 layer GPT2 are typically confined to individual decoder blocks, subsequent GPT2 variants scale up to 48 layers, and even larger language models can include 128 or more decoder blocks. These expanded architectures underscore the need to revisit how skip connections are employed during fine-tuning. This paper focuses on long skip connections that link outputs of different decoder blocks, potentially enhancing the model's ability to adapt to new tasks while leveraging pre-trained knowledge.