Large language models (LLMs) have shown exceptional versatility in natural language processing, prompting recent efforts to extend their multimodal capabilities to speech processing through the development of audio large language models (Audio LLMs). While Audio LLMs excel in tasks such as speech recognition and synthesis, it remains unclear how they perform when faced with the auditory cognitive challenges posed by real-world environments, such as audio comprehension and listening recall, particularly in the presence of background noise or overlapping speech. Unlike text-based LLMs, which have access to vast amounts of text data for pre-training, retraining Audio LLMs with diverse auditory cognitive scenes is difficult due to the limited datasets that simulate real-world auditory cognitive scenarios and the challenge of acquiring auditory cognitive labels for training. While test-time compute (TTC) methods have been shown to enhance the capabilities of text-based LLMs during inference, a key challenge lies in designing these TTC methods to improve the auditory capabilities of Audio LLMs. This study aims to address these two research gaps by: i) exploring the auditory cognitive capabilities of Audio LLMs, and ii) enhancing their capabilities using TTC approaches. We have investigated five different Audio LLMs for auditory cognition using a \textit{self-collected} database and have proposed five TTC approaches to enhance auditory cognitive capabilities during inference. Our findings reveal that Audio LLMs performance decreases in more challenging auditory cognitive tasks. The proposed TTC approaches significantly enhance cognitive auditory capabilities, advancing the development of more adaptable and resilient Audio LLMs for practical applications such as assistive listening devices, voice-based AI assistants, and communication technologies.

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