This thesis encompasses five diverse research topics: 1) uncovering the role of indirect wing steering muscles in fruit fly flight stabilization; 2) exploring the interplay between vocal and physical displays in budgerigar social communication; 3) investigating the habenula's role in integrating aversive feedback for motor learning and performance; 4) elucidating the effects of mechanical stress on cartilage tissue via unsupervised learning approach; and, finally, 5) developing a physics-inspired approach to big data visualization through the intensive symmetrized Kullback-Leibler(isKL) embedding technique. The first research investigates the role of indirect steering muscles in maintaining flight stability in fruit flies. These tiny insects rely on rapid and precise adjustments, controlled by highly specialized wing steering muscles, to sustain stable flight. While significant progress has been made over the past decade in understanding how direct wing steering muscles (those attached directly to the sclerite) influence wing motion, the impact of indirect steering muscles (which actuate wing motion by tensioning the thorax) remains largely unexplored. Using the latest connectomic data, we identified the tergopleural muscle as a key candidate for analysis, given its shared synaptic inputs with the basalar muscles, which are essential for pitch stabilization reflexes. Leveraging optogenetic tools and free-flight mechanical experiments, we discovered that fruit flies utilize two distinct pitch stabilization strategies, one of which involves modulating the wing pitch angle through the tergopleural muscle. By employing a torsional spring model, we further identified that the tergopleural muscle regulates one critical parameter: the rest angle, which governs the wing’s pitch response. Humans continuously expand their vocal repertoires throughout their lives, often enhancing their speech with body language. However, conditions like Parkinson’s disease and stroke can significantly impair this multimodal social communication. Despite its importance, there is currently no animal model to investigate the coordination of learned vocalizations and gestures. The second topic establishes a groundwork for understanding how motor systems integrate learned vocalizations with communicative gestures. Budgerigars, known for their dynamic social behaviors and extensive vocal repertoires, provide an ideal model due to their ability to learn socially, engage in complex group dynamics, and exhibit both vocal and gestural communication. This study focused on quantifying their intricate warble songs and analyzing the coupling of these songs with head-bobbing gestures—a visually distinct behavior embedded within their vocalizations. Our findings reveal that socially bonded budgerigars not only share similar songs but also exhibit highly coordinated alignment between song syllables and head-bobbing gestures. They synchronize specific vocal elements with head-bobbing on a millisecond timescale, using silent gaps between syllables to precisely time their gestures. Additionally, acoustically isolated budgerigars, when paired, converged on the same song and pattern of song–head bob coordination, emphasizing the crucial role of social feedback-dependent learning in refining and maintaining multimodal communication. The third topic shifts focus to investigating the role of the lateral habenula (LHb) in birdsong learning and production. LHb is a conserved limbic system structure known in mammals for mediating aversive feedback between the ventral pallidum (VP) and ventral tegmental area (VTA) dopamine neurons. Using viral tract tracing and functional circuit mapping, we discovered that the songbird LHb connects the VP and an auditory cortical region to dopamine neurons that encode song errors. Consistent with findings in mammals, VP stimulation activated LHb activity, while LHb stimulation inhibited dopamine neuron firing. To explore the pathway's role in learning, we lesioned the LHb in juvenile zebra finches and analyzed their songs in adulthood. Birds with LHb lesions exhibited abnormal vocalizations as adults, including prolonged high-pitched notes and species-atypical trills. These findings reveal a VP-LHb-VTA pathway in songbirds with functional parallels to mammalian systems. This study expands our understanding of vocal learning circuits and highlights the essential role of limbic pathways in integrating aversive feedback for motor learning and performance. The fourth topic explores the application of variational autoencoders (VAEs) in analyzing cartilage tissue subjected to mechanical impact. Understanding how cell behaviors are coordinated over time is essential for revealing tissue-scale responses to physiological and injury-related stimuli. Such insights are key to defining normal tissue function and identifying injury-induced events that may lead to chronic disease. However, analyzing these extensive datasets presents significant challenges due to their complexity and size, making it difficult to discern overarching trends and behaviors. To address this, we applied an unsupervised learning approach using VAEs to analyze chondrocyte behavior in cartilage tissue after impact-induced injury. This method uncovered distinct clusters of cell behaviors and identified specific peracute calcium signaling time series associated with long-term cellular outcomes. These findings offer novel insights into the spatial distribution of cell phenotypes and the mechanisms underlying tissue responses to mechanical stress. Finally, for the last topic, we proposed a novel dimensionality reduction technique for visualizing probabilistic data. Specifically, we demonstrated that for a broad class of multiparameter models represented as exponential families, the isKL embedding—based on the symmetrized Kullback-Leibler divergence—yields an explicit and analytically tractable embedding in a Minkowski space with a dimensionality equal to twice the number of model parameters. This approach not only provides exceptional dimensionality reduction but also reveals hidden exponential family structures underlying experiments or simulations when the isKL embedding exhibits a cutoff after $N+N$ dimensions.