The rise of machine learning in material modeling has led to a diverse class of neural-network-based constitutive models (NCMs). Within this landscape, constitutive artificial neural networks (CANNs) occupy an interesting middle ground between highly parameterized black-box NCMs (e.g., ICNNs, ICKANs) and classical hand-crafted constitutive forms: they retain high expressivity while producing compact strain-energy functions composed of a small number of mechanically meaningful terms that are straightforward to deploy in finite-element workflows. To date, CANNs have been predominantly trained in a supervised manner from local stress-strain pairs collected through conventional homogeneous testing (uniaxial, biaxial, shear). Such testing protocols only sample a limited set of loading paths in the six-dimensional stress-strain space, and may therefore poorly generalize to off-path multiaxial deformations. Even when multiple homogeneous loading paths are combined, supervised CANN discovery can remain initialization-sensitive, yielding different constitutive forms with comparable training errors. For biological tissues, acquiring \textit{sufficiently rich} supervised datasets is additionally challenging. Either a single specimen must be transferred between different testing rigs, incurring excessive handling and potential damage or history effects. Alternatively, testing data must be pooled across different specimens, implicitly ignoring inter-sample variability which is expected from intrinsic microstructural variability. To address this gap, we pursue unsupervised CANN discovery from full-field experiments, where intentionally heterogeneous strain fields (e.g., DIC-measured kinematics) paired with global reaction forces interrogate a substantially larger region of stress–strain space without requiring local stress measurements. We introduce COMMET-DISCOVER, a flexible unsupervised NCM discovery framework, and demonstrate robust unsupervised CANN inference on soft biological tissue. Across synthetic and experimental benchmarks, unsupervised CANNs deliver higher out-of-sample R2 over a broader deformation manifold than supervised CANNs trained on classical test data, exhibit reduced sensitivity to measurement noise, and improve model specificity as reflected by fewer competing minima in the loss landscape.