Ø Theoretical objectives and practical relevance, with key references In a context of intensive and repeated innovation (Wheelwright and Clark, 1992; Le Masson et al., 2010), exploratory projects are needed to identify, share and shape the potential of value creation for future developments of new original products and commercial services (Lenfle, 2014). Despite an increasing interest in innovation management, these collective activities remain hard to manage, especially due to the specific knowledge management it requires: variance-seeking learning during exploratory projects has been underlined as success factor for next business development (McGrath, 2001). Looking for variety, exploratory projects are known to face fastidious and hazardous learning process, thus the main goal of the project is to structure and model the knowledge created on a diversity of possible design paths in an expected innovation field: teams gather knowledge on the value of the unknown (De Meyer et al, 02; Gillier et al, 2015). Contributing to overcome this research gap in innovation management, our research deals precisely with the issue of representing the links of dependences between knowledge pieces coming from individuals, collectives or experiences: how to structure, consolidate and present the links between first scraps of knowledge, even if these scraps are unfocused, undefinable even antagonists, to support collaboration in exploratory projects? Ø Approach/Method The theory-building process we propose in the paper build on a single case study (Eisenhardt and Graebner, 2007), conducted within a longitudinal collaborative research (Adler et al, 2004) on innovative capability in SME with Nutriset, a French food company initially specialized in developing and manufacturing products to fight against malnutrition that now expect to develop services for the disease prevention. The case study focuses on the knowledge management of Nutriset’s exploratory project defined as autonomous R&D services platform in Southern countries from December 2015 to September 2016. The exploratory project is still on-going but the first knowledge base was created and consolidated during this seven months’ period. Practitioners and researchers collaborated in experimenting the use of matroid structures (Neel and Neudauer 2009) to model the initial knowledge base through the dependencies and independencies of knowledge pieces gathered in the exploratory project. Ø Data/Findings Matroids structures were developed in the 1930s by mathematicians to describe linear dependence. However, they were not used in knowledge management until recently. In 2015, researchers on design theory have shown they could be used efficiently with C-K design theory to understand and explicit the dynamics of knowledge subsets (Le Masson et al, 2015). In their last publication, authors explained the CK/Ma model describes “new laws for the dynamics of techniques and helps to build strategic alternatives in the design of techniques” (Le Masson et al, 2016, p22). In the collaborative research, we experimented this new approach to structure knowledge dependencies. We will describe step-by-step how matroids structures were used on Nutriset’s exploration across two main managerial focuses: (i) how the matroidal model supports the variance-seeking learning process; (ii) how the model supports the restitution and sharing of the knowledge gathered during exploration to decide what services will be developed in the future. Ø Conclusion and contribution to the field Design theorists recently proposed the CK/Ma model and highlighted the potential of this new approach for knowledge management in innovative design activities. Our research proposes two main contributions: 1/ we experimented the matroid approach in an industrial project as a KM tool; 2/ we analysed the benefits and limits for exploratory projects management.