In difficult information seeking tasks, the majority of topranked documents for an initial query may be non-relevant, and negative relevance feedback may then help find relevant documents. Traditional negative relevance feedback has been studied on document results; we introduce a system and interface for negative feedback in a novel exploratory search setting, where continuous-valued feedback is directly given to keyword features of an inferred probabilistic user intent model. The introduced system allows both positive and negative feedback directly on an interactive visual interface, by letting the user manipulate keywords on an optimized visualization of modeled user intent. Feedback on the interactive intent model lets the user direct the search: Relevance of keywords is estimated from feedback by Bayesian inference, influence of feedback is increased by a novel propagation step, documents are retrieved by likelihoods of relevant versus non-relevant intents, and the most relevant keywords (having the highest upper confidence bounds of relevance) and the most non-relevant ones (having the smallest lower confidence bounds of relevance) are shown as options for further feedback. We carry out task-based information seeking experiments with real users on difficult real tasks; we compare the system to the nearest state of the art baseline allowing positive feedback only, and show negative feedback significantly improves the quality of retrieved information and user satisfaction for difficult tasks.