There is a type of cognition that very definitely has no contribution from consciousness: problem solving by an abrupt insight (Eureka or Aha). This is not a sequential incremental method but a transformation, restructuring or reformulation of the problem. There is no conscious forewarning of the insight. What is known about how the type of cognition works?
Here is Shehl, Sandkuhler, Bhattacharya (2009) Posterior Beta and Anterior Gamma Oscillations Predict Cognitive Insight; abstract:
Pioneering neuroimaging studies on insight have revealed neural correlates of the emotional Aha! component of the insight process, but neural substrates of the cognitive component, such as problem restructuring (a key to transformative reasoning), remain a mystery. Here, multivariate electroencepalogram signals were recorded from human participants while they solved verbal puzzles that could create a small-scale experience of cognitive insight. Individuals responded as soon as they reached a solution and provided a rating of subjective insight. For unsolved puzzles, hints were provided after 60 to 90 sec. Spatio-temporal signatures of brain oscillations were analyzed using Morlet wavelet transform followed by exploratory parallel-factor analysis. A consistent reduction in beta power (1525 Hz) was found over the parieto-occipital and centro-temporal electrode regions on all four conditions(a) correct (vs. incorrect) solutions, (b) solutions without (vs. with) external hint, (c) successful (vs. unsuccessful) utilization of the external hint, and d) self-reported high (vs. low) insight. Gamma band (3070 Hz) power was increased in right fronto-central and frontal electrode regions for conditions (a) and (c). The effects occurred several (up to 8 ) seconds before the behavioral response. Our findings indicate that insight is represented by distinct spectral, spatial, and temporal patterns of neural activity related to presolution cognitive processes that are intrinsic to the problem itself but not exclusively to ones subjective assessment of insight.
This implies that we can unconsciously notice that we are thinking about a problem in an unsuccessful way, search for an more successful framing, and evaluating the new way of thinking about the problem. To me, this hints at working memory not being required in this search for a transformation. Another interesting result is the gamma increase was in the right hemisphere (rather than left or both). This implies that the usually less dominant hemisphere was carrying the load in finding a transformation.
Does this have anything to say about creativity? – apparently not. Here is the abstract from Dietrich, Kanso (2010); A review of EEG, ERP, and neuroimaging studies of creativity and insight:
Creativity is a cornerstone of what makes us human, yet the neural mechanisms underlying creative thinking are poorly understood. A recent surge of interest into the neural underpinnings of creative behavior has produced a banquet of data that is tantalizing but, considered as a whole, deeply self-contradictory. We review the emerging literature and take stock of several long-standing theories and widely held beliefs about creativity. A total of 72 experiments, reported in 63 articles, make up the core of the review. They broadly fall into 3 categories: divergent thinking, artistic creativity, and insight. Electroencephalographic studies of divergent thinking yield highly variegated results. Neuroimaging studies of this paradigm also indicate no reliable changes above and beyond diffuse prefrontal activation. These findings call into question the usefulness of the divergent thinking construct in the search for the neural basis of creativity. A similarly inconclusive picture emerges for studies of artistic performance, except that this paradigm also often yields activation of motor and temporoparietal regions. Neuroelectric and imaging studies of insight are more consistent, reflecting changes in anterior cingulate cortex and prefrontal areas. Taken together, creative thinking does not appear to critically depend on any single mental process or brain region, and it is not especially associated with right brains, defocused attention, low arousal, or alpha synchronization, as sometimes hypothesized. To make creativity tractable in the brain, it must be further subdivided into different types that can be meaningfully associated with specific neurocognitive processes.
Insight may or may not be part of any thinking process creative or not. Creativity is probably so varied and so complex a process that it cannot be correlated with any particular neural picture.