A high-fat, refined sugar diet reduces hippocampal brain-derived neurotrophic factor, neuronal plasticity, and learning.

By R. Molteni, R. Barnard, Z. Ying, Christian K. Roberts, F. Gomez-Pinilla. Neuroscience, 2002

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The Influence of Exercise on Cognitive Abilities (2013, neutral): “exist when measuring the performance of rats to learn a spatial learning and memory task (123).”
Diet‐induced insulin resistance promotes amyloidosis in a transgenic mouse model of Alzheimer's disease (2004, background): “However, we note that recent evidence indicates that high fat-diet may also promote cognitive impairment independent of amyloidosis and could contribute to cognitive impairment observed in insulin-resistant relative to normoglycemic Tg2576 mice (30).”
Potential therapeutic uses of BDNF in neurological and psychiatric disorders (2011, background): “Calorific restriction or certain diets also affect levels of BDN”
The Darwinian concept of stress: benefits of allostasis and costs of allostatic load and the trade-offs in health and disease. (2005, background): “Fortunately , it is now clear that voluntary exercise can increase levels of BDNF and other growth factors , increase CREB phosphorylation , neurogenesis , resistance to brain insult and fat intake , and improve learning and mental performance [ 414 , 417 , 418 ] .”