In addition to the methods presented in RegDwigнt's answer — using synonyms and simply removing the words — two other techniques for avoiding such repetition come to mind.
Replacing "thus" or "therefore" in the conclusion with "since" or "because" in the clause presenting the evidence is perhaps the most straightforward. This technique works better with shorter statements of evidence.
Since neural responses to sensory input, as well as overt reactions, become highly differentiated later in life, it can be assumed that neurons adapt their responses mediated by experience...
Because the neural responses used by the SC to localize stimuli are stochastic, the SC’s task can be described as a statistical inference problem: ...
The second technique would be to use a verb that includes the logical inference such as "indicate", "imply", "show", "demonstrate", or even "allows". Using a participle avoids the need for an explicit subject, but "this" or "such evidence" are adequate subjects. (In fact, "such evidence" might be preferred when the evidence is extensive.)
Neural responses to sensory input become highly differentiated later in life, as do overt reactions, indicating that neurons adapt their responses mediated by experience...
The neural responses used by the SC to localize stimuli are stochastic. This allows the SC’s task to be described as a statistical inference problem: ...
This can include reversing the order of evidence and conclusion.
That neurons adapt their responses mediated by experience can be concluded from the fact that neural responses to sensory input, as well as overt reactions, become highly differentiated later in life.
The SC's task can be treated as a statistical inference problem by recognizing the stochastic nature of the neural responses used by the SC to localize stimuli: ...
(The latter rephrasing is clearly problematic since the colon indicates that a stronger binding to "statistical inference problem" is desired. However, it provides the useful example of "recognize" replacing "show", changing the subject from the evidence to the observer allows further variety in verbs.)