Contrast / Concession

however - introduces a contrast

“The model fits the training data well; however, it generalizes poorly.”

although – to acknowledge an exception or contrast

“Although the method is efficient, it lacks robustness.”

nevertheless – introduces a counterpoint

“The system is unstable; nevertheless, the controller performs well.”

nonetheless – similar to “nevertheless” but slightly more formal

“This assumption is idealized; nonetheless, it simplifies analysis.”

in contrast – to highlight difference explicitly

“In contrast to classical methods, this approach uses quaternion algebra.”

whereas – to contrast two facts

“A increases with time, whereas B remains constant.”

Cause / Effect

therefore – slightly more formal than “so”

“The signal lacks periodicity; therefore, Fourier analysis is insufficient.”

consequently – emphasizes sequential causality

“The sampling was irregular; consequently, standard DFT methods fail.”

thus - “therefore” / “as a result,” often a bit more “mathy/derivation-y” and compact

“The noise is zero-mean; thus, the estimator is unbiased.”

hence – “for this reason”; direct and compact

“The oscillator exhibits sensitivity to initial conditions, hence chaotic.”

Addition / Elaboration

for example - introduces an illustration (same function as e.g., just spelled out and often smoother in prose)

“Several modulation schemes were evaluated; for example, FSK and OFDM were tested under identical SNR conditions.”

moreover – adds emphasis or an additional point

“The approach is accurate; moreover, it is computationally efficient.”

furthermore – adds another layer, often more formal than “also”

“The algorithm is robust. Furthermore, it generalizes well.”

in addition – standard way to expand an argument

“In addition to accuracy, interpretability is considered.”

likewise – introduces a parallel idea or result

“Method A improves performance. Likewise, Method B reduces complexity.”

Clarification / Emphasis

namely - introduces a precise specification of what you just referred to; often implies an exhaustive or defining list

“Two datasets were used, namely the indoor and outdoor measurement campaigns.”

notably – draws attention to a significant detail

“Notably, the system retains stability despite parameter drift.”

in particular – narrows focus to a specific case

“Several features are examined. In particular, phase symmetry is critical.”

indeed – emphasizes agreement or confirmation

“The observed trend matches the theoretical prediction. Indeed, the correlation is high.”