Attenuation, snr, snrm, and errors are all physical measurements of the dsl signal between the mux (the kit which generates the dsl signal at the exchange) and the end users router/modem)
I like my analogies so here goes.
Attenuation is like talking to some one standing at the end of your road. the further away they are the fainter the conversation so you may have to talk more slowly to be understood. dsl works the same way.
SNR is the difference as a ratio in volume of the above conversation over say a nearby radio blurring out or someone mowing the lawn (and typicaly a combination of a lot of these)
SNRM is based on the above but the working of the numbers is more of a tolerance level around the typical snr. so with the above conversation your having you generaly have a typical level of backround noise for your local.
based on the above combinations the exchange equipment via an automated bit of kit works out what speed of conversation it can get away with, and typicaly cranks this figure back by half a meg. (maximum data rate-MDR and actual data rate- ADR) as a reliabilty safety margin.
If everything is hunky dory then things should stay stable. the odd extra bit of noise is neither here nor there unless this changes significantly over a moderate period of time or theres a repeated blast of noise then the dlm adjusts things to suit. no point in trying to hold things as they are because the conversation will become unintelligable or the contact is lost all together (and if things are bad enough this happens regardless of what the dlm tries)
It works the same the other way. If an annoying neighbour moves out along with their loud music you eventualy feel confident enough to speed the conversation up same with the dlm.
in rare occasions the dlm can be nudged manualy as long as there is a better snr compaired to the level the snrm has been set to. if there isn't this difference then tough because te system is coping to it's best ability with the conditions. there is nothing on the system to manualy nudge the snrm the other way. the whol system is geared to allow the fastest speeds that can be reliably maintained for the physical measurements of the signal. Typicaly a problem with sync speed isn't a failue of the DLM, its due to the physical state of the signal
If theres an snr issue around you then it's a case of either locating the source or retuning your set up so it's less sensitive to it.
Sorry that was a very long winded way of explaining what Roseway was saying