Generating Hamiltonian circuits without backtracking from errors

Splitting Without Backtracking

Choices without Backtracking

ly, one possiblc3 mode of interaction bctwccn the the problLm solver and the dntn base is as follows. A list is maintained of c~cry ;\ssumptioll set disco\rcrcd to bc contradictory. Whcncvcr the problem solver discovers Iwo val~~cs with contt.adictr~ry assumptions, the combined assumption set is placed on this list, and cvcry vaIlIC b,iscd on it or any of its super sets is crascd from the daL\ ...

Memristor Hamiltonian Circuits

We prove analytically that 2-element memristiue c'ircuits consisting of a pass'iue I'inearinductor in parallel with a pass,iue memristor, or an act'iue memristiue deuice, can be described explicitly by a Hami,ltonian eqttation, whose solutions can be periodic or damped, and can be represented analytically by the constants of the motion along the circuit Hamiltonian. Generalizations to 3-element...

A note on Hamiltonian circuits

Proof. Let G satisfy the hypothesis of Theorem 1. Clearly, G contains a circuit ; let C be the longest one . If G has no Hamiltonian circuit, there is a vertex x with x ~ C . Since G is s-connected, there are s paths starting at x and terminating in C which are pairwise disjoint apart from x and share with C just their terminal vertices x l, X2, . . ., x s (see [ 11, Theorem 1) . For each i = 1...

Training recurrent networks online without backtracking

We introduce the “NoBackTrack” algorithm to train the parameters of dynamical systems such as recurrent neural networks. This algorithm works in an online, memoryless setting, thus requiring no backpropagation through time, and is scalable, avoiding the large computational and memory cost of maintaining the full gradient of the current state with respect to the parameters. The algorithm essenti...