TC-CRP: Budgeted Integer Learning through Zero-Sum Weight Transfers

Biological synapses have bounded capacity, and their changes are constrained by the units that constitute them. Programmable synaptic devices face corresponding limits in conductance range and write endurance, with each parameter change requiring programming operations. These constraints motivate learning rules that turn desired changes into useful actions within a finite write allowance. We introduce TC-CRP, which converts class-discriminative learning signals into budget-constrained, zero-sum integer weight transfers. Votes identify coordinates worth modifying, and an executor realises their priorities as paired ±1 updates. Each pair costs two unit writes; a batch quota and a cumulative ledger control parameter modification throughout training. Complete-pair commits preserve integer weights, exact row balance and coordinate bounds, making the write allowance enforceable as learning proceeds. With full unobstructed execution, ranked selection maximises per-row alignment with the learning signal over the prescribed unit-action set, providing a principled basis for allocating limited writes. Because coordinates are bounded and the budget is spent across batches, a batch’s proposed changes may require decisions about what to carry forward. Historical accumulation and execution subtraction let later priorities reflect past signals while retaining the same legal actions. At matched write counts on the two primary image tasks, directional selection outperforms a random-coordinate control. TC-CRP thus connects controllable parameter-modification cost with supervised learning and provides a framework for examining how update selection and historical memory use a limited write allowance.