arXiv subjects

Subhashini Jayawardhana

Publications and source records attributed to Subhashini Jayawardhana.

2 recordsLinked to original sources

arXiv2026

Convex Networks Remain Hard to Certify: Dimension-Accuracy Barriers for Lipschitz Constants

Input-convex neural networks permit globally tractable minimization over their inputs, so one might expect their global regularity to be tractable in low input dimension. We prove exact and accuracy-sensitive barriers to this expectation. Given a bias-free one-hidden-layer ReLU network $f(x)=\sum_{r=1}^n \mathrm{ReLU}(a_r^\top x)$ with unit positive output weights, deciding whether its global Euclidean Lipschitz constant is at least a rational threshold is NP-complete and W[1]-hard when parameterized by the input dimension $d$. The same holds on the unit ball and with integral first-layer weights having at most nine nonzeros. More sharply, no deterministic multiplicative approximation scheme runs in $g(d)\mathrm{poly}(\mathcal B,1/\varepsilon)$ time unless FPT equals W[1]. Under the Exponential Time Hypothesis, no such algorithm runs in $g(d)(\mathcal B+1/\varepsilon)^{o(d/\log d)}$ time. Thus accuracy cannot have a polynomial dependence separated from dimension. The exact result resolves the Euclidean case of an open problem posed at COLT 2025 and left open by the ICLR 2026 parameterized hardness theory for general two-layer networks. The approximation barrier is specific to generator-presented zonotopes, complementing known $(1/\varepsilon)^{O(d)}$-time schemes and an analogous barrier for halfspace-presented polytopes. Our lifted-selector reduction has an inverse-polynomial radial gap, proved through a quantitative theorem for rational cyclic zonogons. Equivalently, the results apply to Euclidean zonotope radius and positive-semidefinite binary quadratic maximization parameterized by rank. Convexity makes minimization easy, but it does not make global sensitivity fixed-parameter tractable or permit a dimension-separated fully polynomial accuracy guarantee.

cs.CC↗

arXiv2026

Self-Bounding Regret Matching+ in Potential Games and Product-Simplex Optimization

Regret matching+ (RM+) is parameter free, scale invariant, and central to large game solving, but its only general individual-regret guarantee grows as $\sqrt{T}$. A recent ICLR result used this envelope to prove that RM+ reaches an $ε$-stationary point of a smooth objective over a product of simplices in $O(ε^{-4})$ iterations, or $O(ε^{-8})$ from the standard zero initialization. We give an exact one-step conservation law for RM+. It states that forward utility gain pays for both squared state motion and growth of the regret-state norm. Norm growth is at most $\sqrt{m-1}$ times forward gain for $m$ actions, and the coefficient is sharp. This yields four results for unmodified RM+. Its regret on any utility path is controlled by centered temporal variation. Its regret is uniformly bounded under alternating play in every finite exact potential game, resolving an open question and making squared activation gaps summable. Both certified lazy and ordinary cyclic play attain an $ε^{-2}$ exponent. On any smooth, possibly nonconcave simplex objective, RM+ finds an $ε$-KKT point in $O(ε^{-2})$ iterations. Most broadly, for a smooth objective over an arbitrary product of simplices, cyclic block RM+ attains the same $O(ε^{-2})$ exponent from arbitrary initialization, with an explicit trajectory-dependent constant. The proof controls the finite objective loss caused by low-state blocks and then self-bounds every block state and the total squared path length. Complete proofs cover zero states, sharpness, common-profile stationarity, and robust gain dominance. Oracle-normalized diagnostics compare RM+ with predictive and smooth extra-gradient variants on graphical potential games and dense nonconvex objectives.

cs.GT↗