Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear (O(1/t)) convergence on general smooth and convex objectives, and linear convergence (O(e^{-t})) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.

Fast, stealthy, and cheap--autonomous, semisubmersible drone boats carrying tons of cocaine could be international law enforcement's nightmare scenario. A big one just came ashore. Colombian military officials intercepted this 40-foot-long uncrewed fiberglass "narco sub" in the ocean just off Tayrona National Park. On a bright morning last April, a surveillance plane operated by the Colombian military spotted a 40-foot-long shark-like silhouette idling in the ocean just off Tayrona National Park. It was, unmistakably, a "narco sub," a stealthy fiberglass vessel that sails with its hull almost entirely underwater, used by drug cartels to move cocaine north. The plane's crew radioed it in, and eventually nearby coast guard boats got the order, routine but urgent: Intercept. In Cartagena, about 150 miles from the action, Captain Jaime González Zamudio, commander of the regional coast guard group, sat down at his desk to watch what happened next.

From acomputational point of view,this problem is equivalent to the quadratic assignment problem, and as such is an NP-hard problem (Burkard et al., 1998).

The flexibility of these methods is often limited bytherequirement thatthecutsbeaxisaligned.

We categorize existing implementations2 into 2 kinds: (1) for verification only (typically implemented on CPUs, including DeepZ[35], and DeepPoly[37])3 (2) for training certified defense (typically using more efficient, yet weaker or approximated bounds: convex outer4 adversarial polytope[45], DiffAI[28], IBP[9] andCROWN-IBP[50]). Ourcontributionisnot8 to improve tightness of LiRPA bounds, but the first framework that generalizes to general computational graphs in9 anautomatic manner. In CROWN[50], the quadratic bound is only applied to 2-layer networks and is hard to extend to14 multiplelayers,aswhenpropagatingaquadratic boundtothe3rdlayeritbecomes quadratic (x4)duetocorrelations15 between twoquadratic terms ("order explosion").

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear (O(1/t)) convergence on general smooth and convex objectives, and linear convergence (O(e^{-t})) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.

Neural Information Processing Systems http://nips.cc/

In this paper, we address the graph matching problem.

Technology Engineering OceanGate's'Titan' went on 7 dives with a damaged hull before implosion Investigators found that the submersible's exterior featured'multiple anomalies' as early as 2022. Breakthroughs, discoveries, and DIY tips sent every weekday. The United States National Transportation Safety Board (NTSB) recently concluded its investigation into the OceanGate submersible disaster . According to the summary report released on October 15, an already weakened hull caused the deep sea tourist vessel to implode while it was en route to visit the wreckage of the RMS in June 2023, killing all five passengers on board. But according to their findings, investigators noted that the submersible wasn't damaged shortly before its final voyage.