In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.
Example Output: Shortest path distance in random k-nearest neighbor graphs

Example Input: Populations of neurons in inferotemporal cortex (IT) maintain an explicit code for object identity that also tolerates transformations of object appearance e.g., position, scale, viewing angle [1, 2, 3]. Though the learning rules are not known, recent results [4, 5, 6] suggest the operation of an unsupervised temporal-association-based method e.g., Foldiak’s trace rule [7]. Such methods exploit the temporal continuity of the visual world by assuming that visual experience over short timescales will tend to have invariant identity content. Thus, by associating representations of frames from nearby times, a representation that tolerates whatever transformations occurred in the video may be achieved. Many previous studies verified that such rules can work in simple situations without background clutter, but the presence of visual clutter has remained problematic for this approach. Here we show that temporal association based on large class-specific filters (templates) avoids the problem of clutter. Our system learns in an unsupervised way from natural videos gathered from the internet, and is able to perform a difficult unconstrained face recognition task on natural images: Labeled Faces in the Wild [8]. This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF 1231216. ar X iv :1 40 9. 38 79 v2 [ cs .C V ] 2 4 A pr 2 01 5
Example Output: Unsupervised learning of clutter-resistant visual representations from natural videos

Example Input: We design and analyze minimax-optimal algorithms for online linear optimization games where the player’s choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark strategy. The standard benchmark is the loss of the best strategy chosen from a bounded comparator set. When the the comparison set and the adversary’s gradients satisfy L∞ bounds, we give the value of the game in closed form and prove it approaches √ 2T/π as T → ∞. Interesting algorithms result when we consider soft constraints on the comparator, rather than restricting it to a bounded set. As a warmup, we analyze the game with a quadratic penalty. The value of this game is exactly T/2, and this value is achieved by perhaps the simplest online algorithm of all: unprojected gradient descent with a constant learning rate. We then derive a minimax-optimal algorithm for a much softer penalty function. This algorithm achieves good bounds under the standard notion of regret for any comparator point, without needing to specify the comparator set in advance. The value of this game converges to √ e as T → ∞; we give a closed-form for the exact value as a function of T . The resulting algorithm is natural in unconstrained investment or betting scenarios, since it guarantees at worst constant loss, while allowing for exponential reward against an “easy” adversary.
Example Output:
Minimax Optimal Algorithms for Unconstrained Linear Optimization