A PSPACE Construction of a Hitting Set for the Closure of Small Algebraic Circuits

In this paper we study the complexity of constructing a hitting set for the closure of VP, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given n,s,r in unary outputs a set of n-tuples over the rationals of size poly(n,s,r), with poly(n,s,r) bit complexity, that hits all n-variate polynomials of degree-r that are the limit of size-s algebraic circuits. Previously it was known that a random set of this size is a hitting set, but a construction that is certified to work was only known in EXPSPACE (or EXPH assuming the generalized Riemann hypothesis). As a corollary we get that a host of other algebraic problems such as Noether Normalization Lemma, can also be solved in PSPACE deterministically, where earlier only randomized algorithms and EXPSPACE algorithms (or EXPH assuming the generalized Riemann hypothesis) were known. The proof relies on the new notion of a robust hitting set which is a set of inputs such that any nonzero polynomial that can be computed by a polynomial size algebraic circuit, evaluates to a not too small value on at least one element of the set. Proving the existence of such a robust hitting set is the main technical difficulty in the proof. Our proof uses anti-concentration results for polynomials, basic tools from algebraic geometry and the existential theory of the reals

Making a Science of Model Search: Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures

Many computer vision algorithms depend on configuration settings that are typically hand-tuned in the course of evaluating the algorithm for a particular data set. While such parameter tuning is often presented as being incidental to the algorithm, correctly setting these parameter choices is frequently critical to realizing a method’s full potential. Compounding matters, these parameters often must be re-tuned when the algorithm is applied to a new problem domain, and the tuning process itself often depends on personal experience and intuition in ways that are hard to quantify or describe. Since the performance of a given technique depends on both the fundamental quality of the algorithm and the details of its tuning, it is sometimes difficult to know whether a given technique is genuinely better, or simply better tuned. In this work, we propose a meta-modeling approach to support automated hyperparameter optimization, with the goal of providing practical tools that replace hand-tuning with a reproducible and unbiased optimization process. Our approach is to expose the underlying expression graph of how a performance metric (e.g. classification accuracy on validation examples) is computed from hyperparameters that govern not only how individual processing steps are applied, but even which processing steps are included. A hyperparameter optimization algorithm transforms this graph into a program for optimizing that performance metric. Our approach yields state of the art results on three disparate computer vision problems: a face-matching verification task (LFW), a face identification task (PubFig83) and an object recognition task (CIFAR-10), using a single broad class of feed-forward vision architectures.Engineering and Applied Science

Stabilizer channels for trenches

This disclosure describes a trench profile that includes horizontal stabilizer channels along the sides of the trench. The trench profile enables greater robustness of a trench seal to environmental conditions during a sealant application process. When a sealant is applied, the horizontal stabilizer channels in the sidewalls of the trench create a locking key that prevents the solidified sealant from rising above grade under conditions when the sealant is incompletely secured to the sidewall. The horizontal stabilizer channels prevent solidified sealant from sinking below grade as a result of compression of filler material or the filler rod in the trench. The use of stabilizer channels can reduce repair costs due to sealant failures and mitigate safety hazards that can arise from changes in sealant elevation

Cutting tool for trench stabilization channels

This disclosure describes a cutting tool for cutting horizontal stabilizer channels along sidewalls of trenches. The cutting tool includes a shank with a depth stop, a bearing guide, and a cutting head. The cutting head is configured to make a horizontal cut into the sidewalls of the trench at a specified depth. The depth can be adjusted to accommodate different engineering requirements. The cutting tool is driven by a vertical shaft from an electric or gasoline powered walk behind router. The cutting tool can be utilized to provide horizontal stabilizer channels in trenches that can reduce repair costs due to sealant failures and mitigate safety hazards that can arise from changes in sealant elevation. Additionally, this device can be used with a “straight” router bit to resurface existing sidewalls (cleaning)

Biodegradable filler rod

This disclosure describes a biodegradable filler rod for use in trenches that house cables. The filler rod can be made from materials such as cornstarch and placed above flat fiber laid on the floor of the trench. Access to the filler rod is obtained through entry points provided in the trench. When additional fiber is to be laid in the trench, water is added to the trench which causes the biodegradable filler rod to dissolve, and a new void is created in its place. The additional fiber optic cable is rodded and placed in the void. The biodegradable filler rod provides cost savings for network capacity expansion projects without additional surface area requirements