Related papers: Long multiplication by instruction sequences with …
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
The notion of Boolean logic backpropagation was introduced to build neural networks with weights and activations being Boolean numbers. Most of computations can be done with Boolean logic instead of real arithmetic, both during training and…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
A treap is a classic randomized binary search tree data structure that is easy to implement and supports O(\log n) expected time access. However, classic treaps do not take advantage of the input distribution or patterns in the input. Given…
Can we learn policies in reinforcement learning without rewards? Can we learn a policy just by trying to reach a goal state? We answer these questions positively by proposing a multi-step procedure that first learns a world model that goes…
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
In this brief, we improve the Broad Learning System (BLS) [7] by reducing the computational complexity of the incremental learning for added inputs. We utilize the inverse of a sum of matrices in [8] to improve a step in the pseudoinverse…
We use reverse mathematics to analyze "iterated jump" versions of the following four principles: the atomic model theorem with subenumerable types (AST), the diagonally noncomputable principle (DNR), weak weak K\H{o}nig's lemma (WWKL), and…
We present a simplified computational rule for the back-propagation formulas for artificial neural networks. In this work, we provide a generic two-step rule for the back-propagation algorithm in matrix notation. Moreover, this rule…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
We prove that the binary classifiers of bit strings generated by random wide deep neural networks with ReLU activation function are biased towards simple functions. The simplicity is captured by the following two properties. For any given…
We generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main…
Binary neural networks leverage $\mathrm{Sign}$ function to binarize weights and activations, which require gradient estimators to overcome its non-differentiability and will inevitably bring gradient errors during backpropagation. Although…
In many sequential tasks, a model needs to remember relevant events from the distant past to make correct predictions. Unfortunately, a straightforward application of gradient based training requires intermediate computations to be stored…
Model-based reinforcement learning (MBRL) aims to learn a dynamic model to reduce the number of interactions with real-world environments. However, due to estimation error, rollouts in the learned model, especially those of long horizons,…
In continual learning, a model learns incrementally over time while minimizing interference between old and new tasks. One of the most widely used approaches in continual learning is referred to as replay. Replay methods support interleaved…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Meta-learning, the notion of learning to learn, enables learning systems to quickly and flexibly solve new tasks. This usually involves defining a set of outer-loop meta-parameters that are then used to update a set of inner-loop…