Thomas D. Ahle

Henry Ling-Hei Tsang, Thomas Dybdahl Ahle

Embedding tables are used by machine learning systems to work with categorical features. In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during training. We suggest Clustered Compositional Embeddings (CCE) which combines clustering-based compression like quantization to codebooks with dynamic methods like The Hashing Trick and Compositional Embeddings (Shi et al., 2020). Experimentally CCE achieves the best of both worlds: The high compression rate of codebook-based quantization, but *dynamically* like hashing-based methods, so it can be used during training. Theoretically, we prove that CCE is guaranteed to converge to the optimal codebook and give a tight bound for the number of iterations required.

Thomas D. Ahle, Sahar Karimi, Peter Tak Peter Tang

Bayesian Neural Networks (BNN) have emerged as a crucial approach for interpreting ML predictions. By sampling from the posterior distribution, data scientists may estimate the uncertainty of an inference. Unfortunately many inference samples are often needed, the overhead of which greatly hinder BNN's wide adoption. To mitigate this, previous work proposed propagating the first and second moments of the posterior directly through the network. However, on its own this method is even slower than sampling, so the propagated variance needs to be approximated such as assuming independence between neural nodes. The resulting trade-off between quality and inference time did not match even plain Monte Carlo sampling. Our contribution is a more principled variance propagation framework based on "spiked covariance matrices", which smoothly interpolates between quality and inference time. This is made possible by a new fast algorithm for updating a diagonal-plus-low-rank matrix approximation under various operations. We tested our algorithm against sampling based MC Dropout and Variational Inference on a number of downstream uncertainty themed tasks, such as calibration and out-of-distribution testing. We find that Favour is as fast as performing 2-3 inference samples, while matching the performance of 10-100 samples. In summary, this work enables the use of BNN in the realm of performance critical tasks where they have previously been out of reach.

Jan Ole Ernst, Dmitri Michelangelo Saberi, Derek Christ et al.

The primary goal of Design Verification (DV) is to ensure that a proposed chip design implementation (either in code, or physical form) exactly matches its specification and is free of functional errors in order to avoid costly re-designs. Achieving this often demands extensive manual interpretation, translating the specification document into a formal, testable representation. While AI has made progress in DV, current approaches typically focus on narrow, isolated tasks rather than full end-to-end specification compliance of modern chip designs, failing to capture the complexity of real-world verification. Our method automatically formalizes natural language memory chip specifications, for industry relevant Dynamic Random Access Memory (DRAM) standards, into a formal representation called DRAMPyML that can be used for downstream DV tasks like the generation of SystemVerilog assertions, stimulus, and functional coverage. We also release our benchmarking dataset, DRAMBench, which can be used to evaluate the evolution of model capabilities (and new approaches) at hardware autoformalization.

Denis Melanson, Mohammad Abu Khater, Maxwell Aifer et al.

Recent breakthroughs in artificial intelligence (AI) algorithms have highlighted the need for novel computing hardware in order to truly unlock the potential for AI. Physics-based hardware, such as thermodynamic computing, has the potential to provide a fast, low-power means to accelerate AI primitives, especially generative AI and probabilistic AI. In this work, we present the first continuous-variable thermodynamic computer, which we call the stochastic processing unit (SPU). Our SPU is composed of RLC circuits, as unit cells, on a printed circuit board, with 8 unit cells that are all-to-all coupled via switched capacitances. It can be used for either sampling or linear algebra primitives, and we demonstrate Gaussian sampling and matrix inversion on our hardware. The latter represents the first thermodynamic linear algebra experiment. We also illustrate the applicability of the SPU to uncertainty quantification for neural network classification. We envision that this hardware, when scaled up in size, will have significant impact on accelerating various probabilistic AI applications.

Thomas D. Ahle, Francesco Silvestri

Tensor Core Units (TCUs) are hardware accelerators developed for deep neural networks, which efficiently support the multiplication of two dense $\sqrt{m}\times \sqrt{m}$ matrices, where $m$ is a given hardware parameter. In this paper, we show that TCUs can speed up similarity search problems as well. We propose algorithms for the Johnson-Lindenstrauss dimensionality reduction and for similarity join that, by leveraging TCUs, achieve a $\sqrt{m}$ speedup up with respect to traditional approaches.

Thomas D. Ahle, Jakob B. T. Knudsen

We construct a matrix $M\in R^{m\otimes d^c}$ with just $m=O(c\,λ\,\varepsilon^{-2}\text{poly}\log1/\varepsilonδ)$ rows, which preserves the norm $\|Mx\|_2=(1\pm\varepsilon)\|x\|_2$ of all $x$ in any given $λ$ dimensional subspace of $ R^d$ with probability at least $1-δ$. This matrix can be applied to tensors $x^{(1)}\otimes\dots\otimes x^{(c)}\in R^{d^c}$ in $O(c\, m \min\{d,m\})$ time -- hence the name "Tensor Sketch". (Here $x\otimes y = \text{asvec}(xy^T) = [x_1y_1, x_1y_2,\dots,x_1y_m,x_2y_1,\dots,x_ny_m]\in R^{nm}$.) This improves upon earlier Tensor Sketch constructions by Pagh and Pham~[TOCT 2013, SIGKDD 2013] and Avron et al.~[NIPS 2014] which require $m=Ω(3^cλ^2δ^{-1})$ rows for the same guarantees. The factors of $λ$, $\varepsilon^{-2}$ and $\log1/δ$ can all be shown to be necessary making our sketch optimal up to log factors. With another construction we get $λ$ times more rows $m=\tilde O(c\,λ^2\,\varepsilon^{-2}(\log1/δ)^3)$, but the matrix can be applied to any vector $x^{(1)}\otimes\dots\otimes x^{(c)}\in R^{d^c}$ in just $\tilde O(c\, (d+m))$ time. This matches the application time of Tensor Sketch while still improving the exponential dependencies in $c$ and $\log1/δ$. Technically, we show two main lemmas: (1) For many Johnson Lindenstrauss (JL) constructions, if $Q,Q'\in R^{m\times d}$ are independent JL matrices, the element-wise product $Qx \circ Q'y$ equals $M(x\otimes y)$ for some $M\in R^{m\times d^2}$ which is itself a JL matrix. (2) If $M^{(i)}\in R^{m\times md}$ are independent JL matrices, then $M^{(1)}(x \otimes (M^{(2)}y \otimes \dots)) = M(x\otimes y\otimes \dots)$ for some $M\in R^{m\times d^c}$ which is itself a JL matrix. Combining these two results give an efficient sketch for tensors of any size.