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1. Tiny Pointers

   https://doi.org/10.1145/3700594  

   Bender, Michael A ; Conway, Alex ; Farach-Colton, Martín ; Kuszmaul, William ; Tagliavini, Guido ( October 2024 , ACM Transactions on Algorithms)

   This paper introduces a new data-structural object that we call the tiny pointer. In many applications, traditional\(\log n\)-bit pointers can be replaced with\(o(\log n)\)-bit tiny pointers at the cost of only a constant-factor time overhead and a small probability of failure. We develop a comprehensive theory of tiny pointers, and give optimal constructions for both fixed-size tiny pointers (i.e., settings in which all of the tiny pointers must be the same size) and variable-size tiny pointers (i.e., settings in which the average tiny-pointer size must be small, but some tiny pointers can be larger). If a tiny pointer references an item in an array filled to load factor\(1-\delta\), then the optimal tiny-pointer size is\(\Theta(\log\log\log n+\log\delta^{-1})\)bits in the fixed-size case, and\(\Theta(\log\delta^{-1})\)expected bits in the variable-size case.

   Our tiny-pointer constructions also require us to revisit several classic problems having to do with balls and bins; these results may be of independent interest.

   Using tiny pointers, we apply tiny pointers to five classic data-structure problems. We show that:

   A data structure storing\(n\)\(v\)-bit values for\(n\)keys with constant-factor time modifications/queries can be implemented to take space\(nv+O(n\log^{(r)}n)\)bits, for any constant\(r\gt0\), as long as the user stores a tiny pointer of expected size\(O(1)\)with each key—here,\(\log^{(r)}n\)is the\(r\)-th iterated logarithm.

   Any binary search tree can be made succinct, meaning that it achieves\((1+o(1))\)times the optimal space, with constant-factor time overhead, and can even be made to be within\(O(n)\)bits of optimal if we allow for\(O(\log^{*}n)\)-time modifications—this holds even for rotation-based trees such as the splay tree and the red-black tree.

   Any fixed-capacity key-value dictionary can be made stable (i.e., items do not move once inserted) with constant-factor time overhead and\((1+o(1))\)-factor space overhead.

   Any key-value dictionary that requires uniform-size values can be made to support arbitrary-size values with constant-factor time overhead and with an additional space consumption of\(\log^{(r)}n+O(\log j)\)bits per\(j\)-bit value for an arbitrary constant\(r\gt0\)of our choice.

   Given an external-memory array\(A\)of size\((1+\varepsilon)n\)containing a dynamic set of up to\(n\)key-value pairs, it is possible to maintain an internal-memory stash of size\(O(n\log\varepsilon^{-1})\)bits so that the location of any key-value pair in\(A\)can be computed in constant time (and with no IOs).

   In each case tiny pointers allow for us to take a natural space-inefficient solution that uses pointers and make it space-efficient for free.

    

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2. CHARM 2.0: Composing Heterogeneous Accelerators for Deep Learning on Versal ACAP Architecture

   https://doi.org/10.1145/3686163  

   Zhuang, Jinming ; Lau, Jason ; Ye, Hanchen ; Yang, Zhuoping ; Ji, Shixin ; Lo, Jack ; Denolf, Kristof ; Neuendorffer, Stephen ; Jones, Alex ; Hu, Jingtong ; et al ( August 2024 , ACM Transactions on Reconfigurable Technology and Systems)

   Dense matrix multiply (MM) serves as one of the most heavily used kernels in deep learning applications. To cope with the high computation demands of these applications, heterogeneous architectures featuring both FPGA and dedicated ASIC accelerators have emerged as promising platforms. For example, the AMD/Xilinx Versal ACAP architecture combines general-purpose CPU cores and programmable logic with AI Engine processors optimized for AI/ML. An array of 400 AI Engine processors executing at 1 GHz can provide up to 6.4 TFLOPS performance for 32-bit floating-point (FP32) data. However, machine learning models often contain both large and small MM operations. While large MM operations can be parallelized efficiently across many cores, small MM operations typically cannot. We observe that executing some small MM layers from the BERT natural language processing model on a large, monolithic MM accelerator in Versal ACAP achieved less than 5% of the theoretical peak performance. Therefore, one key question arises:How can we design accelerators to fully use the abundant computation resources under limited communication bandwidth for end-to-end applications with multiple MM layers of diverse sizes?

   We identify the biggest system throughput bottleneck resulting from the mismatch between massive computation resources of one monolithic accelerator and the various MM layers of small sizes in the application. To resolve this problem, we propose the CHARM framework to composemultiple diverse MM accelerator architecturesworking concurrently on different layers within one application. CHARM includes analytical models which guide design space exploration to determine accelerator partitions and layer scheduling. To facilitate system designs, CHARM automatically generates code, enabling thorough onboard design verification. We deploy the CHARM framework on four different deep learning applications in FP32, INT16, and INT8 data types, including BERT, ViT, NCF, and MLP, on the AMD/Xilinx Versal ACAP VCK190 evaluation board. Our experiments show that we achieve 1.46 TFLOPS, 1.61 TFLOPS, 1.74 TFLOPS, and 2.94 TFLOPS inference throughput for BERT, ViT, NCF, and MLP in FP32 data type, respectively, which obtain 5.29\(\times\), 32.51\(\times\), 1.00\(\times\), and 1.00\(\times\)throughput gains compared to one monolithic accelerator. CHARM achieves the maximum throughput of 1.91 TOPS, 1.18 TOPS, 4.06 TOPS, and 5.81 TOPS in the INT16 data type for the four applications. The maximum throughput achieved by CHARM in the INT8 data type is 3.65 TOPS, 1.28 TOPS, 10.19 TOPS, and 21.58 TOPS, respectively. We have open-sourced our tools, including detailed step-by-step guides to reproduce all the results presented in this paper and to enable other users to learn and leverage CHARM framework and tools in their end-to-end systems:https://github.com/arc-research-lab/CHARM.

    

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3. Smoothed Analysis with Adaptive Adversaries

   https://doi.org/10.1145/3656638  

   Haghtalab, Nika ; Roughgarden, Tim ; Shetty, Abhishek ( June 2024 , Journal of the ACM)

   We prove novel algorithmic guarantees for several online problems in the smoothed analysis model. In this model, at each time step an adversary chooses an input distribution with density function bounded above pointwise by \(\tfrac{1}{\sigma }\)times that of the uniform distribution; nature then samples an input from this distribution. Here, σ is a parameter that interpolates between the extremes of worst-case and average case analysis. Crucially, our results hold foradaptiveadversaries that can base their choice of input distribution on the decisions of the algorithm and the realizations of the inputs in the previous time steps. An adaptive adversary can nontrivially correlate inputs at different time steps with each other and with the algorithm’s current state; this appears to rule out the standard proof approaches in smoothed analysis.

   This paper presents a general technique for proving smoothed algorithmic guarantees against adaptive adversaries, in effect reducing the setting of an adaptive adversary to the much simpler case of an oblivious adversary (i.e., an adversary that commits in advance to the entire sequence of input distributions). We apply this technique to prove strong smoothed guarantees for three different problems:(1)

   Online learning: We consider the online prediction problem, where instances are generated from an adaptive sequence of σ-smooth distributions and the hypothesis class has VC dimensiond. We bound the regret by\(\tilde{O}(\sqrt {T d\ln (1/\sigma)} + d\ln (T/\sigma))\)and provide a near-matching lower bound. Our result shows that under smoothed analysis, learnability against adaptive adversaries is characterized by the finiteness of the VC dimension. This is as opposed to the worst-case analysis, where online learnability is characterized by Littlestone dimension (which is infinite even in the extremely restricted case of one-dimensional threshold functions). Our results fully answer an open question of Rakhlin et al. [64].

   (2)

   Online discrepancy minimization: We consider the setting of the online Komlós problem, where the input is generated from an adaptive sequence of σ-smooth and isotropic distributions on the ℓ₂unit ball. We bound the ℓ_∞norm of the discrepancy vector by\(\tilde{O}(\ln ^2(\frac{nT}{\sigma }))\). This is as opposed to the worst-case analysis, where the tight discrepancy bound is\(\Theta (\sqrt {T/n})\). We show such\(\mathrm{polylog}(nT/\sigma)\)discrepancy guarantees are not achievable for non-isotropic σ-smooth distributions.

   (3)

   Dispersion in online optimization: We consider online optimization with piecewise Lipschitz functions where functions with ℓ discontinuities are chosen by a smoothed adaptive adversary and show that the resulting sequence is\(({\sigma }/{\sqrt {T\ell }}, \tilde{O}(\sqrt {T\ell }))\)-dispersed. That is, every ball of radius\({\sigma }/{\sqrt {T\ell }}\)is split by\(\tilde{O}(\sqrt {T\ell })\)of the partitions made by these functions. This result matches the dispersion parameters of Balcan et al. [13] for oblivious smooth adversaries, up to logarithmic factors. On the other hand, worst-case sequences are trivially (0,T)-dispersed.¹

    

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4. Sketching Approximability of All Finite CSPs

   https://doi.org/10.1145/3649435  

   Chou, Chi-Ning ; Golovnev, Alexander ; Sudan, Madhu ; Velusamy, Santhoshini ( April 2024 , Journal of the ACM)

   A constraint satisfaction problem (CSP),\(\textsf {Max-CSP}(\mathcal {F})\), is specified by a finite set of constraints\(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\)for positive integersqandk. An instance of the problem onnvariables is given bymapplications of constraints from\(\mathcal {F}\)to subsequences of thenvariables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied.

   In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family\(\mathcal {F}\)and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in\(o(\sqrt {n})\)space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems.

   We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case ofq=k=2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of\(\mathcal {F}\)support a distribution on\([q]^k\)with uniform marginals.

   Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variablesq= 2, binary constraintsk=2, and singleton families\(|\mathcal {F}|=1\)and only considered the setting where constraints are placed on literals rather than variables.

   Our positive results show wide applicability of bias-based algorithms used previously by [47] and [41], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [56], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to generalq-ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes.

    

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5. Improving Fault Tolerance for FPGA SoCs through Post-Radiation Design Analysis

   https://doi.org/10.1145/3674841  

   Wilson, Andrew Elbert ; Baker, Nathan ; Campbell, Ethan ; Wirthlin, Michael ( September 2024 , ACM Transactions on Reconfigurable Technology and Systems)

   FPGAs have been shown to operate reliably within harsh radiation environments by employing single-event upset (SEU) mitigation techniques, such as configuration scrubbing, triple-modular redundancy, error correction coding, and radiation aware implementation techniques. The effectiveness of these techniques, however, is limited when using complex system-level designs that employ complex I/O interfaces with single-point failures. In previous work, a complex SoC system running Linux applied several of these techniques only to obtain an improvement of 14\(\times\)in mean time to failure (MTTF). A detailed post-radiation fault analysis found that the limitations in reliability were due to the DDR interface, the global clock network, and interconnect. This article applied a number of design-specific SEU mitigation techniques to address the limitations in reliability of this design. These changes include triplicating the global clock, optimizing the placement of the reduction output voters and input flip-flops, and employing a mapping technique called “striping.” The application of these techniques improved MTTF of the mitigated design by a factor of 1.54\(\times\)and thus provides a 22.8X\(\times\)MTTF improvement over the unmitigated design. A post-radiation fault analysis using BFAT was also performed to find the remaining design vulnerabilities.

    

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