Abraham Itzhak Weinberg

Reservoir computing (RC) offers a computationally cheap alternative to backpropagationthrough-time for temporal modeling: a fixed, randomly initialized recurrent substrate (the reservoir) projects an input stream into a high-dimensional state space, and only a lightweight readout is trained. This efficiency comes at the cost of a readout that is typically a plain linear or ridge regression model, with no mechanism for incorporating domain knowledge expressed as logical rules. We introduce EchoLogic Networks (ELN), a neurosymbolic architecture that augments the readout's training objective with differentiable fuzzy-logic penalties derived from symbolic constraints-a product t-norm for mutual exclusion and a Łukasiewicz-style implication for temporal precedence rules-while leaving the reservoir untouched. We identify and address an optimization pathology in the naive formulation: without an asymmetric-gradient correction, the model satisfies an implication rule "A ⇒ C" by suppressing the antecedent A rather than raising the consequent C. We further distill the trained readout into a shallow, human-auditable decision tree over reservoir states. On a controlled synthetic benchmark, EchoLogic improves F1 on the rule-implied event from 0.504 ± 0.043 to 0.621 ± 0.030 across 20 independent seeds (Wilcoxon signed-rank p = 1.9 × 10-6 , paired Cohen's d = 3.94), with no measurable cost to unrelated event classes. A controlled ablation isolates the asymmetric-gradient correction as necessary, not cosmetic: removing it lets accuracy on the antecedent class collapse from 0.506 to 0.257. The distilled surrogate reaches 0.982 ± 0.003 held-out fidelity to the full model. We report the method's benefit as a function of reservoir size, spectral radius, and rule reliability, and we present an honest compute-accuracy comparison against a fully backpropagation-trained LSTM: EchoLogic reaches its accuracy plateau roughly an order of magnitude faster, but the LSTM's final ceiling is substantially higher given sufficient training time. We argue this is the correct scientific framing-a speed/ceiling trade-off, not a contest EchoLogic needs to win-and we discuss the central open threat to validity: all experiments here are generated from the same rules injected into the training objective, and validation on an independently-sourced real-world rule set remains the necessary next step.

Quantum reservoir computing (QRC) is often motivated by the hope that quantum dynamics can provide computational resources unavailable to classical reservoirs of matched size. We introduce QuIP (Quantum Information-Processing capacity), a framework for auditing this claim directly: a physically motivated quantum reservoir (a fixed disordered Ising Hamiltonian evolved as a Floquet map, with a deterministic input-qubit reset that gives the reservoir a genuine fading-memory property) is scored with the standard Information Processing Capacity (IPC) framework of Dambre et al. (2012) against a matched classical Echo State Network (ESN), while its quantum resource content (entanglement entropy and a stabilizer-Rényi-entropy "magic" monotone) is measured via quantum-trajectory unraveling. Across an interactionstrength sweep, we find a non-monotonic capacity curve with an interior maximum: an interior optimum at which the reservoir extracts the most computational capacity per unit of quantum resource consumed. However, under matched hyperparameters the classical baseline outperforms the quantum reservoir throughout the sweep (paired t-test, p < 10-5), and this gap widens rather than narrows as system size grows from n = 4 to n = 8 qubits at fixed hyperparameters. A best-tuned comparison (coordinate-ascent tuning of both systems) narrows but does not close the gap. We additionally report a provable symmetry lemma explaining why even-degree IPC contributions vanish identically for the classical reservoir (and an empirically consistent but unproven analogue for the quantum case), a null result for cross-delay (multiplicative) capacity in both systems, and a Fokker-Planck description of the quantum reservoir's entanglement buildup that matches its empirical stationary distribution. We discuss these results in the context of recent theoretical work relating QRC performance to entanglement-spectrum statistics and nonstabilizerness, and outline what remains to establish a genuine, resource-costed quantum advantage in this setting.

Token pruning can reduce large language model (LLM) inference cost by removing tokens unlikely to contribute to subsequent computation. We introduce QuTrim, a position-aware quantum-inspired variational scorer for token-level pruning, implemented as a small variational quantum circuit and simulated classically. QuTrim combines PCA-reduced token-embedding representations with two positional features describing each token's normalized distance from the beginning and end of the sequence. We evaluate QuTrim against a parameter-matched classical MLP, random pruning, an embedding-norm heuristic, and a training-free position/attention-sink heuristic. In a short-sentence evaluation (n = 40 sentences, 5 seeds), QuTrim is statistically indistinguishable from the classical MLP across all pruning ratios, significantly outperforms random pruning at aggressive pruning levels, and consistently exceeds the embedding-norm heuristic. Although the position/sink heuristic remains stronger in this setting, the difference is reduced relative to content-only scoring. In a more realistic long-context evaluation, where only the context is pruned and perplexity is measured on a held-out continuation, QuTrim significantly outperforms the classical MLP and random pruning at all six pruning ratios and the embedding-norm heuristic at four of six ratios. It is statistically indistinguishable from the strongest baseline, the position/sink heuristic, at every ratio (p adj > 0.4 throughout). Additional ablations examine the contributions of positional information and circuit capacity. Statistical evaluation uses multi-seed training, paired Wilcoxon tests, Benjamini-Hochberg correction, and rank-biserial effect sizes. These results show that a compact position-aware variational quantuminspired scorer can provide competitive token-importance estimates and, in long-context pruning, match a strong training-free positional heuristic while outperforming a parameter-matched classical neural baseline.

Equidistant letter sequences (ELS)-subsequences formed by reading a text at a fixed skip interval-have been the basis of a series of claims, originating in a 1994 study, that the Hebrew text of the Torah encodes information unavailable to its putative authors. These claims were subsequently and comprehensively refuted in later statistical work, which showed that the original result was an artifact of large researcher degrees of freedom rather than a genuine textual property. In this paper we (i) define and implement four novel two-dimensional geometric generalizations of ELS search, in which the letters of a target string are placed on the vertices of a hexagram ("Star of David") pattern rather than along a single linear skip; (ii) implement a proximity-based multi-word cluster search in the tradition of the original ELS studies; (iii) validate the entire pipeline with a pre-registered permutation test against letter-shuffled control texts, applied to a positive-control replication using a verifiable, independently-sourced dataset of ten Israeli Prime Ministers' names and Hebrew-calendar birth/death dates, structurally analogous to a Prime-Minister/President/Knesset-Speaker experiment already reported (and found non-significant) in the refutation literature; (iv) apply the same pipeline to a second, independent case study of three generic thematic word pairs; and (v) introduce a shape-specificity control that generalizes the hexagram placement to arbitrary regular polygons and a circular baseline, directly testing whether the six-fold, Star-of-David symmetry carries any special weight. Across all ten Prime Ministers and all six thematic-phrase conditions we find no statistically significant positive clustering (all sixteen non-zero z-scores are negative, several strongly so), consistent with the prior literature, and the shape-specificity control shows the hexagon to be the least distinguishable of six tested shapes (z = 0.02), providing no evidence that hexagram geometry is special. We document and discuss the striking consistency of negative z-scores across every experiment in this paper, which we attribute to a systematic limitation of i.i.d. letter-shuffle null models: such models destroy the local n-gram structure of natural language and are therefore not merely noisy but plausibly conservative relative to a genuine alternative-text control. We release the full analysis pipeline as a public, reproducible Colab notebook.

We introduce the Kibitzer game: a repeated Attacker-Defender security game augmented with a third, strategic, non-participant informant-the Kibitzer-modeled on unsolicited security signals such as intrusion-detection alerts or threat-intelligence feeds. Unlike a mediator in the classical sense, the Kibitzer has no commitment power, is not chosen by either player, and has its own incentive: a reputational payoff for being trusted, coupled with a cost of vigilance. The Attacker can additionally corrupt the Kibitzer's signal at a cost. The Defender does not know the Kibitzer's reliability a priori and must learn how much to trust it. We study this game both analytically, deriving a partial-equilibrium threshold at which the Attacker's optimal corruption effort saturates, and computationally, via smoothed fictitious play (multiplicativeweights no-regret learning). Simulation shows a sharp equilibrium collapse: when corruption is cheap enough to always be worthwhile, the Kibitzer's own accuracy investment rationally falls to zero, and the analytical threshold consistently under-predicts the simulated transition point by roughly 3-4×, indicating that the trust-corruption feedback loop across all three players amplifies the collapse beyond what single-agent best-response reasoning would suggest. We further show that Bayesian trust-discounting reliably dominates both blind trust and ignoring the signal entirely, though a much simpler moving-average heuristic captures nearly all of this benefit in our tested regime-a result we report honestly as evidence against overclaiming the value of Bayesian machinery in this setting. We discuss implications for the economics of threat-intelligence procurement and directions for a full equilibrium characterization.

Estimating the probability that a queueing system violates a service-level agreement-e.g., that a customer's waiting time exceeds a threshold-is a rare-event estimation problem that, for most queueing models beyond the memoryless M/M/1 case, has no closed-form solution and must be estimated by classical Monte Carlo simulation. Quantum Amplitude Estimation (QAE) offers a proven quadratic reduction in the number of oracle calls needed to estimate such probabilities relative to classical sampling. We introduce Q-WAIT, an algorithm that discretizes a queue's stationary waiting-time or queue-length distribution, loads it into a quantum register via amplitude encoding, and applies Iterative Quantum Amplitude Estimation (IQAE) with an integer-comparator oracle to estimate SLA-violation probabilities. Unlike prior work applying QAE to Monte Carlo replacement in finance, we (i) apply the method to queueing performance metrics, including a non-Markovian G/G/1 queue with heavy-tailed service times built from a discrete-event simulation rather than a closed form, and (ii) benchmark against a classical baseline held to the same distribution-free statistical rigor as IQAE's own confidence interval, rather than an optimistic baseline that assumes the estimated probability in advance. On a simulator, we empirically recover the predicted query-complexity exponents (quantum:-1.43, classical:-2.00, versus theoretical-1 and-2), with a growing empirical speedup from 7× to 30× as target precision tightens, and show that the required oracle circuit's depth, two-qubit gate count, and ancilla overhead all scale linearly with the number of discretization qubits (R 2 = 1.000). We report these results, together with their methodological caveats and NISQera feasibility limits, as a basis for further work on quantum-accelerated queueing performance analysis.