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Greg Anderson

Publications and source records attributed to Greg Anderson.

14 recordsLinked to original sources

Determinants of hyperparameter robustness in connectome reservoir computing

Reservoir computing provides a controlled setting for studying how recurrent network architectureshapes computation: input signals are projected into a high-dimensional state space by a fixed nonlinear dynamical system, and only the readout is trained. However, reservoir performance can be dependent on hyperparameters; this paper asks which recurrent network features support robustness to those parameter changes. We characterize computational performance using memory capacity (MC), truncated single-delay information-processing capacity (IPC), and kernel rank (KR). Generalization across input histories is measured using generalization rank (GR), while hyperparameter robustness is quantified using the coefficient of variation (CV) of each metric across sweeps of target spectral radius, input scaling, leak rate, and neuron bias. To examine the architectural determinants of robustness, we construct perturbations that alter connectivity topology, excitatory/inhibitory sign structure, weight magnitudes, and weight placement while preserving complementary properties. Across these experiments, the C. elegans connectome consistently occupies a relatively low-variance regime. The central result is a performance-robustness tradeoff: architecture variants with higher task-agnostic performance also tend to exhibit greater hyperparameter sensitivity and poorer common-tail generalization. Across the E/I edge balance sweeps and shuffle controls, this tradeoff is closely associated with the raw spectral radius before normalization. Because every perturbed matrix is rescaled to the same target radius, matrices with lower raw spectral radius receive greater global amplification of their recurrent weights. The observed differences among architectures therefore characterize the joint effects of structural variation and architecture-specific global rescaling under spectral-radius normalization.

q-bio.NC

Certifiably Robust Reinforcement Learning through Model-Based Abstract Interpretation

We present a reinforcement learning (RL) framework in which the learned policy comes with a machine-checkable certificate of provable adversarial robustness. Our approach, called CAROL, learns a model of the environment. In each learning iteration, it uses the current version of this model and an external abstract interpreter to construct a differentiable signal for provable robustness. This signal is used to guide learning, and the abstract interpretation used to construct it directly leads to the robustness certificate returned at convergence. We give a theoretical analysis that bounds the worst-case accumulative reward of CAROL. We also experimentally evaluate CAROL on four MuJoCo environments with continuous state and action spaces. On these tasks, CAROL learns policies that, when contrasted with policies from the state-of-the-art robust RL algorithms, exhibit: (i) markedly enhanced certified performance lower bounds; and (ii) comparable performance under empirical adversarial attacks.

cs.LG

Guiding Safe Exploration with Weakest Preconditions

In reinforcement learning for safety-critical settings, it is often desirable for the agent to obey safety constraints at all points in time, including during training. We present a novel neurosymbolic approach called SPICE to solve this safe exploration problem. SPICE uses an online shielding layer based on symbolic weakest preconditions to achieve a more precise safety analysis than existing tools without unduly impacting the training process. We evaluate the approach on a suite of continuous control benchmarks and show that it can achieve comparable performance to existing safe learning techniques while incurring fewer safety violations. Additionally, we present theoretical results showing that SPICE converges to the optimal safe policy under reasonable assumptions.

cs.LG

Neurosymbolic Reinforcement Learning with Formally Verified Exploration

We present Revel, a partially neural reinforcement learning (RL) framework for provably safe exploration in continuous state and action spaces. A key challenge for provably safe deep RL is that repeatedly verifying neural networks within a learning loop is computationally infeasible. We address this challenge using two policy classes: a general, neurosymbolic class with approximate gradients and a more restricted class of symbolic policies that allows efficient verification. Our learning algorithm is a mirror descent over policies: in each iteration, it safely lifts a symbolic policy into the neurosymbolic space, performs safe gradient updates to the resulting policy, and projects the updated policy into the safe symbolic subset, all without requiring explicit verification of neural networks. Our empirical results show that Revel enforces safe exploration in many scenarios in which Constrained Policy Optimization does not, and that it can discover policies that outperform those learned through prior approaches to verified exploration.

cs.LG

Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform misclassifications. In this paper, we present a novel algorithm for verifying robustness properties of neural networks. Our method synergistically combines gradient-based optimization methods for counterexample search with abstraction-based proof search to obtain a sound and ({\delta}-)complete decision procedure. Our method also employs a data-driven approach to learn a verification policy that guides abstract interpretation during proof search. We have implemented the proposed approach in a tool called Charon and experimentally evaluated it on hundreds of benchmarks. Our experiments show that the proposed approach significantly outperforms three state-of-the-art tools, namely AI^2 , Reluplex, and Reluval.

cs.PL

Learning Abstractions for Program Synthesis

Many example-guided program synthesis techniques use abstractions to prune the search space. While abstraction-based synthesis has proven to be very powerful, a domain expert needs to provide a suitable abstract domain, together with the abstract transformers of each DSL construct. However, coming up with useful abstractions can be non-trivial, as it requires both domain expertise and knowledge about the synthesizer. In this paper, we propose a new technique for learning abstractions that are useful for instantiating a general synthesis framework in a new domain. Given a DSL and a small set of training problems, our method uses tree interpolation to infer reusable predicate templates that speed up synthesis in a given domain. Our method also learns suitable abstract transformers by solving a certain kind of second-order constraint solving problem in a data-driven way. We have implemented the proposed method in a tool called ATLAS and evaluate it in the context of the BLAZE meta-synthesizer. Our evaluation shows that (a) ATLAS can learn useful abstract domains and transformers from few training problems, and (b) the abstractions learned by ATLAS allow BLAZE to achieve significantly better results compared to manually-crafted abstractions.

cs.PL

A law of large numbers for finite-range dependent random matrices

We consider random hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has algebraic Stieltjes transform by an argument based on dimension theory of noetherian local rings.

math.PR

A CLT for a band matrix model

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poincare type. Special cases treated, with an explicit evaluation of limiting variances, are generalized Wigner and Wishart matrices.

math.PR

A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds

We prove an estimate for solutions to the linearized Ricci flow system on closed 3-manifolds. This estimate is a generalization of Hamilton's pinching is preserved estimate for the Ricci curvatures of solutions to the Ricci flow on 3-manifolds with positive Ricci curvature. In our estimate we make no assumption on the curvature of the initial metric. We show that the norm of the solution of the Lichnerowicz Laplacian heat equation (coupled to the Ricci flow) is bounded by a constant (depending on time) times the scalar curvature plus a constant. This relies on a Bochner type formula and establishing the nonnegativity of a degree 4 homogeneous polynomial in 6 variables.

math.DG

The Reach of Fermilab Tevatron Upgrades for SU(5) Supergravity Models with Non-universal Gaugino Masses

We explore the reach of luminosity upgrades of the Fermilab Tevatron collider for SU(5) supergravity models in which non-universal GUT-scale gaugino masses arise via a vacuum expectation value for the auxiliary component of a superfield that transforms as a 24, 75 or 200 dimensional representation of SU(5). This results in a different pattern of sparticle masses and mixing angles from what is expected in the minimal supergravity model (mSUGRA) with universal GUT scale gaugino masses. We find that the resulting signal cross sections, and hence the reach of the Tevatron, are sensitive to the gaugino masses at the GUT scale. In the 24 model, the large splitting amongst the two lightest neutralinos leads to SUSY events containing many isolated leptons, including events with a real leptonic Z boson plus jets plus missing energy signal which is visible over much of parameter space. In contrast, in the 75 and 200 models, the reach via leptonic SUSY signals is greatly reduced relative to mSUGRA, and the signal is usually visible only via the canonical $\eslt +$jets channel.

hep-ph

Naturalness Lowers the Upper Bound on the Lightest Higgs Boson Mass in Supersymmetry

We quantify the extent to which naturalness is lost as experimental lower bounds on the Higgs boson mass increase, and we compute the natural upper bound on the lightest supersymmetric Higgs boson mass. We find that it would be unnatural for the mass of the lightest supersymmetric Higgs boson to saturate it's maximal upper bound. In the absence of significant fine-tuning, the lightest Higgs boson mass should lie below $120$ GeV, and in the most natural cases it should be lighter than $108$ GeV. For modest $tan \beta$, these bounds are significantly lower. Our results imply that a failure to observe a light Higgs boson in pre-LHC experiments could provide a serious challenge to the principal motivation for weak-scale supersymmetry.

hep-ph

Challenging weak-scale supersymmetry at colliders

Experimental searches for supersymmetry are entering a new era. As future experiments explore the mass range above the current lower bounds on superpartner masses, a failure to observe signals of superpartner production will begin to erode the central motivation for supersymmetry at the weak scale. In this article we present a detailed examination of which regions of supersymmetric parameter space are most natural and the extent to which weak-scale supersymmetry becomes unnatural if no superpartners are observed at LEP-II, the Tevatron, possible upgrades of these machines, and the LHC.

hep-ph

Naturalness and superpartner masses or when to give up on weak scale supersymmetry

Superpartner masses cannot be arbitrarily heavy if supersymmetric extensions of the standard model explain the stability of the gauge hierarchy. This ancient and hallowed motivation for weak scale supersymmetry is often quoted, yet no reliable determination of this upper limit on superpartner masses exists. In this paper we compute upper bounds on superpartner masses in the minimal supersymmetric model, and we identify which values of the superpartner masses correspond to the most natural explanation of the hierarchy stability. We compare the most natural value of these masses and their upper limits to the physics reach of current and future colliders. As a result, we find that supersymmetry could explain weak scale stability naturally even if no superpartners are discovered at LEP II or the Tevatron (even with the Main Injector upgrade). However, we find that supersymmetry cannot provide a complete explanation of weak scale stability, if squarks and gluinos have masses beyond the physics reach of the LHC. Moreover, in the most natural scenarios, many sparticles, for example, charginos, squarks, and gluinos, lie within the physics reach of either LEP II or the Tevatron. Our analysis determines the most natural value of the chargino (squark) ((gluino)) mass consistent with current experimental constraints is $\sim$ 50 (250) ((250)) GeV and the corresponding theoretical upper bound is $\sim$ 250 (700) ((800)) GeV.

hep-ph

Measures of fine tuning

Fine-tuning criteria are frequently used to place upper limits on the masses of superpartners in supersymmetric extensions of the standard model. However, commonly used prescriptions for quantifying naturalness have some important shortcomings. Motivated by this, we propose new criteria for quantifying fine tuning that can be used to place upper limits on superpartner masses with greater fidelity. In addition, our analysis attempts to make explicit the assumptions implicit in quantifications of naturalness. We apply our criteria to the minimal supersymmetric extension of the standard model, and we find that the scale of supersymmetry breaking can be larger than previous methods indicate.

hep-ph